partial commit in static_2

propagating the new ground library to static_2 begins

diff --git a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma
index 705338db358cfcb9294afdf7a18dd64e2b45060c..1adadac595bb4c31cf10356170b8a72bc1b39f56 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma
@@ -34,7 +34,7 @@ lemma rexs_tc: ∀R,L1,L2,T,f. 𝐈❪f❫ → TC … (sex cfull (cext2 R) f) L1
                L1 ⪤*[R,T] L2.
 #R #L1 #L2 #T #f #Hf #H elim H -L2
 [ elim (frees_total L1 T) | #L elim (frees_total L T) ]
                L1 ⪤*[R,T] L2.
 #R #L1 #L2 #T #f #Hf #H elim H -L2
 [ elim (frees_total L1 T) | #L elim (frees_total L T) ]

-/5 width=7 by sex_sdj, rexs_step_dx, sdj_isid_sn, inj, ex2_intro/
+/5 width=7 by sex_sdj, rexs_step_dx, pr_sdj_isi_sn, inj, ex2_intro/

 qed.
 
 (* Advanced eliminators *****************************************************)
 qed.
 
 (* Advanced eliminators *****************************************************)

diff --git a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma
index fd50b7a6df35420f99f48740fa6379d14215039d..39059adfcf3acb5d75d060c36f6dea0d8abb05ae 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma
@@ -48,8 +48,8 @@ lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
 | #L0 #L2 #_ #HL02 * #L * #f0 #Hf0 #HL1 #HL0
   lapply (req_rex_trans … HL0 … HL02) -L0 // * #f1 #Hf1 #HL2
   elim (sex_sdj_split_sn … ceq_ext … HL2 f0 ?) -HL2
 | #L0 #L2 #_ #HL02 * #L * #f0 #Hf0 #HL1 #HL0
   lapply (req_rex_trans … HL0 … HL02) -L0 // * #f1 #Hf1 #HL2
   elim (sex_sdj_split_sn … ceq_ext … HL2 f0 ?) -HL2

-  [ #L0 #HL0 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ]
-  lapply (sex_sdj … HL0 f1 ?) /2 width=1 by sdj_isid_sn/ #H
+  [ #L0 #HL0 #HL02 |*: /2 width=1 by ext2_refl, pr_sdj_isi_dx/ ]
+  lapply (sex_sdj … HL0 f1 ?) /2 width=1 by pr_sdj_isi_sn/ #H

   elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f2 #Hf2 #Hf21
   lapply (sle_sex_trans … HL02 … Hf21) -f1 // #HL02
   lapply (sex_co ?? cfull (CTC … (cext2 R)) … HL1) -HL1 /2 width=1 by ext2_inv_tc/ #HL1
   elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f2 #Hf2 #Hf21
   lapply (sle_sex_trans … HL02 … Hf21) -f1 // #HL02
   lapply (sex_co ?? cfull (CTC … (cext2 R)) … HL1) -HL1 /2 width=1 by ext2_inv_tc/ #HL1

diff --git a/matita/matita/contribs/lambdadelta/static_2/notation/functions/uparrow_1_0.ma b/matita/matita/contribs/lambdadelta/static_2/notation/functions/uparrow_1_0.ma
new file mode 100644 (file)
index 0000000..e4bb638
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/notation/functions/uparrow_1_0.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⇡[ term 46 h ] )"
+   non associative with precedence 46
+   for @{ 'UpArrow_1_0 $h }.

diff --git a/matita/matita/contribs/lambdadelta/static_2/notation/functions/uparrowstar_2_0.ma b/matita/matita/contribs/lambdadelta/static_2/notation/functions/uparrowstar_2_0.ma
new file mode 100644 (file)
index 0000000..a4ca8f2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/notation/functions/uparrowstar_2_0.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⇡*[ term 46 h, term 46 n ] )"
+   non associative with precedence 46
+   for @{ 'UpArrowStar_2_0 $h $n }.

diff --git a/matita/matita/contribs/lambdadelta/static_2/notation/functions/upspoon_2.ma b/matita/matita/contribs/lambdadelta/static_2/notation/functions/upspoon_2.ma
deleted file mode 100644 (file)
index c04bf22..0000000
--- a/matita/matita/contribs/lambdadelta/static_2/notation/functions/upspoon_2.ma
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
-
-notation "hvbox( ⫯[ term 46 h ] break term 46 s )"
-   non associative with precedence 46
-   for @{ 'UpSpoon $h $s }.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops.ma
index 407f8cc4f30adcac171cd55e70e367e4077f650f..b459df118e8147ad0ba72201cc7752ed266f26db 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops.ma
@@ -26,7 +26,7 @@ include "static_2/relocation/lifts_bind.ma".
 (* Basic_2A1: includes: drop_atom drop_pair drop_drop drop_skip
                         drop_refl_atom_O2 drop_drop_lt drop_skip_lt
 *)
 (* Basic_2A1: includes: drop_atom drop_pair drop_drop drop_skip
                         drop_refl_atom_O2 drop_drop_lt drop_skip_lt
 *)

-inductive drops (b:bool): rtmap → relation lenv ≝
+inductive drops (b:bool): pr_map → relation lenv ≝

 | drops_atom: ∀f. (b = Ⓣ → 𝐈❪f❫) → drops b (f) (⋆) (⋆)
 | drops_drop: ∀f,I,L1,L2. drops b f L1 L2 → drops b (↑f) (L1.ⓘ[I]) L2
 | drops_skip: ∀f,I1,I2,L1,L2.
 | drops_atom: ∀f. (b = Ⓣ → 𝐈❪f❫) → drops b (f) (⋆) (⋆)
 | drops_drop: ∀f,I,L1,L2. drops b f L1 L2 → drops b (↑f) (L1.ⓘ[I]) L2
 | drops_skip: ∀f,I1,I2,L1,L2.


@@ -38,7 +38,7 @@ interpretation "generic slicing (local environment)"
    'RDropStar b f L1 L2 = (drops b f L1 L2).
 
 interpretation "uniform slicing (local environment)"
    'RDropStar b f L1 L2 = (drops b f L1 L2).
 
 interpretation "uniform slicing (local environment)"

-   'RDrop i L1 L2 = (drops true (uni i) L1 L2).
+   'RDrop i L1 L2 = (drops true (pr_uni i) L1 L2).

 
 definition d_liftable1: predicate (relation2 lenv term) ≝
                         λR. ∀K,T. R K T → ∀b,f,L. ⇩*[b,f] L ≘ K →
 
 definition d_liftable1: predicate (relation2 lenv term) ≝
                         λR. ∀K,T. R K T → ∀b,f,L. ⇩*[b,f] L ≘ K →


@@ -102,9 +102,9 @@ lemma drops_atom_F: ∀f. ⇩*[Ⓕ,f] ⋆ ≘ ⋆.
 #f @drops_atom #H destruct
 qed.
 
 #f @drops_atom #H destruct
 qed.
 

-lemma drops_eq_repl_back: ∀b,L1,L2. eq_repl_back … (λf. ⇩*[b,f] L1 ≘ L2).
+lemma drops_eq_repl_back: ∀b,L1,L2. pr_eq_repl_back … (λf. ⇩*[b,f] L1 ≘ L2).

 #b #L1 #L2 #f1 #H elim H -f1 -L1 -L2
 #b #L1 #L2 #f1 #H elim H -f1 -L1 -L2

-[ /4 width=3 by drops_atom, isid_eq_repl_back/
+[ /4 width=3 by drops_atom, pr_isi_eq_repl_back/

 | #f1 #I #L1 #L2 #_ #IH #f2 #H elim (eq_inv_nx … H) -H
   /3 width=3 by drops_drop/
 | #f1 #I1 #I2 #L1 #L2 #_ #HI #IH #f2 #H elim (eq_inv_px … H) -H
 | #f1 #I #L1 #L2 #_ #IH #f2 #H elim (eq_inv_nx … H) -H
   /3 width=3 by drops_drop/
 | #f1 #I1 #I2 #L1 #L2 #_ #HI #IH #f2 #H elim (eq_inv_px … H) -H


@@ -112,8 +112,8 @@ lemma drops_eq_repl_back: ∀b,L1,L2. eq_repl_back … (λf. ⇩*[b,f] L1 ≘ L2
 ]
 qed-.
 
 ]
 qed-.
 

-lemma drops_eq_repl_fwd: ∀b,L1,L2. eq_repl_fwd … (λf. ⇩*[b,f] L1 ≘ L2).
-#b #L1 #L2 @eq_repl_sym /2 width=3 by drops_eq_repl_back/ (**) (* full auto fails *)
+lemma drops_eq_repl_fwd: ∀b,L1,L2. pr_eq_repl_fwd … (λf. ⇩*[b,f] L1 ≘ L2).
+#b #L1 #L2 @pr_eq_repl_sym /2 width=3 by drops_eq_repl_back/ (**) (* full auto fails *)

 qed-.
 
 (* Basic_2A1: includes: drop_FT *)
 qed-.
 
 (* Basic_2A1: includes: drop_FT *)


@@ -166,8 +166,8 @@ fact drops_inv_drop1_aux: ∀b,f,X,Y. ⇩*[b,f] X ≘ Y → ∀g,I,K. X = K.ⓘ[
                           ⇩*[b,g] K ≘ Y.
 #b #f #X #Y * -f -X -Y
 [ #f #Hf #g #J #K #H destruct
                           ⇩*[b,g] K ≘ Y.
 #b #f #X #Y * -f -X -Y
 [ #f #Hf #g #J #K #H destruct

-| #f #I #L1 #L2 #HL #g #J #K #H1 #H2 <(injective_next … H2) -g destruct //
-| #f #I1 #I2 #L1 #L2 #_ #_ #g #J #K #_ #H2 elim (discr_push_next … H2)
+| #f #I #L1 #L2 #HL #g #J #K #H1 #H2 <(eq_inv_pr_next_bi … H2) -g destruct //
+| #f #I1 #I2 #L1 #L2 #_ #_ #g #J #K #_ #H2 elim (eq_inv_pr_push_next … H2)

 ]
 qed-.
 
 ]
 qed-.
 


@@ -180,8 +180,8 @@ fact drops_inv_skip1_aux: ∀b,f,X,Y. ⇩*[b,f] X ≘ Y → ∀g,I1,K1. X = K1.
                           ∃∃I2,K2. ⇩*[b,g] K1 ≘ K2 & ⇧*[g] I2 ≘ I1 & Y = K2.ⓘ[I2].
 #b #f #X #Y * -f -X -Y
 [ #f #Hf #g #J1 #K1 #H destruct
                           ∃∃I2,K2. ⇩*[b,g] K1 ≘ K2 & ⇧*[g] I2 ≘ I1 & Y = K2.ⓘ[I2].
 #b #f #X #Y * -f -X -Y
 [ #f #Hf #g #J1 #K1 #H destruct

-| #f #I #L1 #L2 #_ #g #J1 #K1 #_ #H2 elim (discr_next_push … H2)
-| #f #I1 #I2 #L1 #L2 #HL #HI #g #J1 #K1 #H1 #H2 <(injective_push … H2) -g destruct
+| #f #I #L1 #L2 #_ #g #J1 #K1 #_ #H2 elim (eq_inv_pr_next_push … H2)
+| #f #I1 #I2 #L1 #L2 #HL #HI #g #J1 #K1 #H1 #H2 <(eq_inv_pr_push_bi … H2) -g destruct

   /2 width=5 by ex3_2_intro/
 ]
 qed-.
   /2 width=5 by ex3_2_intro/
 ]
 qed-.


@@ -196,8 +196,8 @@ fact drops_inv_skip2_aux: ∀b,f,X,Y. ⇩*[b,f] X ≘ Y → ∀g,I2,K2. Y = K2.
                           ∃∃I1,K1. ⇩*[b,g] K1 ≘ K2 & ⇧*[g] I2 ≘ I1 & X = K1.ⓘ[I1].
 #b #f #X #Y * -f -X -Y
 [ #f #Hf #g #J2 #K2 #H destruct
                           ∃∃I1,K1. ⇩*[b,g] K1 ≘ K2 & ⇧*[g] I2 ≘ I1 & X = K1.ⓘ[I1].
 #b #f #X #Y * -f -X -Y
 [ #f #Hf #g #J2 #K2 #H destruct

-| #f #I #L1 #L2 #_ #g #J2 #K2 #_ #H2 elim (discr_next_push … H2)
-| #f #I1 #I2 #L1 #L2 #HL #HV #g #J2 #K2 #H1 #H2 <(injective_push … H2) -g destruct
+| #f #I #L1 #L2 #_ #g #J2 #K2 #_ #H2 elim (eq_inv_pr_next_push … H2)
+| #f #I1 #I2 #L1 #L2 #HL #HV #g #J2 #K2 #H1 #H2 <(eq_inv_pr_push_bi … H2) -g destruct

   /2 width=5 by ex3_2_intro/
 ]
 qed-.
   /2 width=5 by ex3_2_intro/
 ]
 qed-.


@@ -215,9 +215,9 @@ fact drops_fwd_drop2_aux: ∀b,f2,X,Y. ⇩*[b,f2] X ≘ Y → ∀I,K. Y = K.ⓘ[
 #b #f2 #X #Y #H elim H -f2 -X -Y
 [ #f2 #Hf2 #J #K #H destruct
 | #f2 #I #L1 #L2 #_ #IHL #J #K #H elim (IHL … H) -IHL
 #b #f2 #X #Y #H elim H -f2 -X -Y
 [ #f2 #Hf2 #J #K #H destruct
 | #f2 #I #L1 #L2 #_ #IHL #J #K #H elim (IHL … H) -IHL

-  /3 width=7 by after_next, ex3_2_intro, drops_drop/
+  /3 width=7 by pr_after_next, ex3_2_intro, drops_drop/

 | #f2 #I1 #I2 #L1 #L2 #HL #_ #_ #J #K #H destruct
 | #f2 #I1 #I2 #L1 #L2 #HL #_ #_ #J #K #H destruct

-  lapply (after_isid_dx 𝐢 … f2) /3 width=9 by after_push, ex3_2_intro, drops_drop/
+  lapply (pr_after_isi_dx 𝐢 … f2) /3 width=9 by pr_after_push, ex3_2_intro, drops_drop/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -230,7 +230,7 @@ lemma drops_fwd_drop2: ∀b,f2,I,X,K. ⇩*[b,f2] X ≘ K.ⓘ[I] →
 (* Basic_2A1: includes: drop_refl *)
 lemma drops_refl: ∀b,L,f. 𝐈❪f❫ → ⇩*[b,f] L ≘ L.
 #b #L elim L -L /2 width=1 by drops_atom/
 (* Basic_2A1: includes: drop_refl *)
 lemma drops_refl: ∀b,L,f. 𝐈❪f❫ → ⇩*[b,f] L ≘ L.
 #b #L elim L -L /2 width=1 by drops_atom/

-#L #I #IHL #f #Hf elim (isid_inv_gen … Hf) -Hf
+#L #I #IHL #f #Hf elim (pr_isi_inv_gen … Hf) -Hf

 /3 width=1 by drops_skip, liftsb_refl/
 qed.
 
 /3 width=1 by drops_skip, liftsb_refl/
 qed.
 


@@ -240,23 +240,23 @@ qed.
 (* Basic_2A1: includes: drop_inv_O2 *)
 lemma drops_fwd_isid: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → 𝐈❪f❫ → L1 = L2.
 #b #f #L1 #L2 #H elim H -f -L1 -L2 //
 (* Basic_2A1: includes: drop_inv_O2 *)
 lemma drops_fwd_isid: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → 𝐈❪f❫ → L1 = L2.
 #b #f #L1 #L2 #H elim H -f -L1 -L2 //

-[ #f #I #L1 #L2 #_ #_ #H elim (isid_inv_next … H) //
-| /5 width=5 by isid_inv_push, liftsb_fwd_isid, eq_f2, sym_eq/
+[ #f #I #L1 #L2 #_ #_ #H elim (pr_isi_inv_next … H) //
+| /5 width=5 by pr_isi_inv_push, liftsb_fwd_isid, eq_f2, sym_eq/

 ]
 qed-.
 
 lemma drops_after_fwd_drop2: ∀b,f2,I,X,K. ⇩*[b,f2] X ≘ K.ⓘ[I] →
                              ∀f1,f. 𝐈❪f1❫ → f2 ⊚ ↑f1 ≘ f → ⇩*[b,f] X ≘ K.
 #b #f2 #I #X #K #H #f1 #f #Hf1 #Hf elim (drops_fwd_drop2 … H) -H
 ]
 qed-.
 
 lemma drops_after_fwd_drop2: ∀b,f2,I,X,K. ⇩*[b,f2] X ≘ K.ⓘ[I] →
                              ∀f1,f. 𝐈❪f1❫ → f2 ⊚ ↑f1 ≘ f → ⇩*[b,f] X ≘ K.
 #b #f2 #I #X #K #H #f1 #f #Hf1 #Hf elim (drops_fwd_drop2 … H) -H

-#g1 #g #Hg1 #Hg #HK lapply (after_mono_eq … Hg … Hf ??) -Hg -Hf
-/3 width=5 by drops_eq_repl_back, isid_inv_eq_repl, eq_next/
+#g1 #g #Hg1 #Hg #HK lapply (pr_after_mono_eq … Hg … Hf ??) -Hg -Hf
+/3 width=5 by drops_eq_repl_back, pr_isi_inv_eq_repl, pr_eq_next/

 qed-.
 
 (* Forward lemmas with test for finite colength *****************************)
 
 lemma drops_fwd_isfin: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐅❪f❫.
 #f #L1 #L2 #H elim H -f -L1 -L2
 qed-.
 
 (* Forward lemmas with test for finite colength *****************************)
 
 lemma drops_fwd_isfin: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐅❪f❫.
 #f #L1 #L2 #H elim H -f -L1 -L2

-/3 width=1 by isfin_next, isfin_push, isfin_isid/
+/3 width=1 by pr_isf_next, pr_isf_push, pr_isf_isi/

 qed-.
 
 (* Properties with test for uniformity **************************************)
 qed-.
 
 (* Properties with test for uniformity **************************************)


@@ -274,8 +274,8 @@ lemma drops_inv_isuni: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐔❪f❫ →
                        ∃∃g,I,K. ⇩*[Ⓣ,g] K ≘ L2 & 𝐔❪g❫ & L1 = K.ⓘ[I] & f = ↑g.
 #f #L1 #L2 * -f -L1 -L2
 [ /4 width=1 by or_introl, conj/
                        ∃∃g,I,K. ⇩*[Ⓣ,g] K ≘ L2 & 𝐔❪g❫ & L1 = K.ⓘ[I] & f = ↑g.
 #f #L1 #L2 * -f -L1 -L2
 [ /4 width=1 by or_introl, conj/

-| /4 width=7 by isuni_inv_next, ex4_3_intro, or_intror/
-| /7 width=6 by drops_fwd_isid, liftsb_fwd_isid, isuni_inv_push, isid_push, or_introl, conj, eq_f2, sym_eq/
+| /4 width=7 by pr_isu_inv_next, ex4_3_intro, or_intror/
+| /7 width=6 by drops_fwd_isid, liftsb_fwd_isid, pr_isu_inv_push, pr_isi_push, or_introl, conj, eq_f2, sym_eq/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -283,10 +283,10 @@ qed-.
 lemma drops_inv_bind1_isuni: ∀b,f,I,K,L2. 𝐔❪f❫ → ⇩*[b,f] K.ⓘ[I] ≘ L2 →
                              (𝐈❪f❫ ∧ L2 = K.ⓘ[I]) ∨
                              ∃∃g. 𝐔❪g❫ & ⇩*[b,g] K ≘ L2 & f = ↑g.
 lemma drops_inv_bind1_isuni: ∀b,f,I,K,L2. 𝐔❪f❫ → ⇩*[b,f] K.ⓘ[I] ≘ L2 →
                              (𝐈❪f❫ ∧ L2 = K.ⓘ[I]) ∨
                              ∃∃g. 𝐔❪g❫ & ⇩*[b,g] K ≘ L2 & f = ↑g.

-#b #f #I #K #L2 #Hf #H elim (isuni_split … Hf) -Hf * #g #Hg #H0 destruct
+#b #f #I #K #L2 #Hf #H elim (pr_isu_split … Hf) -Hf * #g #Hg #H0 destruct

 [ lapply (drops_inv_skip1 … H) -H * #Z #Y #HY #HZ #H destruct
   <(drops_fwd_isid … HY Hg) -Y >(liftsb_fwd_isid … HZ Hg) -Z
 [ lapply (drops_inv_skip1 … H) -H * #Z #Y #HY #HZ #H destruct
   <(drops_fwd_isid … HY Hg) -Y >(liftsb_fwd_isid … HZ Hg) -Z

-  /4 width=3 by isid_push, or_introl, conj/
+  /4 width=3 by pr_isi_push, or_introl, conj/

 | lapply (drops_inv_drop1 … H) -H /3 width=4 by ex3_intro, or_intror/
 ]
 qed-.
 | lapply (drops_inv_drop1 … H) -H /3 width=4 by ex3_intro, or_intror/
 ]
 qed-.


@@ -306,8 +306,8 @@ qed-.
 
 lemma drops_inv_bind2_isuni_next: ∀b,f,I,K,L1. 𝐔❪f❫ → ⇩*[b,↑f] L1 ≘ K.ⓘ[I] →
                                   ∃∃I1,K1. ⇩*[b,f] K1 ≘ K.ⓘ[I] & L1 = K1.ⓘ[I1].
 
 lemma drops_inv_bind2_isuni_next: ∀b,f,I,K,L1. 𝐔❪f❫ → ⇩*[b,↑f] L1 ≘ K.ⓘ[I] →
                                   ∃∃I1,K1. ⇩*[b,f] K1 ≘ K.ⓘ[I] & L1 = K1.ⓘ[I1].

-#b #f #I #K #L1 #Hf #H elim (drops_inv_bind2_isuni … H) -H /2 width=3 by isuni_next/ -Hf *
-[ #H elim (isid_inv_next … H) -H //
+#b #f #I #K #L1 #Hf #H elim (drops_inv_bind2_isuni … H) -H /2 width=3 by pr_isu_next/ -Hf *
+[ #H elim (pr_isi_inv_next … H) -H //

 | /2 width=4 by ex2_2_intro/
 ]
 qed-.
 | /2 width=4 by ex2_2_intro/
 ]
 qed-.


@@ -317,11 +317,11 @@ fact drops_inv_TF_aux: ∀f,L1,L2. ⇩*[Ⓕ,f] L1 ≘ L2 → 𝐔❪f❫ →
 #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #_ #_ #J #K #H destruct
 | #f #I #L1 #L2 #_ #IH #Hf #J #K #H destruct
 #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #_ #_ #J #K #H destruct
 | #f #I #L1 #L2 #_ #IH #Hf #J #K #H destruct

-  /4 width=3 by drops_drop, isuni_inv_next/
+  /4 width=3 by drops_drop, pr_isu_inv_next/

 | #f #I1 #I2 #L1 #L2 #HL12 #HI21 #_ #Hf #J #K #H destruct
 | #f #I1 #I2 #L1 #L2 #HL12 #HI21 #_ #Hf #J #K #H destruct

-  lapply (isuni_inv_push … Hf ??) -Hf [1,2: // ] #Hf
+  lapply (pr_isu_inv_push … Hf ??) -Hf [1,2: // ] #Hf

   <(drops_fwd_isid … HL12) -K // <(liftsb_fwd_isid … HI21) -I1
   <(drops_fwd_isid … HL12) -K // <(liftsb_fwd_isid … HI21) -I1

-  /3 width=3 by drops_refl, isid_push/
+  /3 width=3 by drops_refl, pr_isi_push/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -344,18 +344,18 @@ qed-.
 (* Basic_1: was: drop_S *)
 (* Basic_2A1: was: drop_fwd_drop2 *)
 lemma drops_isuni_fwd_drop2: ∀b,f,I,X,K. 𝐔❪f❫ → ⇩*[b,f] X ≘ K.ⓘ[I] → ⇩*[b,↑f] X ≘ K.
 (* Basic_1: was: drop_S *)
 (* Basic_2A1: was: drop_fwd_drop2 *)
 lemma drops_isuni_fwd_drop2: ∀b,f,I,X,K. 𝐔❪f❫ → ⇩*[b,f] X ≘ K.ⓘ[I] → ⇩*[b,↑f] X ≘ K.

-/3 width=7 by drops_after_fwd_drop2, after_isid_isuni/ qed-.
+/3 width=7 by drops_after_fwd_drop2, pr_after_isu_isi_next/ qed-.

 
 (* Inversion lemmas with uniform relocations ********************************)
 
 lemma drops_inv_atom2: ∀b,L,f. ⇩*[b,f] L ≘ ⋆ →
                        ∃∃n,f1. ⇩*[b,𝐔❨n❩] L ≘ ⋆ & 𝐔❨n❩ ⊚ f1 ≘ f.
 #b #L elim L -L
 
 (* Inversion lemmas with uniform relocations ********************************)
 
 lemma drops_inv_atom2: ∀b,L,f. ⇩*[b,f] L ≘ ⋆ →
                        ∃∃n,f1. ⇩*[b,𝐔❨n❩] L ≘ ⋆ & 𝐔❨n❩ ⊚ f1 ≘ f.
 #b #L elim L -L

-[ /3 width=4 by drops_atom, after_isid_sn, ex2_2_intro/
-| #L #I #IH #f #H elim (pn_split f) * #g #H0 destruct
+[ /3 width=4 by drops_atom, pr_after_isi_sn, ex2_2_intro/
+| #L #I #IH #f #H elim (pr_map_split_tl f) * #g #H0 destruct

   [ elim (drops_inv_skip1 … H) -H #J #K #_ #_ #H destruct
   | lapply (drops_inv_drop1 … H) -H #HL
   [ elim (drops_inv_skip1 … H) -H #J #K #_ #_ #H destruct
   | lapply (drops_inv_drop1 … H) -H #HL

-    elim (IH … HL) -IH -HL /3 width=8 by drops_drop, after_next, ex2_2_intro/
+    elim (IH … HL) -IH -HL /3 width=8 by drops_drop, pr_after_next, ex2_2_intro/

   ]
 ]
 qed-.
   ]
 ]
 qed-.


@@ -363,7 +363,7 @@ qed-.
 lemma drops_inv_succ: ∀L1,L2,i. ⇩[↑i] L1 ≘ L2 →
                       ∃∃I,K. ⇩[i] K ≘ L2 & L1 = K.ⓘ[I].
 #L1 #L2 #i #H elim (drops_inv_isuni … H) -H // *
 lemma drops_inv_succ: ∀L1,L2,i. ⇩[↑i] L1 ≘ L2 →
                       ∃∃I,K. ⇩[i] K ≘ L2 & L1 = K.ⓘ[I].
 #L1 #L2 #i #H elim (drops_inv_isuni … H) -H // *

-[ #H elim (isid_inv_next … H) -H //
+[ #H elim (pr_isi_inv_next … H) -H //

 | /2 width=4 by ex2_2_intro/
 ]
 qed-.
 | /2 width=4 by ex2_2_intro/
 ]
 qed-.


@@ -383,18 +383,18 @@ lemma drops_split_trans: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → ∀f1,f2. f1 ⊚
 #b #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #H0f #f1 #f2 #Hf #Hf1 @(ex2_intro … (⋆)) @drops_atom
   #H lapply (H0f H) -b
 #b #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #H0f #f1 #f2 #Hf #Hf1 @(ex2_intro … (⋆)) @drops_atom
   #H lapply (H0f H) -b

-  #H elim (after_inv_isid3 … Hf H) -f //
-| #f #I #L1 #L2 #HL12 #IHL12 #f1 #f2 #Hf #Hf1 elim (after_inv_xxn … Hf) -Hf [1,3: * |*: // ]
+  #H elim (pr_after_inv_isi … Hf H) -f //
+| #f #I #L1 #L2 #HL12 #IHL12 #f1 #f2 #Hf #Hf1 elim (pr_after_inv_next … Hf) -Hf [1,3: * |*: // ]

   [ #g1 #g2 #Hf #H1 #H2 destruct
   [ #g1 #g2 #Hf #H1 #H2 destruct

-    lapply (isuni_inv_push … Hf1 ??) -Hf1 [1,2: // ] #Hg1
+    lapply (pr_isu_inv_push … Hf1 ??) -Hf1 [1,2: // ] #Hg1

     elim (IHL12 … Hf) -f
     elim (IHL12 … Hf) -f

-    /4 width=5 by drops_drop, drops_skip, liftsb_refl, isuni_isid, ex2_intro/
+    /4 width=5 by drops_drop, drops_skip, liftsb_refl, pr_isu_isi, ex2_intro/

   | #g1 #Hf #H destruct elim (IHL12 … Hf) -f
   | #g1 #Hf #H destruct elim (IHL12 … Hf) -f

-    /3 width=5 by ex2_intro, drops_drop, isuni_inv_next/
+    /3 width=5 by ex2_intro, drops_drop, pr_isu_inv_next/

   ]
   ]

-| #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #f1 #f2 #Hf #Hf1 elim (after_inv_xxp … Hf) -Hf [2,3: // ]
+| #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #f1 #f2 #Hf #Hf1 elim (pr_after_inv_push … Hf) -Hf [2,3: // ]

   #g1 #g2 #Hf #H1 #H2 destruct elim (liftsb_split_trans … HI21 … Hf) -HI21
   #g1 #g2 #Hf #H1 #H2 destruct elim (liftsb_split_trans … HI21 … Hf) -HI21

-  elim (IHL12 … Hf) -f /3 width=5 by ex2_intro, drops_skip, isuni_fwd_push/
+  elim (IHL12 … Hf) -f /3 width=5 by ex2_intro, drops_skip, pr_isu_fwd_push/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -402,15 +402,15 @@ lemma drops_split_div: ∀b,f1,L1,L. ⇩*[b,f1] L1 ≘ L → ∀f2,f. f1 ⊚ f2
                        ∃∃L2. ⇩*[Ⓕ,f2] L ≘ L2 & ⇩*[Ⓕ,f] L1 ≘ L2.
 #b #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #Hf1 #f2 #f #Hf #Hf2 @(ex2_intro … (⋆)) @drops_atom #H destruct
                        ∃∃L2. ⇩*[Ⓕ,f2] L ≘ L2 & ⇩*[Ⓕ,f] L1 ≘ L2.
 #b #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #Hf1 #f2 #f #Hf #Hf2 @(ex2_intro … (⋆)) @drops_atom #H destruct

-| #f1 #I #L1 #L #HL1 #IH #f2 #f #Hf #Hf2 elim (after_inv_nxx … Hf) -Hf [2,3: // ]
+| #f1 #I #L1 #L #HL1 #IH #f2 #f #Hf #Hf2 elim (pr_after_inv_next_sn … Hf) -Hf [2,3: // ]

   #g #Hg #H destruct elim (IH … Hg) -IH -Hg /3 width=5 by drops_drop, ex2_intro/
 | #f1 #I1 #I #L1 #L #HL1 #HI1 #IH #f2 #f #Hf #Hf2
   #g #Hg #H destruct elim (IH … Hg) -IH -Hg /3 width=5 by drops_drop, ex2_intro/
 | #f1 #I1 #I #L1 #L #HL1 #HI1 #IH #f2 #f #Hf #Hf2

-  elim (after_inv_pxx … Hf) -Hf [1,3: * |*: // ]
+  elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*: // ]

   #g2 #g #Hg #H2 #H0 destruct
   #g2 #g #Hg #H2 #H0 destruct

-  [ lapply (isuni_inv_push … Hf2 ??) -Hf2 [1,2: // ] #Hg2 -IH
-    lapply (after_isid_inv_dx … Hg … Hg2) -Hg #Hg
-    /5 width=7 by drops_eq_repl_back, drops_F, drops_refl, drops_skip, liftsb_eq_repl_back, isid_push, ex2_intro/
-  | lapply (isuni_inv_next … Hf2 ??) -Hf2 [1,2: // ] #Hg2 -HL1 -HI1
+  [ lapply (pr_isu_inv_push … Hf2 ??) -Hf2 [1,2: // ] #Hg2 -IH
+    lapply (pr_after_isi_inv_dx … Hg … Hg2) -Hg #Hg
+    /5 width=7 by drops_eq_repl_back, drops_F, drops_refl, drops_skip, liftsb_eq_repl_back, pr_isi_push, ex2_intro/
+  | lapply (pr_isu_inv_next … Hf2 ??) -Hf2 [1,2: // ] #Hg2 -HL1 -HI1

     elim (IH … Hg) -f1 /3 width=3 by drops_drop, ex2_intro/
   ]
 ]
     elim (IH … Hg) -f1 /3 width=3 by drops_drop, ex2_intro/
   ]
 ]


@@ -421,12 +421,12 @@ qed-.
 lemma drops_tls_at: ∀f,i1,i2. @❪i1,f❫ ≘ i2 →
                     ∀b,L1,L2. ⇩*[b,⫰*[i2]f] L1 ≘ L2 →
                     ⇩*[b,⫯⫰*[↑i2]f] L1 ≘ L2.
 lemma drops_tls_at: ∀f,i1,i2. @❪i1,f❫ ≘ i2 →
                     ∀b,L1,L2. ⇩*[b,⫰*[i2]f] L1 ≘ L2 →
                     ⇩*[b,⫯⫰*[↑i2]f] L1 ≘ L2.

-/3 width=3 by drops_eq_repl_fwd, at_inv_tls/ qed-.
+/3 width=3 by drops_eq_repl_fwd, pr_pat_inv_succ_dx_tls/ qed-.

 
 lemma drops_split_trans_bind2: ∀b,f,I,L,K0. ⇩*[b,f] L ≘ K0.ⓘ[I] → ∀i. @❪O,f❫ ≘ i →
                                ∃∃J,K. ⇩[i]L ≘ K.ⓘ[J] & ⇩*[b,⫰*[↑i]f] K ≘ K0 & ⇧*[⫰*[↑i]f] I ≘ J.
 #b #f #I #L #K0 #H #i #Hf
 
 lemma drops_split_trans_bind2: ∀b,f,I,L,K0. ⇩*[b,f] L ≘ K0.ⓘ[I] → ∀i. @❪O,f❫ ≘ i →
                                ∃∃J,K. ⇩[i]L ≘ K.ⓘ[J] & ⇩*[b,⫰*[↑i]f] K ≘ K0 & ⇧*[⫰*[↑i]f] I ≘ J.
 #b #f #I #L #K0 #H #i #Hf

-elim (drops_split_trans … H) -H [ |5: @(after_uni_dx … Hf) |2,3: skip ] /2 width=1 by after_isid_dx/ #Y #HLY #H
+elim (drops_split_trans … H) -H [ |5: @(pr_after_nat_uni … Hf) |2,3: skip ] /2 width=1 by pr_after_isi_dx/ #Y #HLY #H

 lapply (drops_tls_at … Hf … H) -H #H
 elim (drops_inv_skip2 … H) -H #J #K #HK0 #HIJ #H destruct
 /3 width=5 by drops_inv_gen, ex3_2_intro/
 lapply (drops_tls_at … Hf … H) -H #H
 elim (drops_inv_skip2 … H) -H #J #K #HK0 #HIJ #H destruct
 /3 width=5 by drops_inv_gen, ex3_2_intro/

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
index ab924e9b8ab483f94109dbf75151dce23b05faa6..7b8bebb691e39ceda5411552b510022723f1a2b0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
@@ -26,10 +26,10 @@ theorem drops_conf: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L →
 #b1 #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #_ #b2 #f #L2 #HL2 #f2 #Hf12 elim (drops_inv_atom1 … HL2) -b1 -HL2
   #H #Hf destruct @drops_atom
 #b1 #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #_ #b2 #f #L2 #HL2 #f2 #Hf12 elim (drops_inv_atom1 … HL2) -b1 -HL2
   #H #Hf destruct @drops_atom

-  #H elim (after_inv_isid3 … Hf12) -Hf12 /2 width=1 by/
-| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_nxx … Hf) -Hf [2,3: // ]
+  #H elim (pr_after_inv_isi … Hf12) -Hf12 /2 width=1 by/
+| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (pr_after_inv_next_sn … Hf) -Hf [2,3: // ]

   #g #Hg #H destruct /3 width=3 by drops_inv_drop1/
   #g #Hg #H destruct /3 width=3 by drops_inv_drop1/

-| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*:// ]
+| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*:// ]

   #g2 #g #Hf #H1 #H2 destruct
   [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_div3/
   | /4 width=3 by drops_inv_drop1, drops_drop/
   #g2 #g #Hf #H1 #H2 destruct
   [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_div3/
   | /4 width=3 by drops_inv_drop1, drops_drop/


@@ -47,11 +47,11 @@ theorem drops_trans: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L →
 #b1 #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #Hf1 #b2 #f2 #L2 #HL2 #f #Hf elim (drops_inv_atom1 … HL2) -HL2
   #H #Hf2 destruct @drops_atom #H elim (andb_inv_true_dx … H) -H
 #b1 #f1 #L1 #L #H elim H -f1 -L1 -L
 [ #f1 #Hf1 #b2 #f2 #L2 #HL2 #f #Hf elim (drops_inv_atom1 … HL2) -HL2
   #H #Hf2 destruct @drops_atom #H elim (andb_inv_true_dx … H) -H

-  #H1 #H2 lapply (after_isid_inv_sn … Hf ?) -Hf
-  /3 width=3 by isid_eq_repl_back/
-| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_nxx … Hf) -Hf
+  #H1 #H2 lapply (pr_after_isi_inv_sn … Hf ?) -Hf
+  /3 width=3 by pr_isi_eq_repl_back/
+| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (pr_after_inv_next_sn … Hf) -Hf

   /3 width=3 by drops_drop/
   /3 width=3 by drops_drop/

-| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*: // ]
+| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f2 #L2 #HL2 #f #Hf elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*: // ]

   #g2 #g #Hg #H1 #H2 destruct
   [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_trans/
   | /4 width=3 by drops_inv_drop1, drops_drop/
   #g2 #g #Hg #H1 #H2 destruct
   [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_trans/
   | /4 width=3 by drops_inv_drop1, drops_drop/


@@ -64,20 +64,20 @@ theorem drops_conf_div_isuni:
         𝐔❪f1❫ → 𝐔❪f2❫ → f1 ≡ f2.
 #f1 #L #K #H elim H -f1 -L -K
 [ #f1 #Hf1 #f2 #Hf2 elim (drops_inv_atom1 … Hf2) -Hf2
         𝐔❪f1❫ → 𝐔❪f2❫ → f1 ≡ f2.
 #f1 #L #K #H elim H -f1 -L -K
 [ #f1 #Hf1 #f2 #Hf2 elim (drops_inv_atom1 … Hf2) -Hf2

-  /3 width=1 by isid_inv_eq_repl/
-| #f1 #I #L #K #Hf1 #IH #f2 elim (pn_split f2) *
+  /3 width=1 by pr_isi_inv_eq_repl/
+| #f1 #I #L #K #Hf1 #IH #f2 elim (pr_map_split_tl f2) *

   #g2 #H2 #Hf2 #HU1 #HU2 destruct
   [ elim (drops_inv_skip1 … Hf2) -IH -HU1 -Hf2 #Y2 #X2 #HY2 #_ #H destruct
   #g2 #H2 #Hf2 #HU1 #HU2 destruct
   [ elim (drops_inv_skip1 … Hf2) -IH -HU1 -Hf2 #Y2 #X2 #HY2 #_ #H destruct

-    lapply (drops_fwd_isid … HY2 ?) -HY2 /2 width=3 by isuni_inv_push/ -HU2
+    lapply (drops_fwd_isid … HY2 ?) -HY2 /2 width=3 by pr_isu_inv_push/ -HU2

     #H destruct elim (drops_inv_x_bind_xy … Hf1)
     #H destruct elim (drops_inv_x_bind_xy … Hf1)

-  | /4 width=5 by drops_inv_drop1, isuni_inv_next, eq_next/
+  | /4 width=5 by drops_inv_drop1, pr_isu_inv_next, pr_eq_next/

   ]
   ]

-| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pn_split f2) *
+| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pr_map_split_tl f2) *

   #g2 #H2 #Hf2 #HU1 #HU2 destruct
   [ elim (drops_inv_skip1 … Hf2) -Hf2 #Y2 #X2 #HY2 #_ #H destruct -Hf1
   #g2 #H2 #Hf2 #HU1 #HU2 destruct
   [ elim (drops_inv_skip1 … Hf2) -Hf2 #Y2 #X2 #HY2 #_ #H destruct -Hf1

-    /4 width=5 by isuni_fwd_push, eq_push/
+    /4 width=5 by pr_isu_fwd_push, pr_eq_push/

   | lapply (drops_inv_drop1 … Hf2) -Hf2 -IH -HU2 #Hg2
   | lapply (drops_inv_drop1 … Hf2) -Hf2 -IH -HU2 #Hg2

-    lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by isuni_inv_push/ -HU1
+    lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by pr_isu_inv_push/ -HU1

     #H destruct elim (drops_inv_x_bind_xy … Hg2)
   ]
 ]
     #H destruct elim (drops_inv_x_bind_xy … Hg2)
   ]
 ]


@@ -88,7 +88,7 @@ qed-.
 (* Basic_2A1: includes: drop_mono *)
 lemma drops_mono: ∀b1,f,L,L1. ⇩*[b1,f] L ≘ L1 →
                   ∀b2,L2. ⇩*[b2,f] L ≘ L2 → L1 = L2.
 (* Basic_2A1: includes: drop_mono *)
 lemma drops_mono: ∀b1,f,L,L1. ⇩*[b1,f] L ≘ L1 →
                   ∀b2,L2. ⇩*[b2,f] L ≘ L2 → L1 = L2.

-#b1 #f #L #L1 lapply (after_isid_dx 𝐢 … f)
+#b1 #f #L #L1 lapply (pr_after_isi_dx 𝐢 … f)

 /3 width=8 by drops_conf, drops_fwd_isid/
 qed-.
 
 /3 width=8 by drops_conf, drops_fwd_isid/
 qed-.
 


@@ -135,7 +135,7 @@ lemma drops_conf_div_bind_isuni:
 #f1 #f2 #I1 #I2 #L #K #Hf1 #Hf2 #HU1 #HU2
 lapply (drops_isuni_fwd_drop2 … Hf1) // #H1
 lapply (drops_isuni_fwd_drop2 … Hf2) // #H2
 #f1 #f2 #I1 #I2 #L #K #Hf1 #Hf2 #HU1 #HU2
 lapply (drops_isuni_fwd_drop2 … Hf1) // #H1
 lapply (drops_isuni_fwd_drop2 … Hf2) // #H2

-lapply (drops_conf_div_isuni … H1 … H2 ??) /2 width=3 by isuni_next/ -H1 -H2 -HU1 -HU2 #H
+lapply (drops_conf_div_isuni … H1 … H2 ??) /2 width=3 by pr_isu_next/ -H1 -H2 -HU1 -HU2 #H

 lapply (eq_inv_nn … H ????) -H [5: |*: // ] #H12
 lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0
 lapply (drops_mono … H0 … Hf2) -L #H
 lapply (eq_inv_nn … H ????) -H [5: |*: // ] #H12
 lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0
 lapply (drops_mono … H0 … Hf2) -L #H

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
index fe6b2ade8668984a61e59d415ab6e7b0b954d78c..49c4f0206867da6c0862469fd9d59feb811cd594 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
@@ -21,7 +21,7 @@ include "static_2/relocation/drops.ma".
 
 (* Basic_2A1: includes: drop_fwd_length_le4 *)
 lemma drops_fwd_length_le4: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → |L2| ≤ |L1|.
 
 (* Basic_2A1: includes: drop_fwd_length_le4 *)
 lemma drops_fwd_length_le4: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → |L2| ≤ |L1|.

-#b #f #L1 #L2 #H elim H -f -L1 -L2 /2 width=1 by le_S, le_S_S/
+#b #f #L1 #L2 #H elim H -f -L1 -L2 /2 width=1 by nle_succ_dx, nle_succ_bi/

 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq1 *)
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq1 *)


@@ -46,9 +46,9 @@ qed-.
 lemma drops_fwd_fcla: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 →
                       ∃∃n. 𝐂❪f❫ ≘ n & |L1| = |L2| + n.
 #f #L1 #L2 #H elim H -f -L1 -L2
 lemma drops_fwd_fcla: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 →
                       ∃∃n. 𝐂❪f❫ ≘ n & |L1| = |L2| + n.
 #f #L1 #L2 #H elim H -f -L1 -L2

-[ /4 width=3 by fcla_isid, ex2_intro/
-| #f #I #L1 #L2 #_ * >length_bind /3 width=3 by fcla_next, ex2_intro, eq_f/
-| #f #I1 #I2 #L1 #L2 #_ #_ * >length_bind >length_bind /3 width=3 by fcla_push, ex2_intro/
+[ /4 width=3 by pr_fcla_isi, ex2_intro/
+| #f #I #L1 #L2 #_ * >length_bind /3 width=3 by pr_fcla_next, ex2_intro, eq_f/
+| #f #I1 #I2 #L1 #L2 #_ #_ * >length_bind >length_bind /3 width=3 by pr_fcla_push, ex2_intro/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -56,7 +56,7 @@ qed-.
 lemma drops_fcla_fwd: ∀f,L1,L2,n. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐂❪f❫ ≘ n →
                       |L1| = |L2| + n.
 #f #l1 #l2 #n #Hf #Hn elim (drops_fwd_fcla … Hf) -Hf
 lemma drops_fcla_fwd: ∀f,L1,L2,n. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐂❪f❫ ≘ n →
                       |L1| = |L2| + n.
 #f #l1 #l2 #n #Hf #Hn elim (drops_fwd_fcla … Hf) -Hf

-#k #Hm #H <(fcla_mono … Hm … Hn) -f //
+#k #Hm #H <(pr_fcla_mono … Hm … Hn) -f //

 qed-.
 
 lemma drops_fwd_fcla_le2: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 →
 qed-.
 
 lemma drops_fwd_fcla_le2: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 →


@@ -68,13 +68,13 @@ qed-.
 lemma drops_fcla_fwd_le2: ∀f,L1,L2,n. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐂❪f❫ ≘ n →
                           n ≤ |L1|.
 #f #L1 #L2 #n #H #Hn elim (drops_fwd_fcla_le2 … H) -H
 lemma drops_fcla_fwd_le2: ∀f,L1,L2,n. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐂❪f❫ ≘ n →
                           n ≤ |L1|.
 #f #L1 #L2 #n #H #Hn elim (drops_fwd_fcla_le2 … H) -H

-#k #Hm #H <(fcla_mono … Hm … Hn) -f //
+#k #Hm #H <(pr_fcla_mono … Hm … Hn) -f //

 qed-.
 
 lemma drops_fwd_fcla_lt2: ∀f,L1,I2,K2. ⇩*[Ⓣ,f] L1 ≘ K2.ⓘ[I2] →
                           ∃∃n. 𝐂❪f❫ ≘ n & n < |L1|.
 #f #L1 #I2 #K2 #H elim (drops_fwd_fcla … H) -H
 qed-.
 
 lemma drops_fwd_fcla_lt2: ∀f,L1,I2,K2. ⇩*[Ⓣ,f] L1 ≘ K2.ⓘ[I2] →
                           ∃∃n. 𝐂❪f❫ ≘ n & n < |L1|.
 #f #L1 #I2 #K2 #H elim (drops_fwd_fcla … H) -H

-#n #Hf #H >H -L1 /3 width=3 by le_S_S, ex2_intro/
+#n #Hf #H >H -L1 /3 width=3 by nle_succ_bi, ex2_intro/

 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt2 *)
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt2 *)


@@ -82,20 +82,20 @@ lemma drops_fcla_fwd_lt2: ∀f,L1,I2,K2,n.
                           ⇩*[Ⓣ,f] L1 ≘ K2.ⓘ[I2] → 𝐂❪f❫ ≘ n →
                           n < |L1|.
 #f #L1 #I2 #K2 #n #H #Hn elim (drops_fwd_fcla_lt2 … H) -H
                           ⇩*[Ⓣ,f] L1 ≘ K2.ⓘ[I2] → 𝐂❪f❫ ≘ n →
                           n < |L1|.
 #f #L1 #I2 #K2 #n #H #Hn elim (drops_fwd_fcla_lt2 … H) -H

-#k #Hm #H <(fcla_mono … Hm … Hn) -f //
+#k #Hm #H <(pr_fcla_mono … Hm … Hn) -f //

 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt4 *)
 lemma drops_fcla_fwd_lt4: ∀f,L1,L2,n. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐂❪f❫ ≘ n → 0 < n →
                           |L2| < |L1|.
 #f #L1 #L2 #n #H #Hf #Hn lapply (drops_fcla_fwd … H Hf) -f
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt4 *)
 lemma drops_fcla_fwd_lt4: ∀f,L1,L2,n. ⇩*[Ⓣ,f] L1 ≘ L2 → 𝐂❪f❫ ≘ n → 0 < n →
                           |L2| < |L1|.
 #f #L1 #L2 #n #H #Hf #Hn lapply (drops_fcla_fwd … H Hf) -f

-/2 width=1 by lt_minus_to_plus_r/ qed-.
+/2 width=1 by nlt_inv_minus_dx/ qed-.

 
 (* Basic_2A1: includes: drop_inv_length_eq *)
 lemma drops_inv_length_eq: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 → |L1| = |L2| → 𝐈❪f❫.
 #f #L1 #L2 #H #HL12 elim (drops_fwd_fcla … H) -H
 
 (* Basic_2A1: includes: drop_inv_length_eq *)
 lemma drops_inv_length_eq: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 → |L1| = |L2| → 𝐈❪f❫.
 #f #L1 #L2 #H #HL12 elim (drops_fwd_fcla … H) -H

-#n #Hn <HL12 -L2 #H lapply (discr_plus_x_xy … H) -H
-/2 width=3 by fcla_inv_xp/
+#n #Hn <HL12 -L2 #H lapply (nplus_refl_sn … H) -H
+/2 width=3 by pr_fcla_inv_zero/

 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq2 *)
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq2 *)


@@ -104,7 +104,7 @@ theorem drops_fwd_length_eq2: ∀f,L1,L2,K1,K2. ⇩*[Ⓣ,f] L1 ≘ K1 → ⇩*[
 #f #L1 #L2 #K1 #K2 #HLK1 #HLK2 #HL12
 elim (drops_fwd_fcla … HLK1) -HLK1 #n1 #Hn1 #H1 >H1 -L1
 elim (drops_fwd_fcla … HLK2) -HLK2 #n2 #Hn2 #H2 >H2 -L2
 #f #L1 #L2 #K1 #K2 #HLK1 #HLK2 #HL12
 elim (drops_fwd_fcla … HLK1) -HLK1 #n1 #Hn1 #H1 >H1 -L1
 elim (drops_fwd_fcla … HLK2) -HLK2 #n2 #Hn2 #H2 >H2 -L2

-<(fcla_mono … Hn2 … Hn1) -f //
+<(pr_fcla_mono … Hn2 … Hn1) -f //

 qed-.
 
 theorem drops_conf_div: ∀f1,f2,L1,L2. ⇩*[Ⓣ,f1] L1 ≘ L2 → ⇩*[Ⓣ,f2] L1 ≘ L2 →
 qed-.
 
 theorem drops_conf_div: ∀f1,f2,L1,L2. ⇩*[Ⓣ,f1] L1 ≘ L2 → ⇩*[Ⓣ,f2] L1 ≘ L2 →


@@ -112,7 +112,7 @@ theorem drops_conf_div: ∀f1,f2,L1,L2. ⇩*[Ⓣ,f1] L1 ≘ L2 → ⇩*[Ⓣ,f2]
 #f1 #f2 #L1 #L2 #H1 #H2
 elim (drops_fwd_fcla … H1) -H1 #n1 #Hf1 #H1
 elim (drops_fwd_fcla … H2) -H2 #n2 #Hf2 >H1 -L1 #H
 #f1 #f2 #L1 #L2 #H1 #H2
 elim (drops_fwd_fcla … H1) -H1 #n1 #Hf1 #H1
 elim (drops_fwd_fcla … H2) -H2 #n2 #Hf2 >H1 -L1 #H

-lapply (injective_plus_r … H) -L2 #H destruct /2 width=3 by ex2_intro/
+lapply (eq_inv_nplus_bi_sn … H) -L2 #H destruct /2 width=3 by ex2_intro/

 qed-.
 
 theorem drops_conf_div_fcla: ∀f1,f2,L1,L2,n1,n2.
 qed-.
 
 theorem drops_conf_div_fcla: ∀f1,f2,L1,L2,n1,n2.


@@ -121,5 +121,5 @@ theorem drops_conf_div_fcla: ∀f1,f2,L1,L2,n1,n2.
 #f1 #f2 #L1 #L2 #n1 #n2 #Hf1 #Hf2 #Hn1 #Hn2
 lapply (drops_fcla_fwd … Hf1 Hn1) -f1 #H1
 lapply (drops_fcla_fwd … Hf2 Hn2) -f2 >H1 -L1
 #f1 #f2 #L1 #L2 #n1 #n2 #Hf1 #Hf2 #Hn1 #Hn2
 lapply (drops_fcla_fwd … Hf1 Hn1) -f1 #H1
 lapply (drops_fcla_fwd … Hf2 Hn2) -f2 >H1 -L1

-/2 width=1 by injective_plus_r/
+/2 width=1 by eq_inv_nplus_bi_sn/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_lex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_lex.ma
index 1201b75fad73f3510fc4ba781a6ce75cdfc24ef0..4e261897dd387e0e8a7a7fc8cebc5dfd7eca976d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_lex.ma
@@ -37,7 +37,7 @@ lemma lex_liftable_dedropable_sn (R): c_reflexive … R →
                                       d_liftable2_sn … lifts R → dedropable_sn R.
 #R #H1R #H2R #b #f #L1 #K1 #HLK1 #K2 * #f1 #Hf1 #HK12
 elim (sex_liftable_co_dedropable_sn … HLK1 … HK12) -K1
                                       d_liftable2_sn … lifts R → dedropable_sn R.
 #R #H1R #H2R #b #f #L1 #K1 #HLK1 #K2 * #f1 #Hf1 #HK12
 elim (sex_liftable_co_dedropable_sn … HLK1 … HK12) -K1

-/3 width=6 by cext2_d_liftable2_sn, cfull_lift_sn, ext2_refl, coafter_isid_dx, ex3_intro, ex2_intro/
+/3 width=6 by cext2_d_liftable2_sn, cfull_lift_sn, ext2_refl, pr_coafter_isi_dx, ex3_intro, ex2_intro/

 qed-.
 
 (* Inversion lemmas with generic extension **********************************)
 qed-.
 
 (* Inversion lemmas with generic extension **********************************)


@@ -46,14 +46,14 @@ qed-.
 lemma lex_dropable_sn (R): dropable_sn R.
 #R #b #f #L1 #K1 #HLK1 #H1f #L2 * #f2 #Hf2 #HL12
 elim (sex_co_dropable_sn … HLK1 … HL12) -L1
 lemma lex_dropable_sn (R): dropable_sn R.
 #R #b #f #L1 #K1 #HLK1 #H1f #L2 * #f2 #Hf2 #HL12
 elim (sex_co_dropable_sn … HLK1 … HL12) -L1

-/3 width=3 by coafter_isid_dx, ex2_intro/
+/3 width=3 by pr_coafter_isi_dx, ex2_intro/

 qed-.
 
 (* Basic_2A1: was: lpx_sn_dropable *)
 lemma lex_dropable_dx (R): dropable_dx R.
 #R #L1 #L2 * #f2 #Hf2 #HL12 #b #f #K2 #HLK2 #Hf
 elim (sex_co_dropable_dx … HL12 … HLK2) -L2
 qed-.
 
 (* Basic_2A1: was: lpx_sn_dropable *)
 lemma lex_dropable_dx (R): dropable_dx R.
 #R #L1 #L2 * #f2 #Hf2 #HL12 #b #f #K2 #HLK2 #Hf
 elim (sex_co_dropable_dx … HL12 … HLK2) -L2

-/3 width=5 by coafter_isid_dx, ex2_intro/
+/3 width=5 by pr_coafter_isi_dx, ex2_intro/

 qed-.
 
 (* Basic_2A1: includes: lpx_sn_drop_conf *)
 qed-.
 
 (* Basic_2A1: includes: lpx_sn_drop_conf *)


@@ -65,7 +65,7 @@ elim (sex_drops_conf_push … HL12 … HLK1 Hf f2) -L1 -Hf
 [ #Z2 #K2 #HLK2 #HK12 #H
   elim (ext2_inv_pair_sn … H) -H #V2 #HV12 #H destruct
   /3 width=5 by ex3_2_intro, ex2_intro/
 [ #Z2 #K2 #HLK2 #HK12 #H
   elim (ext2_inv_pair_sn … H) -H #V2 #HV12 #H destruct
   /3 width=5 by ex3_2_intro, ex2_intro/

-| /3 width=3 by coafter_isid_dx, isid_push/
+| /3 width=3 by pr_coafter_isi_dx, pr_isi_push/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -78,6 +78,6 @@ elim (sex_drops_trans_push … HL12 … HLK2 Hf f2) -L2 -Hf
 [ #Z1 #K1 #HLK1 #HK12 #H
   elim (ext2_inv_pair_dx … H) -H #V1 #HV12 #H destruct
   /3 width=5 by ex3_2_intro, ex2_intro/
 [ #Z1 #K1 #HLK1 #HK12 #H
   elim (ext2_inv_pair_dx … H) -H #V1 #HV12 #H destruct
   /3 width=5 by ex3_2_intro, ex2_intro/

-| /3 width=3 by coafter_isid_dx, isid_push/
+| /3 width=3 by pr_coafter_isi_dx, pr_isi_push/

 ]
 qed-.
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
index aeff28ceeda71426dc782d6ea008e1d5b2e11c4a..18017d88ae41fcce0471faaf4616ddc7d0a98620 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
@@ -26,19 +26,19 @@ lemma sex_co_dropable_sn (RN) (RP):
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I1 #L1 #K1 #_ #IH #Hf #f2 #X #H #f1 #Hf2
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I1 #L1 #K1 #_ #IH #Hf #f2 #X #H #f1 #Hf2

-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H2 destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H2 destruct

   elim (sex_inv_push1 … H) -H #I2 #L2 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -g2
   elim (sex_inv_push1 … H) -H #I2 #L2 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -g2

-  /3 width=3 by isuni_inv_next, drops_drop, ex2_intro/
+  /3 width=3 by pr_isu_inv_next, drops_drop, ex2_intro/

 | #f #I1 #J1 #L1 #K1 #HLK #HJI1 #IH #Hf #f2 #X #H #f1 #Hf2
 | #f #I1 #J1 #L1 #K1 #HLK #HJI1 #IH #Hf #f2 #X #H #f1 #Hf2

-  lapply (isuni_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
+  lapply (pr_isu_inv_push … Hf ??) -Hf [3: |*: // ] #Hf

   lapply (drops_fwd_isid … HLK … Hf) -HLK #H0 destruct
   lapply (liftsb_fwd_isid … HJI1 … Hf) -HJI1 #H0 destruct
   lapply (drops_fwd_isid … HLK … Hf) -HLK #H0 destruct
   lapply (liftsb_fwd_isid … HJI1 … Hf) -HJI1 #H0 destruct

-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct

   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H destruct
   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H destruct

-  elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by isuni_isid/ #K2 #HK12 #HLK2
+  elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by pr_isu_isi/ #K2 #HK12 #HLK2

   lapply (drops_fwd_isid … HLK2 … Hf) -HLK2 #H0 destruct
   lapply (drops_fwd_isid … HLK2 … Hf) -HLK2 #H0 destruct

-  /4 width=3 by drops_refl, sex_next, sex_push, isid_push, ex2_intro/
+  /4 width=3 by drops_refl, sex_next, sex_push, pr_isi_push, ex2_intro/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -49,13 +49,13 @@ lemma sex_liftable_co_dedropable_bi (RN) (RP):
       f ~⊚ f1 ≘ f2 → L1 ⪤[RN,RP,f2] L2.
 #RN #RP #HRN #HRP #f2 #L1 #L2 #H elim H -f2 -L1 -L2 //
 #g2 #I1 #I2 #L1 #L2 #HL12 #HI12 #IH #f1 #Y1 #Y2 #HK12 #b #f #HY1 #HY2 #H
       f ~⊚ f1 ≘ f2 → L1 ⪤[RN,RP,f2] L2.
 #RN #RP #HRN #HRP #f2 #L1 #L2 #H elim H -f2 -L1 -L2 //
 #g2 #I1 #I2 #L1 #L2 #HL12 #HI12 #IH #f1 #Y1 #Y2 #HK12 #b #f #HY1 #HY2 #H

-[ elim (coafter_inv_xxn … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct
+[ elim (pr_coafter_inv_next … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct

   elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
   elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
   elim (sex_inv_next … HK12) -HK12 #HK12 #HJ12
   elim (HRN … HJ12 … HLK1 … HJI1) -HJ12 -HJI1 #Z #Hz
   >(liftsb_mono … Hz … HJI2) -Z /3 width=9 by sex_next/
   elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
   elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
   elim (sex_inv_next … HK12) -HK12 #HK12 #HJ12
   elim (HRN … HJ12 … HLK1 … HJI1) -HJ12 -HJI1 #Z #Hz
   >(liftsb_mono … Hz … HJI2) -Z /3 width=9 by sex_next/

-| elim (coafter_inv_xxp … H) [1,2: |*: // ] -H *
+| elim (pr_coafter_inv_push … H) [1,2: |*: // ] -H *

   [ #g #g1 #Hg2 #H1 #H2 destruct
     elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
     elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
   [ #g #g1 #Hg2 #H1 #H2 destruct
     elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
     elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct


@@ -78,11 +78,11 @@ lemma sex_liftable_co_dedropable_sn (RN) (RP):
 [ #f #Hf #X #f1 #H #f2 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=4 by drops_atom, sex_atom, ex3_intro/
 | #f #I1 #L1 #K1 #_ #IHLK1 #K2 #f1 #HK12 #f2 #Hf2
 [ #f #Hf #X #f1 #H #f2 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=4 by drops_atom, sex_atom, ex3_intro/
 | #f #I1 #L1 #K1 #_ #IHLK1 #K2 #f1 #HK12 #f2 #Hf2

-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct

   elim (IHLK1 … HK12 … Hg2) -K1
   /3 width=6 by drops_drop, sex_next, sex_push, ex3_intro/
 | #f #I1 #J1 #L1 #K1 #HLK1 #HJI1 #IHLK1 #X #f1 #H #f2 #Hf2
   elim (IHLK1 … HK12 … Hg2) -K1
   /3 width=6 by drops_drop, sex_next, sex_push, ex3_intro/
 | #f #I1 #J1 #L1 #K1 #HLK1 #HJI1 #IHLK1 #X #f1 #H #f2 #Hf2

-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct

   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #J2 #K2 #HK12 #HJ12 #H destruct
   [ elim (H2RP … HJ12 … HLK1 … HJI1) | elim (H2RN … HJ12 … HLK1 … HJI1) ] -J1
   elim (IHLK1 … HK12 … Hg2) -K1
   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #J2 #K2 #HK12 #HJ12 #H destruct
   [ elim (H2RP … HJ12 … HLK1 … HJI1) | elim (H2RN … HJ12 … HLK1 … HJI1) ] -J1
   elim (IHLK1 … HK12 … Hg2) -K1


@@ -98,18 +98,18 @@ fact sex_dropable_dx_aux (RN) (RP):
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 lapply (sex_inv_atom2 … H) -H
   #H destruct /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I2 #L2 #K2 #_ #IH #Hf #f2 #X #HX #f1 #Hf2
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 lapply (sex_inv_atom2 … H) -H
   #H destruct /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I2 #L2 #K2 #_ #IH #Hf #f2 #X #HX #f1 #Hf2

-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct

   elim (sex_inv_push2 … HX) -HX #I1 #L1 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -L2 -I2 -g2
   elim (sex_inv_push2 … HX) -HX #I1 #L1 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -L2 -I2 -g2

-  /3 width=3 by drops_drop, isuni_inv_next, ex2_intro/
+  /3 width=3 by drops_drop, pr_isu_inv_next, ex2_intro/

 | #f #I2 #J2 #L2 #K2 #_ #HJI2 #IH #Hf #f2 #X #HX #f1 #Hf2
 | #f #I2 #J2 #L2 #K2 #_ #HJI2 #IH #Hf #f2 #X #HX #f1 #Hf2

-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct

   [ elim (sex_inv_push2 … HX) | elim (sex_inv_next2 … HX) ] -HX #I1 #L1 #HL12 #HI12 #H destruct
   [ elim (sex_inv_push2 … HX) | elim (sex_inv_next2 … HX) ] -HX #I1 #L1 #HL12 #HI12 #H destruct

-  elim (IH … HL12 … Hg2) -L2 -g2 /2 width=3 by isuni_fwd_push/ #K1 #HLK1 #HK12
-  lapply (isuni_inv_push … Hf ??) -Hf [3,6: |*: // ] #Hf
+  elim (IH … HL12 … Hg2) -L2 -g2 /2 width=3 by pr_isu_fwd_push/ #K1 #HLK1 #HK12
+  lapply (pr_isu_inv_push … Hf ??) -Hf [3,6: |*: // ] #Hf

   lapply (liftsb_fwd_isid … HJI2 … Hf) #H destruct -HJI2
   lapply (drops_fwd_isid … HLK1 … Hf) #H destruct -HLK1
   lapply (liftsb_fwd_isid … HJI2 … Hf) #H destruct -HJI2
   lapply (drops_fwd_isid … HLK1 … Hf) #H destruct -HLK1

-  /4 width=5 by sex_next, sex_push, drops_refl, isid_push, ex2_intro/
+  /4 width=5 by sex_next, sex_push, drops_refl, pr_isi_push, ex2_intro/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -205,16 +205,16 @@ lemma sex_sdj_split_dx (R1) (R2) (RP):
 [ #f1 #_ #L2 #H #f2 #_
   lapply (sex_inv_atom1 … H) -H #H destruct
   /2 width=3 by sex_atom, ex2_intro/
 [ #f1 #_ #L2 #H #f2 #_
   lapply (sex_inv_atom1 … H) -H #H destruct
   /2 width=3 by sex_atom, ex2_intro/

-| #K1 #I1 #IH #f1 elim (pn_split f1) * #g1 #H destruct
+| #K1 #I1 #IH #f1 elim (pr_map_split_tl f1) * #g1 #H destruct

   #HR #L2 #H #f2 #Hf
   [ elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
   #HR #L2 #H #f2 #Hf
   [ elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct

-    elim (sdj_inv_px … Hf ??) -Hf [1,3: * |*: // ] #g2 #Hg #H destruct
+    elim (pr_sdj_inv_push_sn … Hf ??) -Hf [1,3: * |*: // ] #g2 #Hg #H destruct

     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [1,3: /3 width=5 by sex_next, sex_push, ex2_intro/
     |2,4: /3 width=3 by drops_drop/
     ]
   | elim (sex_inv_next1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [1,3: /3 width=5 by sex_next, sex_push, ex2_intro/
     |2,4: /3 width=3 by drops_drop/
     ]
   | elim (sex_inv_next1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct

-    elim (sdj_inv_nx … Hf ??) -Hf [|*: // ] #g2 #Hg #H destruct
+    elim (pr_sdj_inv_next_sn … Hf ??) -Hf [|*: // ] #g2 #Hg #H destruct

     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [ /5 width=11 by sex_next, sex_push, drops_refl, ex2_intro/
     | /3 width=3 by drops_drop/
     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [ /5 width=11 by sex_next, sex_push, drops_refl, ex2_intro/
     | /3 width=3 by drops_drop/

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma
index 975b01523d5fe71972abe1270b33e7188475292b..97b730cc82d8983ce20be9581b520f48ce5deb6b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma
@@ -23,9 +23,9 @@ include "static_2/relocation/drops.ma".
 (* Basic_2A1: includes: drop_fwd_lw *)
 lemma drops_fwd_lw: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → ♯❨L2❩ ≤ ♯❨L1❩.
 #b #f #L1 #L2 #H elim H -f -L1 -L2 //
 (* Basic_2A1: includes: drop_fwd_lw *)
 lemma drops_fwd_lw: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → ♯❨L2❩ ≤ ♯❨L1❩.
 #b #f #L1 #L2 #H elim H -f -L1 -L2 //

-[ /2 width=3 by transitive_le/
+[ /2 width=3 by nle_trans/

 | #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 normalize
 | #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 normalize

-  >(liftsb_fwd_bw … HI21) -HI21 /2 width=1 by monotonic_le_plus_l/
+  >(liftsb_fwd_bw … HI21) -HI21 /2 width=1 by nle_plus_bi_dx/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -34,9 +34,9 @@ lemma drops_fwd_lw_lt: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 →
                        (𝐈❪f❫ → ⊥) → ♯❨L2❩ < ♯❨L1❩.
 #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #Hf #Hnf elim Hnf -Hnf /2 width=1 by/
                        (𝐈❪f❫ → ⊥) → ♯❨L2❩ < ♯❨L1❩.
 #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #Hf #Hnf elim Hnf -Hnf /2 width=1 by/

-| /3 width=3 by drops_fwd_lw, le_to_lt_to_lt/
+| /3 width=3 by drops_fwd_lw, nle_nlt_trans/

 | #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #H normalize in ⊢ (?%%);
 | #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #H normalize in ⊢ (?%%);

-  >(liftsb_fwd_bw … HI21) -I2 /5 width=3 by isid_push, monotonic_lt_plus_l/
+  >(liftsb_fwd_bw … HI21) -I2 /5 width=3 by pr_isi_push, nlt_plus_bi_dx/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -45,12 +45,12 @@ qed-.
 (* Basic_2A1: includes: drop_fwd_rfw *)
 lemma drops_bind2_fwd_rfw: ∀b,f,I,L,K,V. ⇩*[b,f] L ≘ K.ⓑ[I]V → ∀T. ♯❨K,V❩ < ♯❨L,T❩.
 #b #f #I #L #K #V #HLK lapply (drops_fwd_lw … HLK) -HLK
 (* Basic_2A1: includes: drop_fwd_rfw *)
 lemma drops_bind2_fwd_rfw: ∀b,f,I,L,K,V. ⇩*[b,f] L ≘ K.ⓑ[I]V → ∀T. ♯❨K,V❩ < ♯❨L,T❩.
 #b #f #I #L #K #V #HLK lapply (drops_fwd_lw … HLK) -HLK

-normalize in ⊢ (%→?→?%%); /3 width=3 by le_to_lt_to_lt, monotonic_lt_plus_r/
+normalize in ⊢ (%→?→?%%); /3 width=3 by nle_nlt_trans, nlt_plus_bi_sn/

 qed-.
 
 (* Advanced inversion lemma *************************************************)
 
 lemma drops_inv_x_bind_xy: ∀b,f,I,L. ⇩*[b,f] L ≘ L.ⓘ[I] → ⊥.
 #b #f #I #L #H lapply (drops_fwd_lw … H) -b -f
 qed-.
 
 (* Advanced inversion lemma *************************************************)
 
 lemma drops_inv_x_bind_xy: ∀b,f,I,L. ⇩*[b,f] L ≘ L.ⓘ[I] → ⊥.
 #b #f #I #L #H lapply (drops_fwd_lw … H) -b -f

-/2 width=4 by lt_le_false/ (**) (* full auto is a bit slow: 19s *)
+/2 width=4 by nlt_ge_false/ (**) (* full auto is a bit slow: 19s *)

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma
index 2c3e5548c6937f90a7b181fc7f3f45f94ac6c8a0..02ba4bedc837ea1318c83fb27239cb9456ca0f35 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma
@@ -44,7 +44,7 @@ lemma lex_atom (R): ⋆ ⪤[R] ⋆.
 lemma lex_bind (R): ∀I1,I2,K1,K2. K1 ⪤[R] K2 → cext2 R K1 I1 I2 →
                     K1.ⓘ[I1] ⪤[R] K2.ⓘ[I2].
 #R #I1 #I2 #K1 #K2 * #f #Hf #HK12 #HI12
 lemma lex_bind (R): ∀I1,I2,K1,K2. K1 ⪤[R] K2 → cext2 R K1 I1 I2 →
                     K1.ⓘ[I1] ⪤[R] K2.ⓘ[I2].
 #R #I1 #I2 #K1 #K2 * #f #Hf #HK12 #HI12

-/3 width=3 by sex_push, isid_push, ex2_intro/
+/3 width=3 by sex_push, pr_isi_push, ex2_intro/

 qed.
 
 (* Basic_2A1: was: lpx_sn_refl *)
 qed.
 
 (* Basic_2A1: was: lpx_sn_refl *)


@@ -80,7 +80,7 @@ qed-.
 lemma lex_inv_bind_sn (R): ∀I1,L2,K1. K1.ⓘ[I1] ⪤[R] L2 →
                            ∃∃I2,K2. K1 ⪤[R] K2 & cext2 R K1 I1 I2 & L2 = K2.ⓘ[I2].
 #R #I1 #L2 #K1 * #f #Hf #H
 lemma lex_inv_bind_sn (R): ∀I1,L2,K1. K1.ⓘ[I1] ⪤[R] L2 →
                            ∃∃I2,K2. K1 ⪤[R] K2 & cext2 R K1 I1 I2 & L2 = K2.ⓘ[I2].
 #R #I1 #L2 #K1 * #f #Hf #H

-lapply (sex_eq_repl_fwd … H (⫯f) ?) -H /2 width=1 by eq_push_inv_isid/ #H
+lapply (sex_eq_repl_fwd … H (⫯f) ?) -H /2 width=1 by pr_isi_inv_eq_push/ #H

 elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
 /3 width=5 by ex2_intro, ex3_2_intro/
 qed-.
 elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
 /3 width=5 by ex2_intro, ex3_2_intro/
 qed-.


@@ -93,7 +93,7 @@ qed-.
 lemma lex_inv_bind_dx (R): ∀I2,L1,K2. L1 ⪤[R] K2.ⓘ[I2] →
                            ∃∃I1,K1. K1 ⪤[R] K2 & cext2 R K1 I1 I2 & L1 = K1.ⓘ[I1].
 #R #I2 #L1 #K2 * #f #Hf #H
 lemma lex_inv_bind_dx (R): ∀I2,L1,K2. L1 ⪤[R] K2.ⓘ[I2] →
                            ∃∃I1,K1. K1 ⪤[R] K2 & cext2 R K1 I1 I2 & L1 = K1.ⓘ[I1].
 #R #I2 #L1 #K2 * #f #Hf #H

-lapply (sex_eq_repl_fwd … H (⫯f) ?) -H /2 width=1 by eq_push_inv_isid/ #H
+lapply (sex_eq_repl_fwd … H (⫯f) ?) -H /2 width=1 by pr_isi_inv_eq_push/ #H

 elim (sex_inv_push2 … H) -H #I1 #K1 #HK12 #HI12 #H destruct
 /3 width=5 by ex3_2_intro, ex2_intro/
 qed-.
 elim (sex_inv_push2 … H) -H #I1 #K1 #HK12 #HI12 #H destruct
 /3 width=5 by ex3_2_intro, ex2_intro/
 qed-.


@@ -154,8 +154,8 @@ lemma lex_ind (R) (Q:relation2 …):
               ∀L1,L2. L1 ⪤[R] L2 → Q L1 L2.
 #R #Q #IH1 #IH2 #IH3 #L1 #L2 * #f @pull_2 #H
 elim H -f -L1 -L2 // #f #I1 #I2 #K1 #K2 @pull_4 #H
               ∀L1,L2. L1 ⪤[R] L2 → Q L1 L2.
 #R #Q #IH1 #IH2 #IH3 #L1 #L2 * #f @pull_2 #H
 elim H -f -L1 -L2 // #f #I1 #I2 #K1 #K2 @pull_4 #H

-[ elim (isid_inv_next … H)
-| lapply (isid_inv_push … H ??)
+[ elim (pr_isi_inv_next … H)
+| lapply (pr_isi_inv_push … H ??)

 ] -H [5:|*: // ] #Hf @pull_2 #H
 elim H -H /3 width=3 by ex2_intro/
 qed-.
 ] -H [5:|*: // ] #Hf @pull_2 #H
 elim H -H /3 width=3 by ex2_intro/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lex_tc.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lex_tc.ma
index 2f86bf51cb80d4dcf65f0848172917c8077b25aa..51039cd8d23232e77768800969464f1fa06e1b37 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lex_tc.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lex_tc.ma
@@ -47,7 +47,7 @@ lemma lex_CTC (R): s_rs_transitive … R (λ_. lex R) →
                    TC … (lex R) ⊆ lex (CTC … R).
 #R #HR #L1 #L2 #HL12
 lapply (monotonic_TC … (sex cfull (cext2 R) 𝐢) … HL12) -HL12
                    TC … (lex R) ⊆ lex (CTC … R).
 #R #HR #L1 #L2 #HL12
 lapply (monotonic_TC … (sex cfull (cext2 R) 𝐢) … HL12) -HL12

-[ #L1 #L2 * /3 width=3 by sex_eq_repl_fwd, eq_id_inv_isid/
+[ #L1 #L2 * /3 width=3 by sex_eq_repl_fwd, pr_isi_inv_eq_id/

 | /5 width=9 by s_rs_transitive_lex_inv_isid, sex_tc_dx, sex_co, ext2_tc, ex2_intro/
 ]
 qed-.
 | /5 width=9 by s_rs_transitive_lex_inv_isid, sex_tc_dx, sex_co, ext2_tc, ex2_intro/
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
index 2dceb17d013503356e068cf3054639d099effecf..f019c66d6cb3fa61170a17457061e3f2d375a13f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
@@ -23,7 +23,7 @@ include "static_2/syntax/term.ma".
             lift_sort lift_lref_lt lift_lref_ge lift_bind lift_flat
             lifts_nil lifts_cons
 *)
             lift_sort lift_lref_lt lift_lref_ge lift_bind lift_flat
             lifts_nil lifts_cons
 *)

-inductive lifts: rtmap → relation term ≝
+inductive lifts: pr_map → relation term ≝

 | lifts_sort: ∀f,s. lifts f (⋆s) (⋆s)
 | lifts_lref: ∀f,i1,i2. @❪i1,f❫ ≘ i2 → lifts f (#i1) (#i2)
 | lifts_gref: ∀f,l. lifts f (§l) (§l)
 | lifts_sort: ∀f,s. lifts f (⋆s) (⋆s)
 | lifts_lref: ∀f,i1,i2. @❪i1,f❫ ≘ i2 → lifts f (#i1) (#i2)
 | lifts_gref: ∀f,l. lifts f (§l) (§l)


@@ -39,7 +39,7 @@ interpretation "generic relocation (term)"
    'RLiftStar f T1 T2 = (lifts f T1 T2).
 
 interpretation "uniform relocation (term)"
    'RLiftStar f T1 T2 = (lifts f T1 T2).
 
 interpretation "uniform relocation (term)"

-   'RLift i T1 T2 = (lifts (uni i) T1 T2).
+   'RLift i T1 T2 = (lifts (pr_uni i) T1 T2).

 
 definition liftable2_sn: predicate (relation term) ≝
                          λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⇧*[f] T1 ≘ U1 →
 
 definition liftable2_sn: predicate (relation term) ≝
                          λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⇧*[f] T1 ≘ U1 →


@@ -292,7 +292,7 @@ lemma lifts_inv_push_zero_sn (f):
       ∀X. ⇧*[⫯f]#0 ≘ X → #0 = X.
 #f #X #H
 elim (lifts_inv_lref1 … H) -H #i #Hi #H destruct
       ∀X. ⇧*[⫯f]#0 ≘ X → #0 = X.
 #f #X #H
 elim (lifts_inv_lref1 … H) -H #i #Hi #H destruct

-lapply (at_inv_ppx … Hi ???) -Hi //
+lapply (pr_pat_inv_unit_push … Hi ???) -Hi //

 qed-.
 
 lemma lifts_inv_push_succ_sn (f) (i1):
 qed-.
 
 lemma lifts_inv_push_succ_sn (f) (i1):


@@ -300,30 +300,30 @@ lemma lifts_inv_push_succ_sn (f) (i1):
       ∃∃i2. ⇧*[f]#i1 ≘ #i2 & #(↑i2) = X.
 #f #i1 #X #H
 elim (lifts_inv_lref1 … H) -H #j #Hij #H destruct
       ∃∃i2. ⇧*[f]#i1 ≘ #i2 & #(↑i2) = X.
 #f #i1 #X #H
 elim (lifts_inv_lref1 … H) -H #j #Hij #H destruct

-elim (at_inv_npx … Hij) -Hij [|*: // ] #i2 #Hi12 #H destruct
+elim (pr_pat_inv_succ_push … Hij) -Hij [|*: // ] #i2 #Hi12 #H destruct

 /3 width=3 by lifts_lref, ex2_intro/
 qed-.
 
 (* Inversion lemmas with uniform relocations ********************************)
 
 lemma lifts_inv_lref1_uni: ∀l,Y,i. ⇧[l] #i ≘ Y → Y = #(l+i).
 /3 width=3 by lifts_lref, ex2_intro/
 qed-.
 
 (* Inversion lemmas with uniform relocations ********************************)
 
 lemma lifts_inv_lref1_uni: ∀l,Y,i. ⇧[l] #i ≘ Y → Y = #(l+i).

-#l #Y #i1 #H elim (lifts_inv_lref1 … H) -H /4 width=4 by at_mono, eq_f/
+#l #Y #i1 #H elim (lifts_inv_lref1 … H) -H /4 width=4 by fr2_nat_mono, eq_f/

 qed-.
 
 lemma lifts_inv_lref2_uni: ∀l,X,i2. ⇧[l] X ≘ #i2 →
                            ∃∃i1. X = #i1 & i2 = l + i1.
 #l #X #i2 #H elim (lifts_inv_lref2 … H) -H
 qed-.
 
 lemma lifts_inv_lref2_uni: ∀l,X,i2. ⇧[l] X ≘ #i2 →
                            ∃∃i1. X = #i1 & i2 = l + i1.
 #l #X #i2 #H elim (lifts_inv_lref2 … H) -H

-/3 width=3 by at_inv_uni, ex2_intro/
+/3 width=3 by pr_pat_inv_uni, ex2_intro/

 qed-.
 
 lemma lifts_inv_lref2_uni_ge: ∀l,X,i. ⇧[l] X ≘ #(l + i) → X = #i.
 #l #X #i2 #H elim (lifts_inv_lref2_uni … H) -H
 qed-.
 
 lemma lifts_inv_lref2_uni_ge: ∀l,X,i. ⇧[l] X ≘ #(l + i) → X = #i.
 #l #X #i2 #H elim (lifts_inv_lref2_uni … H) -H

-#i1 #H1 #H2 destruct /4 width=2 by injective_plus_r, eq_f, sym_eq/
+#i1 #H1 #H2 destruct /4 width=2 by eq_inv_nplus_bi_sn, eq_f, sym_eq/

 qed-.
 
 lemma lifts_inv_lref2_uni_lt: ∀l,X,i. ⇧[l] X ≘ #i → i < l → ⊥.
 #l #X #i2 #H elim (lifts_inv_lref2_uni … H) -H
 qed-.
 
 lemma lifts_inv_lref2_uni_lt: ∀l,X,i. ⇧[l] X ≘ #i → i < l → ⊥.
 #l #X #i2 #H elim (lifts_inv_lref2_uni … H) -H

-#i1 #_ #H1 #H2 destruct /2 width=4 by lt_le_false/
+#i1 #_ #H1 #H2 destruct /2 width=4 by nlt_ge_false/

 qed-.
 
 (* Basic forward lemmas *****************************************************)
 qed-.
 
 (* Basic forward lemmas *****************************************************)


@@ -331,7 +331,7 @@ qed-.
 (* Basic_2A1: includes: lift_inv_O2 *)
 lemma lifts_fwd_isid: ∀f,T1,T2. ⇧*[f] T1 ≘ T2 → 𝐈❪f❫ → T1 = T2.
 #f #T1 #T2 #H elim H -f -T1 -T2
 (* Basic_2A1: includes: lift_inv_O2 *)
 lemma lifts_fwd_isid: ∀f,T1,T2. ⇧*[f] T1 ≘ T2 → 𝐈❪f❫ → T1 = T2.
 #f #T1 #T2 #H elim H -f -T1 -T2

-/4 width=3 by isid_inv_at_mono, isid_push, eq_f2, eq_f/
+/4 width=3 by pr_isi_pat_des, pr_isi_push, eq_f2, eq_f/

 qed-.
 
 (* Basic_2A1: includes: lift_fwd_pair1 *)
 qed-.
 
 (* Basic_2A1: includes: lift_fwd_pair1 *)


@@ -364,20 +364,20 @@ lemma deliftable2_sn_dx (R): symmetric … R → deliftable2_sn R → deliftable
 elim (H1R … U1 … HTU2) -H1R /3 width=3 by ex2_intro/
 qed-.
 
 elim (H1R … U1 … HTU2) -H1R /3 width=3 by ex2_intro/
 qed-.
 

-lemma lifts_eq_repl_back: ∀T1,T2. eq_repl_back … (λf. ⇧*[f] T1 ≘ T2).
+lemma lifts_eq_repl_back: ∀T1,T2. pr_eq_repl_back … (λf. ⇧*[f] T1 ≘ T2).

 #T1 #T2 #f1 #H elim H -T1 -T2 -f1
 #T1 #T2 #f1 #H elim H -T1 -T2 -f1

-/4 width=5 by lifts_flat, lifts_bind, lifts_lref, at_eq_repl_back, eq_push/
+/4 width=5 by lifts_flat, lifts_bind, lifts_lref, pr_pat_eq_repl_back, pr_eq_push/

 qed-.
 
 qed-.
 

-lemma lifts_eq_repl_fwd: ∀T1,T2. eq_repl_fwd … (λf. ⇧*[f] T1 ≘ T2).
-#T1 #T2 @eq_repl_sym /2 width=3 by lifts_eq_repl_back/ (**) (* full auto fails *)
+lemma lifts_eq_repl_fwd: ∀T1,T2. pr_eq_repl_fwd … (λf. ⇧*[f] T1 ≘ T2).
+#T1 #T2 @pr_eq_repl_sym /2 width=3 by lifts_eq_repl_back/ (**) (* full auto fails *)

 qed-.
 
 (* Basic_1: includes: lift_r *)
 (* Basic_2A1: includes: lift_refl *)
 lemma lifts_refl: ∀T,f. 𝐈❪f❫ → ⇧*[f] T ≘ T.
 #T elim T -T *
 qed-.
 
 (* Basic_1: includes: lift_r *)
 (* Basic_2A1: includes: lift_refl *)
 lemma lifts_refl: ∀T,f. 𝐈❪f❫ → ⇧*[f] T ≘ T.
 #T elim T -T *

-/4 width=3 by lifts_flat, lifts_bind, lifts_lref, isid_inv_at, isid_push/
+/4 width=3 by lifts_flat, lifts_bind, lifts_lref, pr_isi_inv_pat, pr_isi_push/

 qed.
 
 (* Basic_2A1: includes: lift_total *)
 qed.
 
 (* Basic_2A1: includes: lift_total *)


@@ -397,7 +397,7 @@ lemma lifts_push_zero (f): ⇧*[⫯f]#0 ≘ #0.
 lemma lifts_push_lref (f) (i1) (i2): ⇧*[f]#i1 ≘ #i2 → ⇧*[⫯f]#(↑i1) ≘ #(↑i2).
 #f1 #i1 #i2 #H
 elim (lifts_inv_lref1 … H) -H #j #Hij #H destruct
 lemma lifts_push_lref (f) (i1) (i2): ⇧*[f]#i1 ≘ #i2 → ⇧*[⫯f]#(↑i1) ≘ #(↑i2).
 #f1 #i1 #i2 #H
 elim (lifts_inv_lref1 … H) -H #j #Hij #H destruct

-/3 width=7 by lifts_lref, at_push/
+/3 width=7 by lifts_lref, pr_pat_push/

 qed.
 
 lemma lifts_lref_uni: ∀l,i. ⇧[l] #i ≘ #(l+i).
 qed.
 
 lemma lifts_lref_uni: ∀l,i. ⇧[l] #i ≘ #(l+i).


@@ -411,7 +411,7 @@ lemma lifts_split_trans: ∀f,T1,T2. ⇧*[f] T1 ≘ T2 →
                          ∃∃T. ⇧*[f1] T1 ≘ T & ⇧*[f2] T ≘ T2.
 #f #T1 #T2 #H elim H -f -T1 -T2
 [ /3 width=3 by lifts_sort, ex2_intro/
                          ∃∃T. ⇧*[f1] T1 ≘ T & ⇧*[f2] T ≘ T2.
 #f #T1 #T2 #H elim H -f -T1 -T2
 [ /3 width=3 by lifts_sort, ex2_intro/

-| #f #i1 #i2 #Hi #f1 #f2 #Ht elim (after_at_fwd … Hi … Ht) -Hi -Ht
+| #f #i1 #i2 #Hi #f1 #f2 #Ht elim (pr_after_pat_des … Hi … Ht) -Hi -Ht

   /3 width=3 by lifts_lref, ex2_intro/
 | /3 width=3 by lifts_gref, ex2_intro/
 | #f #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f1 #f2 #Ht
   /3 width=3 by lifts_lref, ex2_intro/
 | /3 width=3 by lifts_gref, ex2_intro/
 | #f #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f1 #f2 #Ht


@@ -429,7 +429,7 @@ lemma lifts_split_div: ∀f1,T1,T2. ⇧*[f1] T1 ≘ T2 →
                        ∃∃T. ⇧*[f2] T2 ≘ T & ⇧*[f] T1 ≘ T.
 #f1 #T1 #T2 #H elim H -f1 -T1 -T2
 [ /3 width=3 by lifts_sort, ex2_intro/
                        ∃∃T. ⇧*[f2] T2 ≘ T & ⇧*[f] T1 ≘ T.
 #f1 #T1 #T2 #H elim H -f1 -T1 -T2
 [ /3 width=3 by lifts_sort, ex2_intro/

-| #f1 #i1 #i2 #Hi #f2 #f #Ht elim (after_at1_fwd … Hi … Ht) -Hi -Ht
+| #f1 #i1 #i2 #Hi #f2 #f #Ht elim (pr_after_des_ist_pat … Hi … Ht) -Hi -Ht

   /3 width=3 by lifts_lref, ex2_intro/
 | /3 width=3 by lifts_gref, ex2_intro/
 | #f1 #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f2 #f #Ht
   /3 width=3 by lifts_lref, ex2_intro/
 | /3 width=3 by lifts_gref, ex2_intro/
 | #f1 #p #I #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f2 #f #Ht


@@ -446,7 +446,7 @@ qed-.
 lemma is_lifts_dec: ∀T2,f. Decidable (∃T1. ⇧*[f] T1 ≘ T2).
 #T1 elim T1 -T1
 [ * [1,3: /3 width=2 by lifts_sort, lifts_gref, ex_intro, or_introl/ ]
 lemma is_lifts_dec: ∀T2,f. Decidable (∃T1. ⇧*[f] T1 ≘ T2).
 #T1 elim T1 -T1
 [ * [1,3: /3 width=2 by lifts_sort, lifts_gref, ex_intro, or_introl/ ]

-  #i2 #f elim (is_at_dec f i2) //
+  #i2 #f elim (is_pr_pat_dec f i2) //

   [ * /4 width=3 by lifts_lref, ex_intro, or_introl/
   | #H @or_intror *
     #X #HX elim (lifts_inv_lref2 … HX) -HX
   [ * /4 width=3 by lifts_lref, ex_intro, or_introl/
   | #H @or_intror *
     #X #HX elim (lifts_inv_lref2 … HX) -HX

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_basic.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_basic.ma
index d6dc490e05e6e8ed7118d56efa5c811d7a5a09d5..2eefef1fc7941a5dd389d2d1683df785544aab78 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_basic.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_basic.ma
@@ -24,13 +24,13 @@ interpretation "basic relocation (term)"
 (* Properties with basic relocation *****************************************)
 
 lemma lifts_lref_lt (m,n,i): i < m → ⇧[m,n] #i ≘ #i.
 (* Properties with basic relocation *****************************************)
 
 lemma lifts_lref_lt (m,n,i): i < m → ⇧[m,n] #i ≘ #i.

-/3 width=1 by lifts_lref, at_basic_lt/ qed.
+/3 width=1 by lifts_lref, pr_pat_basic_lt/ qed.

 
 lemma lifts_lref_ge (m,n,i): m ≤ i → ⇧[m,n] #i ≘ #(n+i).
 
 lemma lifts_lref_ge (m,n,i): m ≤ i → ⇧[m,n] #i ≘ #(n+i).

-/3 width=1 by lifts_lref, at_basic_ge/ qed.
+/3 width=1 by lifts_lref, pr_pat_basic_ge/ qed.

 
 lemma lifts_lref_ge_minus (m,n,i): n+m ≤ i → ⇧[m,n] #(i-n) ≘ #i.
 #m #n #i #Hi
 
 lemma lifts_lref_ge_minus (m,n,i): n+m ≤ i → ⇧[m,n] #(i-n) ≘ #i.
 #m #n #i #Hi

->(plus_minus_m_m i n) in ⊢ (???%);
-/3 width=2 by lifts_lref_ge, le_plus_to_minus_l, le_plus_b/
+>(nplus_minus_sn_refl_sn i n) in ⊢ (???%);
+/3 width=2 by lifts_lref_ge, nle_minus_dx_dx, nle_inv_plus_sn_dx/

 qed.
 qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_bind.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_bind.ma
index 925baceae8a68d329f2c9a5cf83d199800056a3b..3b45f26c32acb1e8dca3fb3913427dc61e8463f8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_bind.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_bind.ma
@@ -17,14 +17,14 @@ include "static_2/relocation/lifts.ma".
 
 (* GENERIC RELOCATION FOR BINDERS *******************************************)
 
 
 (* GENERIC RELOCATION FOR BINDERS *******************************************)
 

-definition liftsb: rtmap → relation bind ≝
+definition liftsb: pr_map → relation bind ≝

            λf. ext2 (lifts f).
 
 interpretation "generic relocation (binder for local environments)"
    'RLiftStar f I1 I2 = (liftsb f I1 I2).
 
 interpretation "uniform relocation (binder for local environments)"
            λf. ext2 (lifts f).
 
 interpretation "generic relocation (binder for local environments)"
    'RLiftStar f I1 I2 = (liftsb f I1 I2).
 
 interpretation "uniform relocation (binder for local environments)"

-   'RLift i I1 I2 = (liftsb (uni i) I1 I2).
+   'RLift i I1 I2 = (liftsb (pr_uni i) I1 I2).

 
 (* Basic_inversion lemmas **************************************************)
 
 
 (* Basic_inversion lemmas **************************************************)
 


@@ -48,7 +48,7 @@ lemma liftsb_inv_pair_dx (f):
 
 (* Basic properties *********************************************************)
 
 
 (* Basic properties *********************************************************)
 

-lemma liftsb_eq_repl_back: ∀I1,I2. eq_repl_back … (λf. ⇧*[f] I1 ≘ I2).
+lemma liftsb_eq_repl_back: ∀I1,I2. pr_eq_repl_back … (λf. ⇧*[f] I1 ≘ I2).

 #I1 #I2 #f1 * -I1 -I2 /3 width=3 by lifts_eq_repl_back, ext2_pair/
 qed-.
 
 #I1 #I2 #f1 * -I1 -I2 /3 width=3 by lifts_eq_repl_back, ext2_pair/
 qed-.
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma
index 3f78beb36186a076a15bf13b79ad588c68a8ec09..406436b9fb115c465e44de28936c73a85cc6be2c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma
@@ -21,7 +21,7 @@ include "static_2/relocation/lifts.ma".
 (* Basic_1: includes: lift_gen_lift *)
 (* Basic_2A1: includes: lift_div_le lift_div_be *)
 theorem lifts_div4: ∀f2,Tf,T. ⇧*[f2] Tf ≘ T → ∀g2,Tg. ⇧*[g2] Tg ≘ T →
 (* Basic_1: includes: lift_gen_lift *)
 (* Basic_2A1: includes: lift_div_le lift_div_be *)
 theorem lifts_div4: ∀f2,Tf,T. ⇧*[f2] Tf ≘ T → ∀g2,Tg. ⇧*[g2] Tg ≘ T →

-                    ∀f1,g1. H_at_div f2 g2 f1 g1 →
+                    ∀f1,g1. H_pr_pat_div f2 g2 f1 g1 →

                     ∃∃T0. ⇧*[f1] T0 ≘ Tf & ⇧*[g1] T0 ≘ Tg.
 #f2 #Tf #T #H elim H -f2 -Tf -T
 [ #f2 #s #g2 #Tg #H #f1 #g1 #_
                     ∃∃T0. ⇧*[f1] T0 ≘ Tf & ⇧*[g1] T0 ≘ Tg.
 #f2 #Tf #T #H elim H -f2 -Tf -T
 [ #f2 #s #g2 #Tg #H #f1 #g1 #_


@@ -36,7 +36,7 @@ theorem lifts_div4: ∀f2,Tf,T. ⇧*[f2] Tf ≘ T → ∀g2,Tg. ⇧*[g2] Tg ≘
 | #f2 #p #I #Vf #V #Tf #T #_ #_ #IHV #IHT #g2 #X #H #f1 #g1 #H0
   elim (lifts_inv_bind2 … H) -H #Vg #Tg #HVg #HTg #H destruct
   elim (IHV … HVg … H0) -IHV -HVg
 | #f2 #p #I #Vf #V #Tf #T #_ #_ #IHV #IHT #g2 #X #H #f1 #g1 #H0
   elim (lifts_inv_bind2 … H) -H #Vg #Tg #HVg #HTg #H destruct
   elim (IHV … HVg … H0) -IHV -HVg

-  elim (IHT … HTg) -IHT -HTg [ |*: /2 width=8 by at_div_pp/ ]
+  elim (IHT … HTg) -IHT -HTg [ |*: /2 width=8 by pr_pat_div_push_bi/ ]

   /3 width=5 by lifts_bind, ex2_intro/
 | #f2 #I #Vf #V #Tf #T #_ #_ #IHV #IHT #g2 #X #H #f1 #g1 #H0
   elim (lifts_inv_flat2 … H) -H #Vg #Tg #HVg #HTg #H destruct
   /3 width=5 by lifts_bind, ex2_intro/
 | #f2 #I #Vf #V #Tf #T #_ #_ #IHV #IHT #g2 #X #H #f1 #g1 #H0
   elim (lifts_inv_flat2 … H) -H #Vg #Tg #HVg #HTg #H destruct


@@ -49,14 +49,14 @@ qed-.
 lemma lifts_div4_one: ∀f,Tf,T. ⇧*[⫯f] Tf ≘ T →
                       ∀T1. ⇧[1] T1 ≘ T →
                       ∃∃T0. ⇧[1] T0 ≘ Tf & ⇧*[f] T0 ≘ T1.
 lemma lifts_div4_one: ∀f,Tf,T. ⇧*[⫯f] Tf ≘ T →
                       ∀T1. ⇧[1] T1 ≘ T →
                       ∃∃T0. ⇧[1] T0 ≘ Tf & ⇧*[f] T0 ≘ T1.

-/4 width=6 by lifts_div4, at_div_id_dx, at_div_pn/ qed-.
+/4 width=6 by lifts_div4, pr_pat_div_id_dx, pr_pat_div_push_next/ qed-.

 
 theorem lifts_div3: ∀f2,T,T2. ⇧*[f2] T2 ≘ T → ∀f,T1. ⇧*[f] T1 ≘ T →
                     ∀f1. f2 ⊚ f1 ≘ f → ⇧*[f1] T1 ≘ T2.
 #f2 #T #T2 #H elim H -f2 -T -T2
 [ #f2 #s #f #T1 #H >(lifts_inv_sort2 … H) -T1 //
 | #f2 #i2 #i #Hi2 #f #T1 #H #f1 #Ht21 elim (lifts_inv_lref2 … H) -H
 
 theorem lifts_div3: ∀f2,T,T2. ⇧*[f2] T2 ≘ T → ∀f,T1. ⇧*[f] T1 ≘ T →
                     ∀f1. f2 ⊚ f1 ≘ f → ⇧*[f1] T1 ≘ T2.
 #f2 #T #T2 #H elim H -f2 -T -T2
 [ #f2 #s #f #T1 #H >(lifts_inv_sort2 … H) -T1 //
 | #f2 #i2 #i #Hi2 #f #T1 #H #f1 #Ht21 elim (lifts_inv_lref2 … H) -H

-  #i1 #Hi1 #H destruct /3 width=6 by lifts_lref, after_fwd_at1/
+  #i1 #Hi1 #H destruct /3 width=6 by lifts_lref, pr_after_des_pat_dx/

 | #f2 #l #f #T1 #H >(lifts_inv_gref2 … H) -T1 //
 | #f2 #p #I #W2 #W #U2 #U #_ #_ #IHW #IHU #f #T1 #H
   elim (lifts_inv_bind2 … H) -H #W1 #U1 #HW1 #HU1 #H destruct
 | #f2 #l #f #T1 #H >(lifts_inv_gref2 … H) -T1 //
 | #f2 #p #I #W2 #W #U2 #U #_ #_ #IHW #IHU #f #T1 #H
   elim (lifts_inv_bind2 … H) -H #W1 #U1 #HW1 #HU1 #H destruct


@@ -75,7 +75,7 @@ theorem lifts_trans: ∀f1,T1,T. ⇧*[f1] T1 ≘ T → ∀f2,T2. ⇧*[f2] T ≘
 #f1 #T1 #T #H elim H -f1 -T1 -T
 [ #f1 #s #f2 #T2 #H >(lifts_inv_sort1 … H) -T2 //
 | #f1 #i1 #i #Hi1 #f2 #T2 #H #f #Ht21 elim (lifts_inv_lref1 … H) -H
 #f1 #T1 #T #H elim H -f1 -T1 -T
 [ #f1 #s #f2 #T2 #H >(lifts_inv_sort1 … H) -T2 //
 | #f1 #i1 #i #Hi1 #f2 #T2 #H #f #Ht21 elim (lifts_inv_lref1 … H) -H

-  #i2 #Hi2 #H destruct /3 width=6 by lifts_lref, after_fwd_at/
+  #i2 #Hi2 #H destruct /3 width=6 by lifts_lref, pr_after_des_pat/

 | #f1 #l #f2 #T2 #H >(lifts_inv_gref1 … H) -T2 //
 | #f1 #p #I #W1 #W #U1 #U #_ #_ #IHW #IHU #f2 #T2 #H
   elim (lifts_inv_bind1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct
 | #f1 #l #f2 #T2 #H >(lifts_inv_gref1 … H) -T2 //
 | #f1 #p #I #W1 #W #U1 #U #_ #_ #IHW #IHU #f2 #T2 #H
   elim (lifts_inv_bind1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct


@@ -89,7 +89,7 @@ qed-.
 lemma lifts_trans4_one (f) (T1) (T2):
                        ∀T. ⇧[1]T1 ≘ T → ⇧*[⫯f]T ≘ T2 →
                        ∃∃T0. ⇧*[f]T1 ≘ T0 & ⇧[1]T0 ≘ T2.
 lemma lifts_trans4_one (f) (T1) (T2):
                        ∀T. ⇧[1]T1 ≘ T → ⇧*[⫯f]T ≘ T2 →
                        ∃∃T0. ⇧*[f]T1 ≘ T0 & ⇧[1]T0 ≘ T2.

-/4 width=6 by lifts_trans, lifts_split_trans, after_uni_one_dx/ qed-.
+/4 width=6 by lifts_trans, lifts_split_trans, pr_after_push_unit/ qed-.

 
 (* Basic_2A1: includes: lift_conf_O1 lift_conf_be *)
 theorem lifts_conf: ∀f1,T,T1. ⇧*[f1] T ≘ T1 → ∀f,T2. ⇧*[f] T ≘ T2 →
 
 (* Basic_2A1: includes: lift_conf_O1 lift_conf_be *)
 theorem lifts_conf: ∀f1,T,T1. ⇧*[f1] T ≘ T1 → ∀f,T2. ⇧*[f] T ≘ T2 →


@@ -97,7 +97,7 @@ theorem lifts_conf: ∀f1,T,T1. ⇧*[f1] T ≘ T1 → ∀f,T2. ⇧*[f] T ≘ T2
 #f1 #T #T1 #H elim H -f1 -T -T1
 [ #f1 #s #f #T2 #H >(lifts_inv_sort1 … H) -T2 //
 | #f1 #i #i1 #Hi1 #f #T2 #H #f2 #Ht21 elim (lifts_inv_lref1 … H) -H
 #f1 #T #T1 #H elim H -f1 -T -T1
 [ #f1 #s #f #T2 #H >(lifts_inv_sort1 … H) -T2 //
 | #f1 #i #i1 #Hi1 #f #T2 #H #f2 #Ht21 elim (lifts_inv_lref1 … H) -H

-  #i2 #Hi2 #H destruct /3 width=6 by lifts_lref, after_fwd_at2/
+  #i2 #Hi2 #H destruct /3 width=6 by lifts_lref, pr_after_des_pat_sn/

 | #f1 #l #f #T2 #H >(lifts_inv_gref1 … H) -T2 //
 | #f1 #p #I #W #W1 #U #U1 #_ #_ #IHW #IHU #f #T2 #H
   elim (lifts_inv_bind1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct
 | #f1 #l #f #T2 #H >(lifts_inv_gref1 … H) -T2 //
 | #f1 #p #I #W #W1 #U #U1 #_ #_ #IHW #IHU #f #T2 #H
   elim (lifts_inv_bind1 … H) -H #W2 #U2 #HW2 #HU2 #H destruct


@@ -112,13 +112,13 @@ qed-.
 
 (* Basic_2A1: includes: lift_inj *)
 lemma lifts_inj: ∀f. is_inj2 … (lifts f).
 
 (* Basic_2A1: includes: lift_inj *)
 lemma lifts_inj: ∀f. is_inj2 … (lifts f).

-#f #T1 #U #H1 #T2 #H2 lapply (after_isid_dx 𝐢  … f)
+#f #T1 #U #H1 #T2 #H2 lapply (pr_after_isi_dx 𝐢  … f)

 /3 width=6 by lifts_div3, lifts_fwd_isid/
 qed-.
 
 (* Basic_2A1: includes: lift_mono *)
 lemma lifts_mono: ∀f,T. is_mono … (lifts f T).
 /3 width=6 by lifts_div3, lifts_fwd_isid/
 qed-.
 
 (* Basic_2A1: includes: lift_mono *)
 lemma lifts_mono: ∀f,T. is_mono … (lifts f T).

-#f #T #U1 #H1 #U2 #H2 lapply (after_isid_sn 𝐢  … f)
+#f #T #U1 #H1 #U2 #H2 lapply (pr_after_isi_sn 𝐢  … f)

 /3 width=6 by lifts_conf, lifts_fwd_isid/
 qed-.
 
 /3 width=6 by lifts_conf, lifts_fwd_isid/
 qed-.
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts_bind.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts_bind.ma
index 0e18b44fd690562e4b1a31736459571f88d2dd3c..c1c66d978db0c10a95436aff098f401334771da8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts_bind.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts_bind.ma
@@ -43,11 +43,11 @@ qed-.
 (* Advanced proprerties *****************************************************)
 
 lemma liftsb_inj: ∀f. is_inj2 … (liftsb f).
 (* Advanced proprerties *****************************************************)
 
 lemma liftsb_inj: ∀f. is_inj2 … (liftsb f).

-#f #T1 #U #H1 #T2 #H2 lapply (after_isid_dx 𝐢  … f)
+#f #T1 #U #H1 #T2 #H2 lapply (pr_after_isi_dx 𝐢  … f)

 /3 width=6 by liftsb_div3, liftsb_fwd_isid/
 qed-.
 
 lemma liftsb_mono: ∀f,T. is_mono … (liftsb f T).
 /3 width=6 by liftsb_div3, liftsb_fwd_isid/
 qed-.
 
 lemma liftsb_mono: ∀f,T. is_mono … (liftsb f T).

-#f #T #U1 #H1 #U2 #H2 lapply (after_isid_sn 𝐢  … f)
+#f #T #U1 #H1 #U2 #H2 lapply (pr_after_isi_sn 𝐢  … f)

 /3 width=6 by liftsb_conf, liftsb_fwd_isid/
 qed-.
 /3 width=6 by liftsb_conf, liftsb_fwd_isid/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqo.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqo.ma
index 0a6831c7211bc81078c195c651cc6adbb9842102..b45a9e7e8d80f9b74f34293b2a0dc087405013c3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqo.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqo.ma
@@ -59,7 +59,7 @@ lemma teqo_inv_lifts_bi: deliftable2_bi teqo.
 | #j #f #X1 #H1 #X2 #H2
   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
   elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct
 | #j #f #X1 #H1 #X2 #H2
   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
   elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct

-  <(at_inj … Hj2 … Hj1) -j -f -i1
+  <(pr_pat_inj … Hj2 … Hj1) -j -f -i1

   /1 width=1 by teqo_lref/
 | #l #f #X1 #H1 #X2 #H2
   >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2
   /1 width=1 by teqo_lref/
 | #l #f #X1 #H1 #X2 #H2
   >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqw.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqw.ma
index 532d0b2364ee4ebdf6f9559a0a22641c1ffd3f5b..d03e0ab401c119b636baa2c4bf5ac703908429d6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqw.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqw.ma
@@ -69,7 +69,7 @@ lemma teqw_inv_lifts_bi: deliftable2_bi teqw.
 | #j #f #X1 #H1 #X2 #H2
   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
   elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct
 | #j #f #X1 #H1 #X2 #H2
   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
   elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct

-  <(at_inj … Hj2 … Hj1) -j -f -i1
+  <(pr_pat_inj … Hj2 … Hj1) -j -f -i1

   /1 width=1 by teqw_lref/
 | #l #f #X1 #H1 #X2 #H2
   >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2
   /1 width=1 by teqw_lref/
 | #l #f #X1 #H1 #X2 #H2
   >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2


@@ -98,7 +98,7 @@ qed-.
 
 lemma teqw_inv_abbr_pos_x_lifts_y_y (T) (f):
       ∀V,U. +ⓓV.U ≃ T → ⇧*[f]T ≘ U → ⊥.
 
 lemma teqw_inv_abbr_pos_x_lifts_y_y (T) (f):
       ∀V,U. +ⓓV.U ≃ T → ⇧*[f]T ≘ U → ⊥.

-@(f_ind … tw) #n #IH #T #Hn #f #V #U #H1 #H2 destruct
+@(wf1_ind_nlt … tw) #n #IH #T #Hn #f #V #U #H1 #H2 destruct

 elim (teqw_inv_abbr_pos_sn … H1) -H1 #X1 #X2 #HX2 #H destruct -V
 elim (lifts_inv_bind1 … H2) -H2 #Y1 #Y2 #_ #HXY2 #H destruct
 /2 width=7 by/
 elim (teqw_inv_abbr_pos_sn … H1) -H1 #X1 #X2 #HX2 #H destruct -V
 elim (lifts_inv_bind1 … H2) -H2 #Y1 #Y2 #_ #HXY2 #H destruct
 /2 width=7 by/

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma
index a5310b63dce69cde3da9653a854b652b927ea979..d0cd506bc8f00549b6cc2aa7cb0177cc0876b149 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma
@@ -29,7 +29,7 @@ interpretation "generic relocation (term vector)"
    'RLiftStar f T1s T2s = (liftsv f T1s T2s).
 
 interpretation "uniform relocation (term vector)"
    'RLiftStar f T1s T2s = (liftsv f T1s T2s).
 
 interpretation "uniform relocation (term vector)"

-   'RLift i T1s T2s = (liftsv (uni i) T1s T2s).
+   'RLift i T1s T2s = (liftsv (pr_uni i) T1s T2s).

 
 (* Basic inversion lemmas ***************************************************)
 
 
 (* Basic inversion lemmas ***************************************************)
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma
index 128cd29749b7cf46787ae7fb6dbf5da5665d9909..224102f015f761e0547d4d074742d2518495dba7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma
@@ -19,7 +19,7 @@ include "static_2/relocation/sex.ma".
 (* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************)
 
 (* Basic_2A1: includes: lreq_atom lreq_zero lreq_pair lreq_succ *)
 (* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************)
 
 (* Basic_2A1: includes: lreq_atom lreq_zero lreq_pair lreq_succ *)

-definition seq: relation3 rtmap lenv lenv ≝
+definition seq: relation3 pr_map lenv lenv ≝

            sex ceq_ext cfull.
 
 interpretation
            sex ceq_ext cfull.
 
 interpretation


@@ -29,11 +29,11 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma seq_eq_repl_back:
 (* Basic properties *********************************************************)
 
 lemma seq_eq_repl_back:

-      ∀L1,L2. eq_repl_back … (λf. L1 ≡[f] L2).
+      ∀L1,L2. pr_eq_repl_back … (λf. L1 ≡[f] L2).

 /2 width=3 by sex_eq_repl_back/ qed-.
 
 lemma seq_eq_repl_fwd:
 /2 width=3 by sex_eq_repl_back/ qed-.
 
 lemma seq_eq_repl_fwd:

-      ∀L1,L2. eq_repl_fwd … (λf. L1 ≡[f] L2).
+      ∀L1,L2. pr_eq_repl_fwd … (λf. L1 ≡[f] L2).

 /2 width=3 by sex_eq_repl_fwd/ qed-.
 
 lemma sle_seq_trans:
 /2 width=3 by sex_eq_repl_fwd/ qed-.
 
 lemma sle_seq_trans:

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/sex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/sex.ma
index 2a6946fcab7ac6441c2109b34fbdfa422e9b625c..47912ace088d171406a07842e3ed6c36bcb6cb69 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/sex.ma
@@ -19,7 +19,7 @@ include "static_2/syntax/lenv.ma".
 
 (* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
 
 
 (* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
 

-inductive sex (RN,RP:relation3 lenv bind bind): rtmap → relation lenv ≝
+inductive sex (RN,RP:relation3 lenv bind bind): pr_map → relation lenv ≝

 | sex_atom: ∀f. sex RN RP f (⋆) (⋆)
 | sex_next: ∀f,I1,I2,L1,L2.
             sex RN RP f L1 L2 → RN L1 I1 I2 →
 | sex_atom: ∀f. sex RN RP f (⋆) (⋆)
 | sex_next: ∀f,I1,I2,L1,L2.
             sex RN RP f L1 L2 → RN L1 I1 I2 →


@@ -37,7 +37,7 @@ definition R_pw_transitive_sex:
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →

-           relation3 rtmap lenv bind ≝
+           relation3 pr_map lenv bind ≝

            λR1,R2,R3,RN,RP,f,L1,I1.
            ∀I. R1 L1 I1 I → ∀L2. L1 ⪤[RN,RP,f] L2 →
            ∀I2. R2 L2 I I2 → R3 L1 I1 I2.
            λR1,R2,R3,RN,RP,f,L1,I1.
            ∀I. R1 L1 I1 I → ∀L2. L1 ⪤[RN,RP,f] L2 →
            ∀I2. R2 L2 I I2 → R3 L1 I1 I2.


@@ -45,7 +45,7 @@ definition R_pw_transitive_sex:
 definition R_pw_confluent1_sex:
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
 definition R_pw_confluent1_sex:
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →

-           relation3 rtmap lenv bind ≝
+           relation3 pr_map lenv bind ≝

            λR1,R2,RN,RP,f,L1,I1.
            ∀I2. R1 L1 I1 I2 → ∀L2. L1 ⪤[RN,RP,f] L2 → R2 L2 I1 I2.
 
            λR1,R2,RN,RP,f,L1,I1.
            ∀I2. R1 L1 I1 I2 → ∀L2. L1 ⪤[RN,RP,f] L2 → R2 L2 I1 I2.
 


@@ -53,7 +53,7 @@ definition R_pw_confluent2_sex:
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →

-           relation3 rtmap lenv bind ≝
+           relation3 pr_map lenv bind ≝

            λR1,R2,RN1,RP1,RN2,RP2,f,L0,I0.
            ∀I1. R1 L0 I0 I1 → ∀I2. R2 L0 I0 I2 →
            ∀L1. L0 ⪤[RN1,RP1,f] L1 → ∀L2. L0 ⪤[RN2,RP2,f] L2 →
            λR1,R2,RN1,RP1,RN2,RP2,f,L0,I0.
            ∀I1. R1 L0 I0 I1 → ∀I2. R2 L0 I0 I2 →
            ∀L1. L0 ⪤[RN1,RP1,f] L1 → ∀L2. L0 ⪤[RN2,RP2,f] L2 →


@@ -63,7 +63,7 @@ definition R_pw_replace3_sex:
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →
            relation3 lenv bind bind → relation3 lenv bind bind →

-           relation3 rtmap lenv bind ≝
+           relation3 pr_map lenv bind ≝

            λR1,R2,RN1,RP1,RN2,RP2,f,L0,I0.
            ∀I1. R1 L0 I0 I1 → ∀I2. R2 L0 I0 I2 →
            ∀L1. L0 ⪤[RN1,RP1,f] L1 → ∀L2. L0 ⪤[RN2,RP2,f] L2 →
            λR1,R2,RN1,RP1,RN2,RP2,f,L0,I0.
            ∀I1. R1 L0 I0 I1 → ∀I2. R2 L0 I0 I2 →
            ∀L1. L0 ⪤[RN1,RP1,f] L1 → ∀L2. L0 ⪤[RN2,RP2,f] L2 →


@@ -87,9 +87,9 @@ fact sex_inv_next1_aux (RN) (RP):
      ∃∃J2,K2. K1 ⪤[RN,RP,g] K2 & RN K1 J1 J2 & Y = K2.ⓘ[J2].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J1 #K1 #H destruct
      ∃∃J2,K2. K1 ⪤[RN,RP,g] K2 & RN K1 J1 J2 & Y = K2.ⓘ[J2].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J1 #K1 #H destruct

-| #f #I1 #I2 #L1 #L2 #HL #HI #g #J1 #K1 #H1 #H2 <(injective_next … H2) -g destruct
+| #f #I1 #I2 #L1 #L2 #HL #HI #g #J1 #K1 #H1 #H2 <(eq_inv_pr_next_bi … H2) -g destruct

   /2 width=5 by ex3_2_intro/
   /2 width=5 by ex3_2_intro/

-| #f #I1 #I2 #L1 #L2 #_ #_ #g #J1 #K1 #_ #H elim (discr_push_next … H)
+| #f #I1 #I2 #L1 #L2 #_ #_ #g #J1 #K1 #_ #H elim (eq_inv_pr_push_next … H)

 ]
 qed-.
 
 ]
 qed-.
 


@@ -104,8 +104,8 @@ fact sex_inv_push1_aux (RN) (RP):
      ∃∃J2,K2. K1 ⪤[RN,RP,g] K2 & RP K1 J1 J2 & Y = K2.ⓘ[J2].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J1 #K1 #H destruct
      ∃∃J2,K2. K1 ⪤[RN,RP,g] K2 & RP K1 J1 J2 & Y = K2.ⓘ[J2].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J1 #K1 #H destruct

-| #f #I1 #I2 #L1 #L2 #_ #_ #g #J1 #K1 #_ #H elim (discr_next_push … H)
-| #f #I1 #I2 #L1 #L2 #HL #HI #g #J1 #K1 #H1 #H2 <(injective_push … H2) -g destruct
+| #f #I1 #I2 #L1 #L2 #_ #_ #g #J1 #K1 #_ #H elim (eq_inv_pr_next_push … H)
+| #f #I1 #I2 #L1 #L2 #HL #HI #g #J1 #K1 #H1 #H2 <(eq_inv_pr_push_bi … H2) -g destruct

   /2 width=5 by ex3_2_intro/
 ]
 qed-.
   /2 width=5 by ex3_2_intro/
 ]
 qed-.


@@ -131,9 +131,9 @@ fact sex_inv_next2_aux (RN) (RP):
      ∃∃J1,K1. K1 ⪤[RN,RP,g] K2 & RN K1 J1 J2 & X = K1.ⓘ[J1].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J2 #K2 #H destruct
      ∃∃J1,K1. K1 ⪤[RN,RP,g] K2 & RN K1 J1 J2 & X = K1.ⓘ[J1].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J2 #K2 #H destruct

-| #f #I1 #I2 #L1 #L2 #HL #HI #g #J2 #K2 #H1 #H2 <(injective_next … H2) -g destruct
+| #f #I1 #I2 #L1 #L2 #HL #HI #g #J2 #K2 #H1 #H2 <(eq_inv_pr_next_bi … H2) -g destruct

   /2 width=5 by ex3_2_intro/
   /2 width=5 by ex3_2_intro/

-| #f #I1 #I2 #L1 #L2 #_ #_ #g #J2 #K2 #_ #H elim (discr_push_next … H)
+| #f #I1 #I2 #L1 #L2 #_ #_ #g #J2 #K2 #_ #H elim (eq_inv_pr_push_next … H)

 ]
 qed-.
 
 ]
 qed-.
 


@@ -148,8 +148,8 @@ fact sex_inv_push2_aux (RN) (RP):
      ∃∃J1,K1. K1 ⪤[RN,RP,g] K2 & RP K1 J1 J2 & X = K1.ⓘ[J1].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #J2 #K2 #g #H destruct
      ∃∃J1,K1. K1 ⪤[RN,RP,g] K2 & RP K1 J1 J2 & X = K1.ⓘ[J1].
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #J2 #K2 #g #H destruct

-| #f #I1 #I2 #L1 #L2 #_ #_ #g #J2 #K2 #_ #H elim (discr_next_push … H)
-| #f #I1 #I2 #L1 #L2 #HL #HI #g #J2 #K2 #H1 #H2 <(injective_push … H2) -g destruct
+| #f #I1 #I2 #L1 #L2 #_ #_ #g #J2 #K2 #_ #H elim (eq_inv_pr_next_push … H)
+| #f #I1 #I2 #L1 #L2 #HL #HI #g #J2 #K2 #H1 #H2 <(eq_inv_pr_push_bi … H2) -g destruct

   /2 width=5 by ex3_2_intro/
 ]
 qed-.
   /2 width=5 by ex3_2_intro/
 ]
 qed-.


@@ -180,7 +180,7 @@ lemma sex_inv_tl (RN) (RP):
       ∀f,I1,I2,L1,L2. L1 ⪤[RN,RP,⫰f] L2 →
       RN L1 I1 I2 → RP L1 I1 I2 →
       L1.ⓘ[I1] ⪤[RN,RP,f] L2.ⓘ[I2].
       ∀f,I1,I2,L1,L2. L1 ⪤[RN,RP,⫰f] L2 →
       RN L1 I1 I2 → RP L1 I1 I2 →
       L1.ⓘ[I1] ⪤[RN,RP,f] L2.ⓘ[I2].

-#RN #RP #f #I1 #I2 #L2 #L2 elim (pn_split f) *
+#RN #RP #f #I1 #I2 #L2 #L2 elim (pr_map_split_tl f) *

 /2 width=1 by sex_next, sex_push/
 qed-.
 
 /2 width=1 by sex_next, sex_push/
 qed-.
 


@@ -190,14 +190,14 @@ lemma sex_fwd_bind (RN) (RP):
       ∀f,I1,I2,L1,L2.
       L1.ⓘ[I1] ⪤[RN,RP,f] L2.ⓘ[I2] → L1 ⪤[RN,RP,⫰f] L2.
 #RN #RP #f #I1 #I2 #L1 #L2 #Hf
       ∀f,I1,I2,L1,L2.
       L1.ⓘ[I1] ⪤[RN,RP,f] L2.ⓘ[I2] → L1 ⪤[RN,RP,⫰f] L2.
 #RN #RP #f #I1 #I2 #L1 #L2 #Hf

-elim (pn_split f) * #g #H destruct
+elim (pr_map_split_tl f) * #g #H destruct

 [ elim (sex_inv_push … Hf) | elim (sex_inv_next … Hf) ] -Hf //
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma sex_eq_repl_back (RN) (RP):
 [ elim (sex_inv_push … Hf) | elim (sex_inv_next … Hf) ] -Hf //
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma sex_eq_repl_back (RN) (RP):

-      ∀L1,L2. eq_repl_back … (λf. L1 ⪤[RN,RP,f] L2).
+      ∀L1,L2. pr_eq_repl_back … (λf. L1 ⪤[RN,RP,f] L2).

 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI #IH #f2 #H
 [ elim (eq_inv_nx … H) -H /3 width=3 by sex_next/
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI #IH #f2 #H
 [ elim (eq_inv_nx … H) -H /3 width=3 by sex_next/


@@ -206,15 +206,15 @@ lemma sex_eq_repl_back (RN) (RP):
 qed-.
 
 lemma sex_eq_repl_fwd (RN) (RP):
 qed-.
 
 lemma sex_eq_repl_fwd (RN) (RP):

-      ∀L1,L2. eq_repl_fwd … (λf. L1 ⪤[RN,RP,f] L2).
-#RN #RP #L1 #L2 @eq_repl_sym /2 width=3 by sex_eq_repl_back/ (**) (* full auto fails *)
+      ∀L1,L2. pr_eq_repl_fwd … (λf. L1 ⪤[RN,RP,f] L2).
+#RN #RP #L1 #L2 @pr_eq_repl_sym /2 width=3 by sex_eq_repl_back/ (**) (* full auto fails *)

 qed-.
 
 lemma sex_refl (RN) (RP):
       c_reflexive … RN → c_reflexive … RP →
       ∀f.reflexive … (sex RN RP f).
 #RN #RP #HRN #HRP #f #L generalize in match f; -f elim L -L //
 qed-.
 
 lemma sex_refl (RN) (RP):
       c_reflexive … RN → c_reflexive … RP →
       ∀f.reflexive … (sex RN RP f).
 #RN #RP #HRN #HRP #f #L generalize in match f; -f elim L -L //

-#L #I #IH #f elim (pn_split f) *
+#L #I #IH #f elim (pr_map_split_tl f) *

 #g #H destruct /2 width=1 by sex_next, sex_push/
 qed.
 
 #g #H destruct /2 width=1 by sex_next, sex_push/
 qed.
 


@@ -246,8 +246,8 @@ lemma sex_co_isid (RN1) (RP1) (RN2) (RP2):
       L1 ⪤[RN2,RP2,f] L2.
 #RN1 #RP1 #RN2 #RP2 #HR #f #L1 #L2 #H elim H -f -L1 -L2 //
 #f #I1 #I2 #K1 #K2 #_ #HI12 #IH #H
       L1 ⪤[RN2,RP2,f] L2.
 #RN1 #RP1 #RN2 #RP2 #HR #f #L1 #L2 #H elim H -f -L1 -L2 //
 #f #I1 #I2 #K1 #K2 #_ #HI12 #IH #H

-[ elim (isid_inv_next … H) -H //
-| /4 width=3 by sex_push, isid_inv_push/
+[ elim (pr_isi_inv_next … H) -H //
+| /4 width=3 by sex_push, pr_isi_inv_push/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -257,9 +257,9 @@ lemma sex_sdj (RN) (RP):
       ∀f2. f1 ∥ f2 → L1 ⪤[RP,RN,f2] L2.
 #RN #RP #HR #f1 #L1 #L2 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H12
       ∀f2. f1 ∥ f2 → L1 ⪤[RP,RN,f2] L2.
 #RN #RP #HR #f1 #L1 #L2 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H12

-[ elim (sdj_inv_nx … H12) -H12 [2,3: // ]
+[ elim (pr_sdj_inv_next_sn … H12) -H12 [2,3: // ]

   #g2 #H #H2 destruct /3 width=1 by sex_push/
   #g2 #H #H2 destruct /3 width=1 by sex_push/

-| elim (sdj_inv_px … H12) -H12 [2,4: // ] *
+| elim (pr_sdj_inv_push_sn … H12) -H12 [2,4: // ] *

   #g2 #H #H2 destruct /3 width=1 by sex_next, sex_push/
 ]
 qed-.
   #g2 #H #H2 destruct /3 width=1 by sex_next, sex_push/
 ]
 qed-.


@@ -270,10 +270,10 @@ lemma sle_sex_trans (RN) (RP):
       ∀f1. f1 ⊆ f2 → L1 ⪤[RN,RP,f1] L2.
 #RN #RP #HR #f2 #L1 #L2 #H elim H -f2 -L1 -L2 //
 #f2 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f1 #H12
       ∀f1. f1 ⊆ f2 → L1 ⪤[RN,RP,f1] L2.
 #RN #RP #HR #f2 #L1 #L2 #H elim H -f2 -L1 -L2 //
 #f2 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f1 #H12

-[ elim (pn_split f1) * ]
-[ /4 width=5 by sex_push, sle_inv_pn/
-| /4 width=5 by sex_next, sle_inv_nn/
-| elim (sle_inv_xp … H12) -H12 [2,3: // ]
+[ elim (pr_map_split_tl f1) * ]
+[ /4 width=5 by sex_push, pr_sle_inv_push_next/
+| /4 width=5 by sex_next, pr_sle_inv_next_bi/
+| elim (pr_sle_inv_push_dx … H12) -H12 [2,3: // ]

   #g1 #H #H1 destruct /3 width=5 by sex_push/
 ]
 qed-.
   #g1 #H #H1 destruct /3 width=5 by sex_push/
 ]
 qed-.


@@ -284,10 +284,10 @@ lemma sle_sex_conf (RN) (RP):
       ∀f2. f1 ⊆ f2 → L1 ⪤[RN,RP,f2] L2.
 #RN #RP #HR #f1 #L1 #L2 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H12
       ∀f2. f1 ⊆ f2 → L1 ⪤[RN,RP,f2] L2.
 #RN #RP #HR #f1 #L1 #L2 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H12

-[2: elim (pn_split f2) * ]
-[ /4 width=5 by sex_push, sle_inv_pp/
-| /4 width=5 by sex_next, sle_inv_pn/
-| elim (sle_inv_nx … H12) -H12 [2,3: // ]
+[2: elim (pr_map_split_tl f2) * ]
+[ /4 width=5 by sex_push, pr_sle_inv_push_bi/
+| /4 width=5 by sex_next, pr_sle_inv_push_next/
+| elim (pr_sle_inv_next_sn … H12) -H12 [2,3: // ]

   #g2 #H #H2 destruct /3 width=5 by sex_next/
 ]
 qed-.
   #g2 #H #H2 destruct /3 width=5 by sex_next/
 ]
 qed-.


@@ -299,9 +299,9 @@ lemma sex_sle_split_sn (R1) (R2) (RP):
 #R1 #R2 #RP #HR1 #HR2 #f #L1 #L2 #H elim H -f -L1 -L2
 [ /2 width=3 by sex_atom, ex2_intro/ ]
 #f #I1 #I2 #L1 #L2 #_ #HI12 #IH #y #H
 #R1 #R2 #RP #HR1 #HR2 #f #L1 #L2 #H elim H -f -L1 -L2
 [ /2 width=3 by sex_atom, ex2_intro/ ]
 #f #I1 #I2 #L1 #L2 #_ #HI12 #IH #y #H

-[ elim (sle_inv_nx … H ??) -H [ |*: // ] #g #Hfg #H destruct
+[ elim (pr_sle_inv_next_sn … H ??) -H [ |*: // ] #g #Hfg #H destruct

   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, ex2_intro/
   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, ex2_intro/

-| elim (sle_inv_px … H ??) -H [1,3: * |*: // ] #g #Hfg #H destruct
+| elim (pr_sle_inv_push_sn … H ??) -H [1,3: * |*: // ] #g #Hfg #H destruct

   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, sex_push, ex2_intro/
 ]
 qed-.
   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, sex_push, ex2_intro/
 ]
 qed-.


@@ -313,9 +313,9 @@ lemma sex_sdj_split_sn (R1) (R2) (RP):
 #R1 #R2 #RP #HR1 #HR2 #f #L1 #L2 #H elim H -f -L1 -L2
 [ /2 width=3 by sex_atom, ex2_intro/ ]
 #f #I1 #I2 #L1 #L2 #_ #HI12 #IH #y #H
 #R1 #R2 #RP #HR1 #HR2 #f #L1 #L2 #H elim H -f -L1 -L2
 [ /2 width=3 by sex_atom, ex2_intro/ ]
 #f #I1 #I2 #L1 #L2 #_ #HI12 #IH #y #H

-[ elim (sdj_inv_nx … H ??) -H [ |*: // ] #g #Hfg #H destruct
+[ elim (pr_sdj_inv_next_sn … H ??) -H [ |*: // ] #g #Hfg #H destruct

   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, sex_push, ex2_intro/
   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, sex_push, ex2_intro/

-| elim (sdj_inv_px … H ??) -H [1,3: * |*: // ] #g #Hfg #H destruct
+| elim (pr_sdj_inv_push_sn … H ??) -H [1,3: * |*: // ] #g #Hfg #H destruct

   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, sex_push, ex2_intro/
 ]
 qed-.
   elim (IH … Hfg) -IH -Hfg /3 width=5 by sex_next, sex_push, ex2_intro/
 ]
 qed-.


@@ -332,7 +332,7 @@ lemma sex_dec (RN) (RP):
   lapply (sex_inv_atom2 … H) -H #H destruct
 | #L2 #I2 #f elim (IH L2 (⫰f)) -IH #HL12
   [2: /4 width=3 by sex_fwd_bind, or_intror/ ]
   lapply (sex_inv_atom2 … H) -H #H destruct
 | #L2 #I2 #f elim (IH L2 (⫰f)) -IH #HL12
   [2: /4 width=3 by sex_fwd_bind, or_intror/ ]

-  elim (pn_split f) * #g #H destruct
+  elim (pr_map_split_tl f) * #g #H destruct

   [ elim (HRP L1 I1 I2) | elim (HRN L1 I1 I2) ] -HRP -HRN #HV12
   [1,3: /3 width=1 by sex_push, sex_next, or_introl/ ]
   @or_intror #H
   [ elim (HRP L1 I1 I2) | elim (HRN L1 I1 I2) ] -HRP -HRN #HV12
   [1,3: /3 width=1 by sex_push, sex_next, or_introl/ ]
   @or_intror #H

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_length.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_length.ma
index 4f2157be259f28e85d6335de9cd5f66bb7b72741..c99c786c68d41be159f2a31c71b5b041e005f3de 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_length.ma
@@ -31,7 +31,7 @@ lemma sex_length_cfull: ∀L1,L2. |L1| = |L2| → ∀f. L1 ⪤[cfull,cfull,f] L2
 [ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
 | #L1 #I1 #IH #Y2 #H #f
   elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct
 [ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
 | #L1 #I1 #IH #Y2 #H #f
   elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct

-  elim (pn_split f) * #g #H destruct /3 width=1 by sex_next, sex_push/
+  elim (pr_map_split_tl f) * #g #H destruct /3 width=1 by sex_next, sex_push/

 ]
 qed.
 
 ]
 qed.
 


@@ -41,6 +41,6 @@ lemma sex_length_isid: ∀R,L1,L2. |L1| = |L2| →
 [ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
 | #L1 #I1 #IH #Y2 #H #f #Hf
   elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct
 [ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
 | #L1 #I1 #IH #Y2 #H #f #Hf
   elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct

-  elim (isid_inv_gen … Hf) -Hf #g #Hg #H destruct /3 width=1 by sex_push/
+  elim (pr_isi_inv_gen … Hf) -Hf #g #Hg #H destruct /3 width=1 by sex_push/

 ]
 qed.
 ]
 qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_sex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_sex.ma
index a92cf28c1ead5f1a28274416a987a6ad6917e5f6..19078cfbe6a5ad84435abbd6ff9e3da79768d65b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_sex.ma
@@ -31,7 +31,7 @@ theorem sex_trans_gen (RN1) (RP1) (RN2) (RP2) (RN) (RP):
   lapply (sex_inv_atom1 … H1) -H1 #H destruct
   lapply (sex_inv_atom1 … H2) -H2 #H destruct
   /2 width=1 by sex_atom/
   lapply (sex_inv_atom1 … H1) -H1 #H destruct
   lapply (sex_inv_atom1 … H2) -H2 #H destruct
   /2 width=1 by sex_atom/

-| #K1 #I1 #IH #f elim (pn_split f) * #g #H destruct
+| #K1 #I1 #IH #f elim (pr_map_split_tl f) * #g #H destruct

   #HN #HP #L0 #H1 #L2 #H2
   [ elim (sex_inv_push1 … H1) -H1 #I0 #K0 #HK10 #HI10 #H destruct
     elim (sex_inv_push1 … H2) -H2 #I2 #K2 #HK02 #HI02 #H destruct
   #HN #HP #L0 #H1 #L2 #H2
   [ elim (sex_inv_push1 … H1) -H1 #I0 #K0 #HK10 #HI10 #H destruct
     elim (sex_inv_push1 … H2) -H2 #I2 #K2 #HK02 #HI02 #H destruct


@@ -57,7 +57,7 @@ theorem sex_trans_id_cfull (R1) (R2) (R3):
 #R1 #R2 #R3 #L1 #L #f #H elim H -L1 -L -f
 [ #f #Hf #L2 #H >(sex_inv_atom1 … H) -L2 // ]
 #f #I1 #I #K1 #K #HK1 #_ #IH #Hf #L2 #H
 #R1 #R2 #R3 #L1 #L #f #H elim H -L1 -L -f
 [ #f #Hf #L2 #H >(sex_inv_atom1 … H) -L2 // ]
 #f #I1 #I #K1 #K #HK1 #_ #IH #Hf #L2 #H

-[ elim (isid_inv_next … Hf) | lapply (isid_inv_push … Hf ??) ] -Hf [5: |*: // ] #Hf
+[ elim (pr_isi_inv_next … Hf) | lapply (pr_isi_inv_push … Hf ??) ] -Hf [5: |*: // ] #Hf

 elim (sex_inv_push1 … H) -H #I2 #K2 #HK2 #_ #H destruct
 /3 width=1 by sex_push/
 qed-.
 elim (sex_inv_push1 … H) -H #I2 #K2 #HK2 #_ #H destruct
 /3 width=1 by sex_push/
 qed-.


@@ -70,7 +70,7 @@ theorem sex_conf (RN1) (RP1) (RN2) (RP2):
 #RN1 #RP1 #RN2 #RP2 #L elim L -L
 [ #f #_ #_ #L1 #H1 #L2 #H2 >(sex_inv_atom1 … H1) >(sex_inv_atom1 … H2) -H2 -H1
   /2 width=3 by sex_atom, ex2_intro/
 #RN1 #RP1 #RN2 #RP2 #L elim L -L
 [ #f #_ #_ #L1 #H1 #L2 #H2 >(sex_inv_atom1 … H1) >(sex_inv_atom1 … H2) -H2 -H1
   /2 width=3 by sex_atom, ex2_intro/

-| #L #I0 #IH #f elim (pn_split f) * #g #H destruct
+| #L #I0 #IH #f elim (pr_map_split_tl f) * #g #H destruct

   #HN #HP #Y1 #H1 #Y2 #H2
   [ elim (sex_inv_push1 … H1) -H1 #I1 #L1 #HL1 #HI01 #H destruct
     elim (sex_inv_push1 … H2) -H2 #I2 #L2 #HL2 #HI02 #H destruct
   #HN #HP #Y1 #H1 #Y2 #H2
   [ elim (sex_inv_push1 … H1) -H1 #I1 #L1 #HL1 #HI01 #H destruct
     elim (sex_inv_push1 … H2) -H2 #I2 #L2 #HL2 #HI02 #H destruct


@@ -94,7 +94,7 @@ lemma sex_repl (RN) (RP) (SN) (SP) (L1) (f):
   lapply (sex_inv_atom1 … HY) -HY #H destruct
   lapply (sex_inv_atom1 … HY1) -HY1 #H destruct
   lapply (sex_inv_atom1 … HY2) -HY2 #H destruct //
   lapply (sex_inv_atom1 … HY) -HY #H destruct
   lapply (sex_inv_atom1 … HY1) -HY1 #H destruct
   lapply (sex_inv_atom1 … HY2) -HY2 #H destruct //

-| #L1 #I1 #IH #f elim (pn_split f) * #g #H destruct
+| #L1 #I1 #IH #f elim (pr_map_split_tl f) * #g #H destruct

   #HN #HP #Y #HY #Y1 #HY1 #Y2 #HY2
   [ elim (sex_inv_push1 … HY) -HY #I2 #L2 #HL12 #HI12 #H destruct
     elim (sex_inv_push1 … HY1) -HY1 #J1 #K1 #HLK1 #HIJ1 #H destruct
   #HN #HP #Y #HY #Y1 #HY1 #Y2 #HY2
   [ elim (sex_inv_push1 … HY) -HY #I2 #L2 #HL12 #HI12 #H destruct
     elim (sex_inv_push1 … HY1) -HY1 #J1 #K1 #HLK1 #HIJ1 #H destruct


@@ -124,10 +124,10 @@ lemma sex_meet (RN) (RP) (L1) (L2):
       ∀f. f1 ⋒ f2 ≘ f → L1 ⪤[RN,RP,f] L2.
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H #f #Hf
       ∀f. f1 ⋒ f2 ≘ f → L1 ⪤[RN,RP,f] L2.
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H #f #Hf

-elim (pn_split f2) * #g2 #H2 destruct
+elim (pr_map_split_tl f2) * #g2 #H2 destruct

 try elim (sex_inv_push … H) try elim (sex_inv_next … H) -H
 try elim (sex_inv_push … H) try elim (sex_inv_next … H) -H

-[ elim (sand_inv_npx … Hf) | elim (sand_inv_nnx … Hf)
-| elim (sand_inv_ppx … Hf) | elim (sand_inv_pnx … Hf)
+[ elim (pr_sand_inv_next_push … Hf) | elim (pr_sand_inv_next_bi … Hf)
+| elim (pr_sand_inv_push_bi … Hf) | elim (pr_sand_inv_push_next … Hf)

 ] -Hf /3 width=5 by sex_next, sex_push/
 qed-.
 
 ] -Hf /3 width=5 by sex_next, sex_push/
 qed-.
 


@@ -137,9 +137,9 @@ lemma sex_join (RN) (RP) (L1) (L2):
       ∀f. f1 ⋓ f2 ≘ f → L1 ⪤[RN,RP,f] L2.
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H #f #Hf
       ∀f. f1 ⋓ f2 ≘ f → L1 ⪤[RN,RP,f] L2.
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H #f #Hf

-elim (pn_split f2) * #g2 #H2 destruct
+elim (pr_map_split_tl f2) * #g2 #H2 destruct

 try elim (sex_inv_push … H) try elim (sex_inv_next … H) -H
 try elim (sex_inv_push … H) try elim (sex_inv_next … H) -H

-[ elim (sor_inv_npx … Hf) | elim (sor_inv_nnx … Hf)
-| elim (sor_inv_ppx … Hf) | elim (sor_inv_pnx … Hf)
+[ elim (pr_sor_inv_next_push … Hf) | elim (pr_sor_inv_next_bi … Hf)
+| elim (pr_sor_inv_push_bi … Hf) | elim (pr_sor_inv_push_next … Hf)

 ] -Hf /3 width=5 by sex_next, sex_push/
 qed-.
 ] -Hf /3 width=5 by sex_next, sex_push/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
index f372e4067fcff842b3ff55d8830dc74411a1eaa9..0a95ed3b0f5720832af36230e9b3f61c57061157 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
@@ -87,8 +87,8 @@ theorem sex_tc_step_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
 #RN #RP #HRP #f #L1 #L #H elim H -f -L1 -L
 [ #f #_ #Y #H -HRP >(sex_inv_atom1 … H) -Y // ]
 #f #I1 #I #L1 #L #HL1 #HI1 #IH #Hf #Y #H
 #RN #RP #HRP #f #L1 #L #H elim H -f -L1 -L
 [ #f #_ #Y #H -HRP >(sex_inv_atom1 … H) -Y // ]
 #f #I1 #I #L1 #L #HL1 #HI1 #IH #Hf #Y #H

-[ elim (isid_inv_next … Hf) -Hf //
-| lapply (isid_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
+[ elim (pr_isi_inv_next … Hf) -Hf //
+| lapply (pr_isi_inv_push … Hf ??) -Hf [3: |*: // ] #Hf

   elim (sex_inv_push1 … H) -H #I2 #L2 #HL2 #HI2 #H destruct
   @sex_push [ /2 width=1 by/ ] -L2 -IH
   @(TC_strap … HI1) -HI1
   elim (sex_inv_push1 … H) -H #I2 #L2 #HL2 #HI2 #H destruct
   @sex_push [ /2 width=1 by/ ] -L2 -IH
   @(TC_strap … HI1) -HI1

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup_weight.ma b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup_weight.ma
index 94642d01448a7f092a9d4c22afbd332eef1cd608..ed22b9e12635135eff3e0c7f94acc47da3905f38 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup_weight.ma
@@ -22,7 +22,7 @@ include "static_2/s_computation/fqup.ma".
 lemma fqup_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂+[b] ❪G2,L2,T2❫ →
                    ♯❨G2,L2,T2❩ < ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 lemma fqup_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂+[b] ❪G2,L2,T2❫ →
                    ♯❨G2,L2,T2❩ < ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2

-/3 width=3 by fqu_fwd_fw, transitive_lt/
+/3 width=3 by fqu_fwd_fw, nlt_trans/

 qed-.
 
 (* Advanced eliminators *****************************************************)
 qed-.
 
 (* Advanced eliminators *****************************************************)


@@ -31,7 +31,7 @@ lemma fqup_wf_ind: ∀b. ∀Q:relation3 …. (
                       ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂+[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                       Q G1 L1 T1
                    ) → ∀G1,L1,T1. Q G1 L1 T1.
                       ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂+[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                       Q G1 L1 T1
                    ) → ∀G1,L1,T1. Q G1 L1 T1.

-#b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct
+#b #Q #HQ @(wf3_ind_nlt … fw) #x #IHx #G1 #L1 #T1 #H destruct

 /4 width=2 by fqup_fwd_fw/
 qed-.
 
 /4 width=2 by fqup_fwd_fw/
 qed-.
 


@@ -39,6 +39,6 @@ lemma fqup_wf_ind_eq: ∀b. ∀Q:relation3 …. (
                          ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂+[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                          ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → Q G2 L2 T2
                       ) → ∀G1,L1,T1. Q G1 L1 T1.
                          ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂+[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                          ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → Q G2 L2 T2
                       ) → ∀G1,L1,T1. Q G1 L1 T1.

-#b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct
+#b #Q #HQ @(wf3_ind_nlt … fw) #x #IHx #G1 #L1 #T1 #H destruct

 /4 width=7 by fqup_fwd_fw/
 qed-.
 /4 width=7 by fqup_fwd_fw/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_weight.ma b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_weight.ma
index 4c0406cf54475954c1f2657ef9fcbdd3d5c497f8..b76988981d1af850e157414452b407d6a976cee9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_weight.ma
@@ -22,7 +22,7 @@ include "static_2/s_computation/fqus.ma".
 lemma fqus_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫ →
                    ♯❨G2,L2,T2❩ ≤ ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -L2 -T2
 lemma fqus_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂*[b] ❪G2,L2,T2❫ →
                    ♯❨G2,L2,T2❩ ≤ ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -L2 -T2

-/3 width=3 by fquq_fwd_fw, transitive_le/
+/3 width=3 by fquq_fwd_fw, nle_trans/

 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 qed-.
 
 (* Advanced inversion lemmas ************************************************)


@@ -30,6 +30,6 @@ qed-.
 lemma fqus_inv_refl_atom3: ∀b,I,G,L,X. ❪G,L,⓪[I]❫ ⬂*[b] ❪G,L,X❫ → ⓪[I] = X.
 #b #I #G #L #X #H elim (fqus_inv_fqu_sn … H) -H * //
 #G0 #L0 #T0 #H1 #H2 lapply (fqu_fwd_fw … H1) lapply (fqus_fwd_fw … H2) -H2 -H1
 lemma fqus_inv_refl_atom3: ∀b,I,G,L,X. ❪G,L,⓪[I]❫ ⬂*[b] ❪G,L,X❫ → ⓪[I] = X.
 #b #I #G #L #X #H elim (fqus_inv_fqu_sn … H) -H * //
 #G0 #L0 #T0 #H1 #H2 lapply (fqu_fwd_fw … H1) lapply (fqus_fwd_fw … H2) -H2 -H1

-#H2 #H1 lapply (le_to_lt_to_lt … H2 H1) -G0 -L0 -T0
-#H elim (lt_le_false … H) -H /2 width=1 by monotonic_le_plus_r/
+#H2 #H1 lapply (nle_nlt_trans … H2 H1) -G0 -L0 -T0
+#H elim (nlt_ge_false … H) -H /2 width=1 by nle_plus_bi_sn/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_teqg.ma b/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_teqg.ma
index bd420fd387aca234dcfd92638552ba095d91572a..366fad94ac70f402f0f12c37901bc1c638a011d1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_teqg.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_teqg.ma
@@ -23,8 +23,8 @@ fact fqu_inv_teqg_aux (S) (b):
      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
      G1 = G2 → |L1| = |L2| → T1 ≛[S] T2 → ⊥.
 #S #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
      G1 = G2 → |L1| = |L2| → T1 ≛[S] T2 → ⊥.
 #S #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2

-[1: #I #G #L #V #_ #H elim (succ_inv_refl_sn … H)
-|6: #I #G #L #T #U #_ #_ #H elim (succ_inv_refl_sn … H)
+[1: #I #G #L #V #_ #H elim (nsucc_inv_refl … H)
+|6: #I #G #L #T #U #_ #_ #H elim (nsucc_inv_refl … H)

 ]
 /2 width=6 by teqg_inv_pair_xy_y, teqg_inv_pair_xy_x/
 qed-.
 ]
 /2 width=6 by teqg_inv_pair_xy_y, teqg_inv_pair_xy_x/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_weight.ma b/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_weight.ma
index 51d3b957f96a0f75e2d8a46e76e43c59905f8fbb..f342603698dbb103e2ba0cb517cee75dc39fa705 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_weight.ma
@@ -24,7 +24,7 @@ lemma fqu_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ 
                   ♯❨G2,L2,T2❩ < ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
 #I #I1 #I2 #G #L #HI12 normalize in ⊢ (?%%); -I1
                   ♯❨G2,L2,T2❩ < ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
 #I #I1 #I2 #G #L #HI12 normalize in ⊢ (?%%); -I1

-<(lifts_fwd_tw … HI12) /3 width=1 by monotonic_lt_plus_r, monotonic_lt_plus_l/
+<(lifts_fwd_tw … HI12) /3 width=1 by nlt_plus_bi_sn, nlt_plus_bi_dx/

 qed-.
 
 (* Advanced eliminators *****************************************************)
 qed-.
 
 (* Advanced eliminators *****************************************************)


@@ -33,5 +33,5 @@ lemma fqu_wf_ind: ∀b. ∀Q:relation3 …. (
                      ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                                  Q G1 L1 T1
                               ) → ∀G1,L1,T1. Q G1 L1 T1.
                      ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                                  Q G1 L1 T1
                               ) → ∀G1,L1,T1. Q G1 L1 T1.

-#b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=2 by fqu_fwd_fw/
+#b #Q #HQ @(wf3_ind_nlt … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=2 by fqu_fwd_fw/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_length.ma b/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_length.ma
index 20bc7f0bd83280df36dc95dbf389ceb5c160fd7f..ed038771f6d204bad9a40b02f74418e315673af1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_length.ma
@@ -22,5 +22,5 @@ include "static_2/s_transition/fquq.ma".
 lemma fquq_fwd_length_lref1: ∀b,G1,G2,L1,L2,T2,i. ❪G1,L1,#i❫ ⬂⸮[b] ❪G2,L2,T2❫ →
                              |L2| ≤ |L1|.
 #b #G1 #G2 #L1 #L2 #T2 #i #H elim H -H [2: * ]
 lemma fquq_fwd_length_lref1: ∀b,G1,G2,L1,L2,T2,i. ❪G1,L1,#i❫ ⬂⸮[b] ❪G2,L2,T2❫ →
                              |L2| ≤ |L1|.
 #b #G1 #G2 #L1 #L2 #T2 #i #H elim H -H [2: * ]

-/3 width=6 by fqu_fwd_length_lref1, lt_to_le/
+/3 width=6 by fqu_fwd_length_lref1, nlt_des_le/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_weight.ma b/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_weight.ma
index 605a539055e572da22cdfca24088447f34278d50..69f303e937abaee084a904e8d317b048bfdacb7e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq_weight.ma
@@ -22,5 +22,5 @@ include "static_2/s_transition/fquq.ma".
 lemma fquq_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
                    ♯❨G2,L2,T2❩ ≤ ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [2: * ]
 lemma fquq_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
                    ♯❨G2,L2,T2❩ ≤ ♯❨G1,L1,T1❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [2: * ]

-/3 width=2 by fqu_fwd_fw, lt_to_le/
+/3 width=2 by fqu_fwd_fw, nlt_des_le/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma
index bb54a3367d3d5029a79bb18ef584b4e1f23639a7..b501bd3a6ae785c70b309eac5d4a30068805ed08 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma
@@ -26,7 +26,7 @@ lemma aaa_lref_drops: ∀I,G,K,V,B,i,L. ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢
 #I #G #K #V #B #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
   #H destruct /2 width=1 by aaa_zero/
 #I #G #K #V #B #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
   #H destruct /2 width=1 by aaa_zero/

-| #i #IH #L <uni_succ #H #HB lapply (drops_inv_bind2_isuni_next … H) -H // *
+| #i #IH #L <pr_uni_succ #H #HB lapply (drops_inv_bind2_isuni_next … H) -H // *

   #Z #Y #HY #H destruct /3 width=1 by aaa_lref/
 ]
 qed.
   #Z #Y #HY #H destruct /3 width=1 by aaa_lref/
 ]
 qed.


@@ -64,7 +64,7 @@ lemma aaa_lifts: ∀G,L1,T1,A. ❪G,L1❫ ⊢ T1 ⁝ A → ∀b,f,L2. ⇩*[b,f]
   elim (aaa_inv_lref_drops … H) -H #J #K1 #V1 #HLK1 #HA
   elim (lifts_inv_lref1 … HX) -HX #i2 #Hf #H destruct
   lapply (drops_trans … HL21 … HLK1 ??) -HL21 [1,2: // ] #H
   elim (aaa_inv_lref_drops … H) -H #J #K1 #V1 #HLK1 #HA
   elim (lifts_inv_lref1 … HX) -HX #i2 #Hf #H destruct
   lapply (drops_trans … HL21 … HLK1 ??) -HL21 [1,2: // ] #H

-  elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK2 #HY
+  elim (drops_split_trans … H) -H [ |*: /2 width=6 by pr_after_nat_uni/ ] #Y #HLK2 #HY

   lapply (drops_tls_at … Hf … HY) -HY #HY -Hf
   elim (drops_inv_skip2 … HY) -HY #Z #K2 #HK21 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #V2 #HV12 #H destruct
   lapply (drops_tls_at … Hf … HY) -HY #HY -Hf
   elim (drops_inv_skip2 … HY) -HY #Z #K2 #HK21 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #V2 #HV12 #H destruct


@@ -103,7 +103,7 @@ lemma aaa_inv_lifts: ∀G,L2,T2,A. ❪G,L2❫ ⊢ T2 ⁝ A → ∀b,f,L1. ⇩*[b
   elim (aaa_inv_lref_drops … H) -H #J #K2 #V2 #HLK2 #HA
   elim (lifts_inv_lref2 … HX) -HX #i1 #Hf #H destruct
   lapply (drops_split_div … HL21 (𝐔❨i1❩) ???) -HL21 [4: * |*: // ] #Y #HLK1 #HY
   elim (aaa_inv_lref_drops … H) -H #J #K2 #V2 #HLK2 #HA
   elim (lifts_inv_lref2 … HX) -HX #i1 #Hf #H destruct
   lapply (drops_split_div … HL21 (𝐔❨i1❩) ???) -HL21 [4: * |*: // ] #Y #HLK1 #HY

-  lapply (drops_conf … HLK2 … HY ??) -HY [1,2: /2 width=6 by after_uni_dx/ ] #HY
+  lapply (drops_conf … HLK2 … HY ??) -HY [1,2: /2 width=6 by pr_after_nat_uni/ ] #HY

   lapply (drops_tls_at … Hf … HY) -HY #HY -Hf
   elim (drops_inv_skip1 … HY) -HY #Z #K1 #HK21 #HZ #H destruct
   elim (liftsb_inv_pair_dx … HZ) -HZ #V1 #HV12 #H destruct
   lapply (drops_tls_at … Hf … HY) -HY #HY -Hf
   elim (drops_inv_skip1 … HY) -HY #Z #K1 #HK21 #HZ #H destruct
   elim (liftsb_inv_pair_dx … HZ) -HZ #V1 #HV12 #H destruct

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqu.ma b/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqu.ma
index 3e7ddc638e7dc1b6efeb241cac1493b799d7c3a1..e70fcc94d1ec32ad18fbaab7f2c32f041d6f6b58 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqu.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqu.ma
@@ -21,11 +21,11 @@ include "static_2/static/feqg_length.ma".
 lemma fqu_fneqg (S) (b) (G1) (G2) (L1) (L2) (T1) (T2):
       ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥.
 #S #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 lemma fqu_fneqg (S) (b) (G1) (G2) (L1) (L2) (T1) (T2):
       ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥.
 #S #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2

-[ /3 width=8 by feqg_fwd_length, succ_inv_refl_sn/
+[ /3 width=8 by feqg_fwd_length, nsucc_inv_refl/

 | /3 width=9 by teqg_inv_pair_xy_x, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_y, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_y, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_y, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_x, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_y, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_y, feqg_fwd_teqg/
 | /3 width=9 by teqg_inv_pair_xy_y, feqg_fwd_teqg/

-| /3 width=8 by feqg_fwd_length, succ_inv_refl_sn/
+| /3 width=8 by feqg_fwd_length, nsucc_inv_refl/

 ]
 qed-.
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees.ma
index e9e6380d408e8c8dc5de8ffdfbc4c41876ddc769..90155762bc9ca1dd8851f34027abafd691cd1ae8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/frees.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/frees.ma
@@ -18,7 +18,7 @@ include "static_2/syntax/lenv.ma".
 
 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
 
 
 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
 

-inductive frees: relation3 lenv term rtmap ≝
+inductive frees: relation3 lenv term pr_map ≝

 | frees_sort: ∀f,L,s. 𝐈❪f❫ → frees L (⋆s) f
 | frees_atom: ∀f,i. 𝐈❪f❫ → frees (⋆) (#i) (⫯*[i]↑f)
 | frees_pair: ∀f,I,L,V. frees L V f →
 | frees_sort: ∀f,L,s. 𝐈❪f❫ → frees L (⋆s) f
 | frees_atom: ∀f,i. 𝐈❪f❫ → frees (⋆) (#i) (⫯*[i]↑f)
 | frees_pair: ∀f,I,L,V. frees L V f →


@@ -182,29 +182,29 @@ lemma frees_inv_flat:
 
 (* Basic properties ********************************************************)
 
 
 (* Basic properties ********************************************************)
 

-lemma frees_eq_repl_back: ∀L,T. eq_repl_back … (λf. L ⊢ 𝐅+❪T❫ ≘ f).
+lemma frees_eq_repl_back: ∀L,T. pr_eq_repl_back … (λf. L ⊢ 𝐅+❪T❫ ≘ f).

 #L #T #f1 #H elim H -f1 -L -T
 #L #T #f1 #H elim H -f1 -L -T

-[ /3 width=3 by frees_sort, isid_eq_repl_back/
+[ /3 width=3 by frees_sort, pr_isi_eq_repl_back/

 | #f1 #i #Hf1 #g2 #H
 | #f1 #i #Hf1 #g2 #H

-  elim (eq_inv_pushs_sn … H) -H #g #Hg #H destruct
+  elim (pr_eq_inv_pushs_sn … H) -H #g #Hg #H destruct

   elim (eq_inv_nx … Hg) -Hg
   elim (eq_inv_nx … Hg) -Hg

-  /3 width=3 by frees_atom, isid_eq_repl_back/
+  /3 width=3 by frees_atom, pr_isi_eq_repl_back/

 | #f1 #I #L #V #_ #IH #g2 #H
   elim (eq_inv_nx … H) -H
   /3 width=3 by frees_pair/
 | #f1 #I #L #Hf1 #g2 #H
   elim (eq_inv_nx … H) -H
 | #f1 #I #L #V #_ #IH #g2 #H
   elim (eq_inv_nx … H) -H
   /3 width=3 by frees_pair/
 | #f1 #I #L #Hf1 #g2 #H
   elim (eq_inv_nx … H) -H

-  /3 width=3 by frees_unit, isid_eq_repl_back/
+  /3 width=3 by frees_unit, pr_isi_eq_repl_back/

 | #f1 #I #L #i #_ #IH #g2 #H
   elim (eq_inv_px … H) -H /3 width=3 by frees_lref/
 | #f1 #I #L #i #_ #IH #g2 #H
   elim (eq_inv_px … H) -H /3 width=3 by frees_lref/

-| /3 width=3 by frees_gref, isid_eq_repl_back/
-| /3 width=7 by frees_bind, sor_eq_repl_back3/
-| /3 width=7 by frees_flat, sor_eq_repl_back3/
+| /3 width=3 by frees_gref, pr_isi_eq_repl_back/
+| /3 width=7 by frees_bind, pr_sor_eq_repl_back/
+| /3 width=7 by frees_flat, pr_sor_eq_repl_back/

 ]
 qed-.
 
 ]
 qed-.
 

-lemma frees_eq_repl_fwd: ∀L,T. eq_repl_fwd … (λf. L ⊢ 𝐅+❪T❫ ≘ f).
-#L #T @eq_repl_sym /2 width=3 by frees_eq_repl_back/
+lemma frees_eq_repl_fwd: ∀L,T. pr_eq_repl_fwd … (λf. L ⊢ 𝐅+❪T❫ ≘ f).
+#L #T @pr_eq_repl_sym /2 width=3 by frees_eq_repl_back/

 qed-.
 
 lemma frees_lref_push: ∀f,i. ⋆ ⊢ 𝐅+❪#i❫ ≘ f → ⋆ ⊢ 𝐅+❪#↑i❫ ≘ ⫯f.
 qed-.
 
 lemma frees_lref_push: ∀f,i. ⋆ ⊢ 𝐅+❪#i❫ ≘ f → ⋆ ⊢ 𝐅+❪#↑i❫ ≘ ⫯f.


@@ -217,7 +217,7 @@ qed.
 
 lemma frees_fwd_isfin: ∀f,L,T. L ⊢ 𝐅+❪T❫ ≘ f → 𝐅❪f❫.
 #f #L #T #H elim H -f -L -T
 
 lemma frees_fwd_isfin: ∀f,L,T. L ⊢ 𝐅+❪T❫ ≘ f → 𝐅❪f❫.
 #f #L #T #H elim H -f -L -T

-/4 width=5 by sor_isfin, isfin_isid, isfin_tl, isfin_pushs, isfin_push, isfin_next/
+/4 width=5 by pr_sor_inv_isf_bi, pr_isf_isi, pr_isf_tl, pr_isf_pushs, pr_isf_push, pr_isf_next/

 qed-.
 
 (* Basic_2A1: removed theorems 30:
 qed-.
 
 (* Basic_2A1: removed theorems 30:

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
index 69e0158e9539e102906928e9c9163d280dee365d..215ba6e1aab18d91fed4eba2a6c3dc8f5d3ab263 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
@@ -91,18 +91,18 @@ lemma frees_lifts:
       ∀f2. f ~⊚ f1 ≘ f2 → L ⊢ 𝐅+❪U❫ ≘ f2.
 #b #f1 #K #T #H lapply (frees_fwd_isfin … H) elim H -f1 -K -T
 [ #f1 #K #s #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3
       ∀f2. f ~⊚ f1 ≘ f2 → L ⊢ 𝐅+❪U❫ ≘ f2.
 #b #f1 #K #T #H lapply (frees_fwd_isfin … H) elim H -f1 -K -T
 [ #f1 #K #s #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3

-  lapply (coafter_isid_inv_dx … H3 … Hf1) -f1 #Hf2
+  lapply (pr_coafter_isi_inv_dx … H3 … Hf1) -f1 #Hf2

   >(lifts_inv_sort1 … H2) -U /2 width=1 by frees_sort/
 | #f1 #i #Hf1 #_ #f #L #H1 #U #H2 #f2 #H3
   elim (lifts_inv_lref1 … H2) -H2 #j #Hij #H destruct
   elim (coafter_fwd_xnx_pushs … Hij H3) -H3 #g2 #Hg2 #H2 destruct
   >(lifts_inv_sort1 … H2) -U /2 width=1 by frees_sort/
 | #f1 #i #Hf1 #_ #f #L #H1 #U #H2 #f2 #H3
   elim (lifts_inv_lref1 … H2) -H2 #j #Hij #H destruct
   elim (coafter_fwd_xnx_pushs … Hij H3) -H3 #g2 #Hg2 #H2 destruct

-  lapply (coafter_isid_inv_dx … Hg2 … Hf1) -f1 #Hf2
+  lapply (pr_coafter_isi_inv_dx … Hg2 … Hf1) -f1 #Hf2

   elim (drops_inv_atom2 … H1) -H1 #n #g #H1 #Hf
   elim (drops_inv_atom2 … H1) -H1 #n #g #H1 #Hf

-  elim (after_at_fwd … Hij … Hf) -f #x #_ #Hj -g -i
-  lapply (at_inv_uni … Hj) -Hj #H destruct
+  elim (pr_after_pat_des … Hij … Hf) -f #x #_ #Hj -g -i
+  lapply (pr_pat_inv_uni … Hj) -Hj #H destruct

   /3 width=8 by frees_atom_drops, drops_trans/
 | #f1 #I #K #V #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3
   /3 width=8 by frees_atom_drops, drops_trans/
 | #f1 #I #K #V #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3

-  lapply (isfin_inv_next … Hf1 ??) -Hf1 [3: |*: // ] #Hf1
+  lapply (pr_isf_inv_next … Hf1 ??) -Hf1 [3: |*: // ] #Hf1

   lapply (lifts_inv_lref1 … H2) -H2 * #j #Hf #H destruct
   elim (drops_split_trans_bind2 … H1) -H1 [ |*: // ] #Z #Y #HLY #HYK #H
   elim (liftsb_inv_pair_sn … H) -H #W #HVW #H destruct
   lapply (lifts_inv_lref1 … H2) -H2 * #j #Hf #H destruct
   elim (drops_split_trans_bind2 … H1) -H1 [ |*: // ] #Z #Y #HLY #HYK #H
   elim (liftsb_inv_pair_sn … H) -H #W #HVW #H destruct


@@ -112,34 +112,34 @@ lemma frees_lifts:
 | #f1 #I #K #Hf1 #_ #f #L #H1 #U #H2 #f2 #H3
   lapply (lifts_inv_lref1 … H2) -H2 * #j #Hf #H destruct
   elim (coafter_fwd_xnx_pushs … Hf H3) -H3 #g2 #H3 #H2 destruct
 | #f1 #I #K #Hf1 #_ #f #L #H1 #U #H2 #f2 #H3
   lapply (lifts_inv_lref1 … H2) -H2 * #j #Hf #H destruct
   elim (coafter_fwd_xnx_pushs … Hf H3) -H3 #g2 #H3 #H2 destruct

-  lapply (coafter_isid_inv_dx … H3 … Hf1) -f1 #Hg2
+  lapply (pr_coafter_isi_inv_dx … H3 … Hf1) -f1 #Hg2

   elim (drops_split_trans_bind2 … H1 … Hf) -H1 -Hf #Z #Y #HLY #_ #H
   lapply (liftsb_inv_unit_sn … H) -H #H destruct
   /2 width=3 by frees_unit_drops/
 | #f1 #I #K #i #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3
   elim (drops_split_trans_bind2 … H1 … Hf) -H1 -Hf #Z #Y #HLY #_ #H
   lapply (liftsb_inv_unit_sn … H) -H #H destruct
   /2 width=3 by frees_unit_drops/
 | #f1 #I #K #i #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3

-  lapply (isfin_inv_push … Hf1 ??) -Hf1 [3: |*: // ] #Hf1
+  lapply (pr_isf_inv_push … Hf1 ??) -Hf1 [3: |*: // ] #Hf1

   lapply (lifts_inv_lref1 … H2) -H2 * #x #Hf #H destruct
   lapply (lifts_inv_lref1 … H2) -H2 * #x #Hf #H destruct

-  elim (at_inv_nxx … Hf) -Hf [ |*: // ] #j #Hf #H destruct
+  elim (pr_pat_inv_succ_sn … Hf) -Hf [ |*: // ] #j #Hf #H destruct

   elim (drops_split_trans_bind2 … H1) -H1 [ |*: // ] #Z #Y #HLY #HYK #_
   elim (coafter_fwd_xpx_pushs … 0 … H3) [ |*: // ] #g2 #H3 #H2 destruct
   lapply (drops_isuni_fwd_drop2 … HLY) -HLY // #HLY
   lapply (IH … HYK … H3) -IH -H3 -HYK [4: |*: /2 width=2 by lifts_lref/ ]
   elim (drops_split_trans_bind2 … H1) -H1 [ |*: // ] #Z #Y #HLY #HYK #_
   elim (coafter_fwd_xpx_pushs … 0 … H3) [ |*: // ] #g2 #H3 #H2 destruct
   lapply (drops_isuni_fwd_drop2 … HLY) -HLY // #HLY
   lapply (IH … HYK … H3) -IH -H3 -HYK [4: |*: /2 width=2 by lifts_lref/ ]

-  >plus_S1 /2 width=3 by frees_lref_pushs/ (**) (* full auto fails *)
+  >nplus_succ_sn /2 width=3 by frees_lref_pushs/ (**) (* full auto fails *)

 | #f1 #K #l #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3
 | #f1 #K #l #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3

-  lapply (coafter_isid_inv_dx … H3 … Hf1) -f1 #Hf2
+  lapply (pr_coafter_isi_inv_dx … H3 … Hf1) -f1 #Hf2

   >(lifts_inv_gref1 … H2) -U /2 width=1 by frees_gref/
 | #f1V #f1T #f1 #p #I #K #V #T #_ #_ #H1f1 #IHV #IHT #H2f1 #f #L #H1 #Y #H2 #f2 #H3
   >(lifts_inv_gref1 … H2) -U /2 width=1 by frees_gref/
 | #f1V #f1T #f1 #p #I #K #V #T #_ #_ #H1f1 #IHV #IHT #H2f1 #f #L #H1 #Y #H2 #f2 #H3

-  elim (sor_inv_isfin3 … H1f1) // #Hf1V #H
-  lapply (isfin_inv_tl … H) -H
+  elim (pr_sor_inv_isf … H1f1) // #Hf1V #H
+  lapply (pr_isf_inv_tl … H) -H

   elim (lifts_inv_bind1 … H2) -H2 #W #U #HVW #HTU #H destruct
   elim (lifts_inv_bind1 … H2) -H2 #W #U #HVW #HTU #H destruct

-  elim (coafter_sor … H3 … H1f1) /2 width=5 by coafter_isfin2_fwd/ -H3 -H1f1 #f2V #f2T #Hf2V #H
-  elim (coafter_inv_tl1 … H) -H
+  elim (pr_sor_coafter_dx_tans … H3 … H1f1) /2 width=5 by pr_coafter_des_ist_isf/ -H3 -H1f1 #f2V #f2T #Hf2V #H
+  elim (pr_coafter_inv_tl_dx … H) -H

   /5 width=5 by frees_bind, drops_skip, ext2_pair/
 | #f1V #f1T #f1 #I #K #V #T #_ #_ #H1f1 #IHV #IHT #H2f1 #f #L #H1 #Y #H2 #f2 #H3
   /5 width=5 by frees_bind, drops_skip, ext2_pair/
 | #f1V #f1T #f1 #I #K #V #T #_ #_ #H1f1 #IHV #IHT #H2f1 #f #L #H1 #Y #H2 #f2 #H3

-  elim (sor_inv_isfin3 … H1f1) //
+  elim (pr_sor_inv_isf … H1f1) //

   elim (lifts_inv_flat1 … H2) -H2 #W #U #HVW #HTU #H destruct
   elim (lifts_inv_flat1 … H2) -H2 #W #U #HVW #HTU #H destruct

-  elim (coafter_sor … H3 … H1f1)
-  /3 width=5 by coafter_isfin2_fwd, frees_flat/
+  elim (pr_sor_coafter_dx_tans … H3 … H1f1)
+  /3 width=5 by pr_coafter_des_ist_isf, frees_flat/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -156,7 +156,7 @@ lemma frees_fwd_coafter:
       ∀b,f2,L,U. L ⊢ 𝐅+❪U❫ ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
       ∀f1. K ⊢ 𝐅+❪T❫ ≘ f1 → f ~⊚ f1 ≘ f2.
       ∀b,f2,L,U. L ⊢ 𝐅+❪U❫ ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
       ∀f1. K ⊢ 𝐅+❪T❫ ≘ f1 → f ~⊚ f1 ≘ f2.

-/4 width=11 by frees_lifts, frees_mono, coafter_eq_repl_back0/ qed-.
+/4 width=11 by frees_lifts, frees_mono, pr_coafter_eq_repl_back/ qed-.

 
 (* Inversion lemmas with generic slicing for local environments *************)
 
 
 (* Inversion lemmas with generic slicing for local environments *************)
 


@@ -173,8 +173,8 @@ lemma frees_inv_lifts_SO:
       ∀K. ⇩*[b,𝐔❨1❩] L ≘ K → ∀T. ⇧[1] T ≘ U →
       K ⊢ 𝐅+❪T❫ ≘ ⫰f.
 #b #f #L #U #H #K #HLK #T #HTU elim(frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
       ∀K. ⇩*[b,𝐔❨1❩] L ≘ K → ∀T. ⇧[1] T ≘ U →
       K ⊢ 𝐅+❪T❫ ≘ ⫰f.
 #b #f #L #U #H #K #HLK #T #HTU elim(frees_inv_lifts_ex … H … HLK … HTU) -b -L -U

-#f1 #Hf #Hf1 elim (coafter_inv_nxx … Hf) -Hf
-/3 width=5 by frees_eq_repl_back, coafter_isid_inv_sn/
+#f1 #Hf #Hf1 elim (pr_coafter_inv_next_sn … Hf) -Hf
+/3 width=5 by frees_eq_repl_back, pr_coafter_isi_inv_sn/

 qed-.
 
 lemma frees_inv_lifts:
 qed-.
 
 lemma frees_inv_lifts:


@@ -182,7 +182,7 @@ lemma frees_inv_lifts:
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
       ∀f1. f ~⊚ f1 ≘ f2 → K ⊢ 𝐅+❪T❫ ≘ f1.
 #b #f2 #L #U #H #f #K #HLK #T #HTU #f1 #Hf2 elim (frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
       ∀f1. f ~⊚ f1 ≘ f2 → K ⊢ 𝐅+❪T❫ ≘ f1.
 #b #f2 #L #U #H #f #K #HLK #T #HTU #f1 #Hf2 elim (frees_inv_lifts_ex … H … HLK … HTU) -b -L -U

-/3 width=7 by frees_eq_repl_back, coafter_inj/
+/3 width=7 by frees_eq_repl_back, pr_coafter_inj/

 qed-.
 
 (* Note: this is used by rex_conf and might be modified *)
 qed-.
 
 (* Note: this is used by rex_conf and might be modified *)


@@ -193,48 +193,48 @@ lemma frees_inv_drops_next:
       ∃∃g2. L2 ⊢ 𝐅+❪V2❫ ≘ g2 & g2 ⊆ g1.
 #f1 #L1 #T1 #H elim H -f1 -L1 -T1
 [ #f1 #L1 #s #Hf1 #I2 #L2 #V2 #j #_ #g1 #H1 -I2 -L1 -s
       ∃∃g2. L2 ⊢ 𝐅+❪V2❫ ≘ g2 & g2 ⊆ g1.
 #f1 #L1 #T1 #H elim H -f1 -L1 -T1
 [ #f1 #L1 #s #Hf1 #I2 #L2 #V2 #j #_ #g1 #H1 -I2 -L1 -s

-  lapply (isid_tls j … Hf1) -Hf1 <H1 -f1 #Hf1
-  elim (isid_inv_next … Hf1) -Hf1 //
+  lapply (pr_isi_tls j … Hf1) -Hf1 <H1 -f1 #Hf1
+  elim (pr_isi_inv_next … Hf1) -Hf1 //

 | #f1 #i #_ #I2 #L2 #V2 #j #H
   elim (drops_inv_atom1 … H) -H #H destruct
 | #f1 #I1 #L1 #V1 #Hf1 #IH #I2 #L2 #V2 *
   [ -IH #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 //
 | #f1 #i #_ #I2 #L2 #V2 #j #H
   elim (drops_inv_atom1 … H) -H #H destruct
 | #f1 #I1 #L1 #V1 #Hf1 #IH #I2 #L2 #V2 *
   [ -IH #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 //

-    #H destruct #g1 #Hgf1 >(injective_next … Hgf1) -g1
+    #H destruct #g1 #Hgf1 >(eq_inv_pr_next_bi … Hgf1) -g1

     /2 width=3 by ex2_intro/
   | -Hf1 #j #HL12 lapply (drops_inv_drop1 … HL12) -HL12
     /2 width=3 by ex2_intro/
   | -Hf1 #j #HL12 lapply (drops_inv_drop1 … HL12) -HL12

-    #HL12 #g1 <tls_xn <tl_next_rew #Hgf1 elim (IH … HL12 … Hgf1) -IH -HL12 -Hgf1
+    #HL12 #g1 <pr_tls_swap <pr_tl_next #Hgf1 elim (IH … HL12 … Hgf1) -IH -HL12 -Hgf1

     /2 width=3 by ex2_intro/
   ]
 | #f1 #I1 #L1 #Hf1 #I2 #L2 #V2 *
   [ #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 // #H destruct
     /2 width=3 by ex2_intro/
   ]
 | #f1 #I1 #L1 #Hf1 #I2 #L2 #V2 *
   [ #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 // #H destruct

-  | #j #_ #g1 #Hgf1 elim (isid_inv_next … Hgf1) -Hgf1 <tls_xn /2 width=1 by isid_tls/
+  | #j #_ #g1 #Hgf1 elim (pr_isi_inv_next … Hgf1) -Hgf1 <pr_tls_swap /2 width=1 by pr_isi_tls/

   ]
 | #f1 #I1 #L1 #i #_ #IH #I2 #L2 #V2 *
   ]
 | #f1 #I1 #L1 #i #_ #IH #I2 #L2 #V2 *

-  [ -IH #_ #g1 #Hgf1 elim (discr_next_push … Hgf1)
+  [ -IH #_ #g1 #Hgf1 elim (eq_inv_pr_next_push … Hgf1)

   | #j #HL12 lapply (drops_inv_drop1 … HL12) -HL12
   | #j #HL12 lapply (drops_inv_drop1 … HL12) -HL12

-    #HL12 #g1 <tls_xn #Hgf1 elim (IH … HL12 … Hgf1) -IH -HL12 -Hgf1
+    #HL12 #g1 <pr_tls_swap #Hgf1 elim (IH … HL12 … Hgf1) -IH -HL12 -Hgf1

     /2 width=3 by ex2_intro/
   ]
 | #f1 #L1 #l #Hf1 #I2 #L2 #V2 #j #_ #g1 #H1 -I2 -L1 -l
     /2 width=3 by ex2_intro/
   ]
 | #f1 #L1 #l #Hf1 #I2 #L2 #V2 #j #_ #g1 #H1 -I2 -L1 -l

-  lapply (isid_tls j … Hf1) -Hf1 <H1 -f1 #Hf1
-  elim (isid_inv_next … Hf1) -Hf1 //
+  lapply (pr_isi_tls j … Hf1) -Hf1 <H1 -f1 #Hf1
+  elim (pr_isi_inv_next … Hf1) -Hf1 //

 | #fV1 #fT1 #f1 #p #I1 #L1 #V1 #T1 #_ #_ #Hf1 #IHV1 #IHT1 #I2 #L2 #V2 #j #HL12 #g1 #Hgf1
 | #fV1 #fT1 #f1 #p #I1 #L1 #V1 #T1 #_ #_ #Hf1 #IHV1 #IHT1 #I2 #L2 #V2 #j #HL12 #g1 #Hgf1

-  lapply (sor_tls … Hf1 j) -Hf1 <Hgf1 -Hgf1 #Hf1
-  elim (sor_xxn_tl … Hf1) [1,2: * |*: // ] -Hf1
+  lapply (pr_sor_tls … Hf1 j) -Hf1 <Hgf1 -Hgf1 #Hf1
+  elim (pr_sor_next_tl … Hf1) [1,2: * |*: // ] -Hf1

   #gV1 #gT1 #Hg1
   [ -IHT1 #H1 #_ elim (IHV1 … HL12 … H1) -IHV1 -HL12 -H1
   #gV1 #gT1 #Hg1
   [ -IHT1 #H1 #_ elim (IHV1 … HL12 … H1) -IHV1 -HL12 -H1

-    /3 width=6 by sor_inv_sle_sn_trans, ex2_intro/
-  | -IHV1 #_ >tls_xn #H2 elim (IHT1 … H2) -IHT1 -H2
-    /3 width=6 by drops_drop, sor_inv_sle_dx_trans, ex2_intro/
+    /3 width=6 by pr_sor_inv_sle_sn_trans, ex2_intro/
+  | -IHV1 #_ >pr_tls_swap #H2 elim (IHT1 … H2) -IHT1 -H2
+    /3 width=6 by drops_drop, pr_sor_inv_sle_dx_trans, ex2_intro/

   ]
 | #fV1 #fT1 #f1 #I1 #L1 #V1 #T1 #_ #_ #Hf1 #IHV1 #IHT1 #I2 #L2 #V2 #j #HL12 #g1 #Hgf1
   ]
 | #fV1 #fT1 #f1 #I1 #L1 #V1 #T1 #_ #_ #Hf1 #IHV1 #IHT1 #I2 #L2 #V2 #j #HL12 #g1 #Hgf1

-  lapply (sor_tls … Hf1 j) -Hf1 <Hgf1 -Hgf1 #Hf1
-  elim (sor_xxn_tl … Hf1) [1,2: * |*: // ] -Hf1
+  lapply (pr_sor_tls … Hf1 j) -Hf1 <Hgf1 -Hgf1 #Hf1
+  elim (pr_sor_next_tl … Hf1) [1,2: * |*: // ] -Hf1

   #gV1 #gT1 #Hg1
   [ -IHT1 #H1 #_ elim (IHV1 … HL12 … H1) -IHV1 -HL12 -H1
   #gV1 #gT1 #Hg1
   [ -IHT1 #H1 #_ elim (IHV1 … HL12 … H1) -IHV1 -HL12 -H1

-    /3 width=6 by sor_inv_sle_sn_trans, ex2_intro/
+    /3 width=6 by pr_sor_inv_sle_sn_trans, ex2_intro/

   | -IHV1 #_ #H2 elim (IHT1 … HL12 … H2) -IHT1 -HL12 -H2
   | -IHV1 #_ #H2 elim (IHT1 … HL12 … H2) -IHT1 -HL12 -H2

-    /3 width=6 by sor_inv_sle_dx_trans, ex2_intro/
+    /3 width=6 by pr_sor_inv_sle_dx_trans, ex2_intro/

   ]
 ]
 qed-.
   ]
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees_fqup.ma
index 0ae38b461d55d3d99f23d8fd0a089c94f5e65551..6868962e64f6782e5a0dacd64b41f796a7408610 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/frees_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/frees_fqup.ma
@@ -39,12 +39,12 @@ lemma frees_total: ∀L,T. ∃f. L ⊢ 𝐅+❪T❫ ≘ f.
 | #p #I #V #T #HG #HL #HT destruct
   elim (IH G L V) // #f1 #HV
   elim (IH G (L.ⓑ[I]V) T) -IH // #f2 #HT
 | #p #I #V #T #HG #HL #HT destruct
   elim (IH G L V) // #f1 #HV
   elim (IH G (L.ⓑ[I]V) T) -IH // #f2 #HT

-  elim (sor_isfin_ex f1 (⫰f2))
-  /3 width=6 by frees_fwd_isfin, frees_bind, isfin_tl, ex_intro/
+  elim (pr_sor_isf_bi f1 (⫰f2))
+  /3 width=6 by frees_fwd_isfin, frees_bind, pr_isf_tl, ex_intro/

 | #I #V #T #HG #HL #HT destruct
   elim (IH G L V) // #f1 #HV
   elim (IH G L T) -IH // #f2 #HT
 | #I #V #T #HG #HL #HT destruct
   elim (IH G L V) // #f1 #HV
   elim (IH G L T) -IH // #f2 #HT

-  elim (sor_isfin_ex f1 f2)
+  elim (pr_sor_isf_bi f1 f2)

   /3 width=6 by frees_fwd_isfin, frees_flat, ex_intro/
 ]
 qed-.
   /3 width=6 by frees_fwd_isfin, frees_flat, ex_intro/
 ]
 qed-.


@@ -57,23 +57,23 @@ theorem frees_bind_void:
 #f1 #L #V #Hf1 #f2 #T #Hf2 #f #Hf #p #I
 elim (frees_total (L.ⓑ[I]V) T) #f0 #Hf0
 lapply (lsubr_lsubf … Hf2 … Hf0) -Hf2 /2 width=5 by lsubr_unit/ #H02
 #f1 #L #V #Hf1 #f2 #T #Hf2 #f #Hf #p #I
 elim (frees_total (L.ⓑ[I]V) T) #f0 #Hf0
 lapply (lsubr_lsubf … Hf2 … Hf0) -Hf2 /2 width=5 by lsubr_unit/ #H02

-elim (pn_split f2) * #g2 #H destruct
+elim (pr_map_split_tl f2) * #g2 #H destruct

 [ elim (lsubf_inv_push2 … H02) -H02 #g0 #Z #Y #H02 #H0 #H destruct
   lapply (lsubf_inv_refl … H02) -H02 #H02
 [ elim (lsubf_inv_push2 … H02) -H02 #g0 #Z #Y #H02 #H0 #H destruct
   lapply (lsubf_inv_refl … H02) -H02 #H02

-  lapply (sor_eq_repl_fwd2 … Hf … H02) -g2 #Hf
+  lapply (pr_sor_eq_repl_fwd_dx … Hf … H02) -g2 #Hf

   /2 width=5 by frees_bind/
 | elim (lsubf_inv_unit2 … H02) -H02 * [ #g0 #Y #_ #_ #H destruct ]
   #z1 #g0 #z #Z #Y #X #H02 #Hz1 #Hz #H0 #H destruct
   lapply (lsubf_inv_refl … H02) -H02 #H02
   lapply (frees_mono … Hz1 … Hf1) -Hz1 #H1
   /2 width=5 by frees_bind/
 | elim (lsubf_inv_unit2 … H02) -H02 * [ #g0 #Y #_ #_ #H destruct ]
   #z1 #g0 #z #Z #Y #X #H02 #Hz1 #Hz #H0 #H destruct
   lapply (lsubf_inv_refl … H02) -H02 #H02
   lapply (frees_mono … Hz1 … Hf1) -Hz1 #H1

-  lapply (sor_eq_repl_back1 … Hz … H02) -g0 #Hz
-  lapply (sor_eq_repl_back2 … Hz … H1) -z1 #Hz
-  lapply (sor_comm … Hz) -Hz #Hz
-  lapply (sor_mono … f Hz ?) // -Hz #H
-  lapply (sor_inv_sle_sn … Hf) -Hf #Hf
-  lapply (frees_eq_repl_back … Hf0 (↑f) ?) /2 width=5 by eq_next/ -z #Hf0
+  lapply (pr_sor_eq_repl_back_sn … Hz … H02) -g0 #Hz
+  lapply (pr_sor_eq_repl_back_dx … Hz … H1) -z1 #Hz
+  lapply (pr_sor_comm … Hz) -Hz #Hz
+  lapply (pr_sor_mono … f Hz ?) // -Hz #H
+  lapply (pr_sor_inv_sle_sn … Hf) -Hf #Hf
+  lapply (frees_eq_repl_back … Hf0 (↑f) ?) /2 width=5 by pr_eq_next/ -z #Hf0

   @(frees_bind … Hf1 Hf0) -Hf1 -Hf0 (**) (* constructor needed *)
   @(frees_bind … Hf1 Hf0) -Hf1 -Hf0 (**) (* constructor needed *)

-  /2 width=1 by sor_sle_dx/
+  /2 width=1 by pr_sor_sle_dx/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -86,19 +86,19 @@ lemma frees_inv_bind_void:
 elim (frees_inv_bind … H) -H #f1 #f2 #Hf1 #Hf2 #Hf
 elim (frees_total (L.ⓧ) T) #f0 #Hf0
 lapply (lsubr_lsubf … Hf0 … Hf2) -Hf2 /2 width=5 by lsubr_unit/ #H20
 elim (frees_inv_bind … H) -H #f1 #f2 #Hf1 #Hf2 #Hf
 elim (frees_total (L.ⓧ) T) #f0 #Hf0
 lapply (lsubr_lsubf … Hf0 … Hf2) -Hf2 /2 width=5 by lsubr_unit/ #H20

-elim (pn_split f0) * #g0 #H destruct
+elim (pr_map_split_tl f0) * #g0 #H destruct

 [ elim (lsubf_inv_push2 … H20) -H20 #g2 #I #Y #H20 #H2 #H destruct
   lapply (lsubf_inv_refl … H20) -H20 #H20
 [ elim (lsubf_inv_push2 … H20) -H20 #g2 #I #Y #H20 #H2 #H destruct
   lapply (lsubf_inv_refl … H20) -H20 #H20

-  lapply (sor_eq_repl_back2 … Hf … H20) -g2 #Hf
+  lapply (pr_sor_eq_repl_back_dx … Hf … H20) -g2 #Hf

   /2 width=5 by ex3_2_intro/
 | elim (lsubf_inv_unit2 … H20) -H20 * [ #g2 #Y #_ #_ #H destruct ]
   #z1 #z0 #g2 #Z #Y #X #H20 #Hz1 #Hg2 #H2 #H destruct
   lapply (lsubf_inv_refl … H20) -H20 #H0
   lapply (frees_mono … Hz1 … Hf1) -Hz1 #H1
   /2 width=5 by ex3_2_intro/
 | elim (lsubf_inv_unit2 … H20) -H20 * [ #g2 #Y #_ #_ #H destruct ]
   #z1 #z0 #g2 #Z #Y #X #H20 #Hz1 #Hg2 #H2 #H destruct
   lapply (lsubf_inv_refl … H20) -H20 #H0
   lapply (frees_mono … Hz1 … Hf1) -Hz1 #H1

-  lapply (sor_eq_repl_back1 … Hg2 … H0) -z0 #Hg2
-  lapply (sor_eq_repl_back2 … Hg2 … H1) -z1 #Hg2
+  lapply (pr_sor_eq_repl_back_sn … Hg2 … H0) -z0 #Hg2
+  lapply (pr_sor_eq_repl_back_dx … Hg2 … H1) -z1 #Hg2

   @(ex3_2_intro … Hf1 Hf0) -Hf1 -Hf0 (**) (* constructor needed *)
   @(ex3_2_intro … Hf1 Hf0) -Hf1 -Hf0 (**) (* constructor needed *)

-  /2 width=3 by sor_comm_23_idem/
+  /2 width=3 by pr_sor_comm_23_idem/

 ]
 qed-.
 
 ]
 qed-.
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees_frees.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees_frees.ma
index 7a10ca0c098b3ceec4c6cc76cb77921afad2dbd2..e35ad94c5d892dfc7e90804fd90f318a6d9c18b1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/frees_frees.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/frees_frees.ma
@@ -20,22 +20,22 @@ include "static_2/static/frees.ma".
 
 theorem frees_mono: ∀f1,L,T. L ⊢ 𝐅+❪T❫ ≘ f1 → ∀f2. L ⊢ 𝐅+❪T❫ ≘ f2 → f1 ≡ f2.
 #f1 #L #T #H elim H -f1 -L -T
 
 theorem frees_mono: ∀f1,L,T. L ⊢ 𝐅+❪T❫ ≘ f1 → ∀f2. L ⊢ 𝐅+❪T❫ ≘ f2 → f1 ≡ f2.
 #f1 #L #T #H elim H -f1 -L -T

-[ /3 width=3 by frees_inv_sort, isid_inv_eq_repl/
+[ /3 width=3 by frees_inv_sort, pr_isi_inv_eq_repl/

 | #f1 #i #Hf1 #g2 #H
   elim (frees_inv_atom … H) -H #f2 #Hf2 #H destruct
 | #f1 #i #Hf1 #g2 #H
   elim (frees_inv_atom … H) -H #f2 #Hf2 #H destruct

-  /4 width=5 by isid_inv_eq_repl, pushs_eq_repl, eq_next/
+  /4 width=5 by pr_isi_inv_eq_repl, pr_pushs_eq_repl, pr_eq_next/

 | #f1 #I #L #V #_ #IH #g2 #H elim (frees_inv_pair … H) -H
 | #f1 #I #L #V #_ #IH #g2 #H elim (frees_inv_pair … H) -H

-  #f2 #Hf2 #H destruct /3 width=5 by eq_next/
+  #f2 #Hf2 #H destruct /3 width=5 by pr_eq_next/

 | #f1 #I #L #Hf1 #g2 #H elim (frees_inv_unit … H) -H
 | #f1 #I #L #Hf1 #g2 #H elim (frees_inv_unit … H) -H

-  #f2 #Hf2 #H destruct /3 width=5 by isid_inv_eq_repl, eq_next/
+  #f2 #Hf2 #H destruct /3 width=5 by pr_isi_inv_eq_repl, pr_eq_next/

 | #f1 #I #L #i #_ #IH #g2 #H elim (frees_inv_lref … H) -H
 | #f1 #I #L #i #_ #IH #g2 #H elim (frees_inv_lref … H) -H

-  #f2 #Hf2 #H destruct /3 width=5 by eq_push/
-| /3 width=3 by frees_inv_gref, isid_inv_eq_repl/
+  #f2 #Hf2 #H destruct /3 width=5 by pr_eq_push/
+| /3 width=3 by frees_inv_gref, pr_isi_inv_eq_repl/

 | #f1V #f1T #f1 #p #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_bind … H) -H
 | #f1V #f1T #f1 #p #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_bind … H) -H

-  #f2V #f2T #HV #HT #Hf2 @(sor_mono … Hf1) -Hf1
-  /5 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1, tl_eq_repl/ (**) (* full auto too slow *)
+  #f2V #f2T #HV #HT #Hf2 @(pr_sor_mono … Hf1) -Hf1
+  /5 width=3 by pr_sor_eq_repl_fwd_dx, pr_sor_eq_repl_fwd_sn, pr_tl_eq_repl/ (**) (* full auto too slow *)

 | #f1V #f1T #f1 #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_flat … H) -H
 | #f1V #f1T #f1 #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_flat … H) -H

-  #f2V #f2T #HV #HT #Hf2 @(sor_mono … Hf1) -Hf1
-  /4 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1/ (**) (* full auto too slow *)
+  #f2V #f2T #HV #HT #Hf2 @(pr_sor_mono … Hf1) -Hf1
+  /4 width=3 by pr_sor_eq_repl_fwd_dx, pr_sor_eq_repl_fwd_sn/ (**) (* full auto too slow *)

 ]
 qed-.
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle.ma
index 659060756188b3c46265e5a6cda5acd723cfc0d6..5eb02293ee16ba9b14fad12344b590bbf531a75a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle.ma
@@ -33,7 +33,7 @@ interpretation "free variables inclusion (term)"
 (* Basic properties *********************************************************)
 
 lemma fsle_sort: ∀L,s1,s2. ❪L,⋆s1❫ ⊆ ❪L,⋆s2❫.
 (* Basic properties *********************************************************)
 
 lemma fsle_sort: ∀L,s1,s2. ❪L,⋆s1❫ ⊆ ❪L,⋆s2❫.

-/3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
+/3 width=8 by frees_sort, pr_sle_refl, ex4_4_intro/ qed.

 
 lemma fsle_gref: ∀L,l1,l2. ❪L,§l1❫ ⊆ ❪L,§l2❫.
 
 lemma fsle_gref: ∀L,l1,l2. ❪L,§l1❫ ⊆ ❪L,§l2❫.

-/3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.
+/3 width=8 by frees_gref, pr_sle_refl, ex4_4_intro/ qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
index 718a74a8a8d578851090954d41f9885c12828304..87d3864ffe6c48f1d331e78242f61706d73c596b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
@@ -46,7 +46,7 @@ lemma fsle_lifts_SO_sn: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ❪K1,V1❫ ⊆ ❪K
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #W1 #HVW1 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #W1 #HVW1 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct

-/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, sle_weak, ex4_4_intro/
+/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, pr_sle_weak, ex4_4_intro/

 qed.
 
 lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ❪K1,T1❫ ⊆ ❪K2,T2❫ →
 qed.
 
 lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ❪K1,T1❫ ⊆ ❪K2,T2❫ →


@@ -56,7 +56,7 @@ lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ❪K1,T1❫ ⊆ ❪K2,T
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #U1 #U2 #HTU1 #HTU2 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #U1 #U2 #HTU1 #HTU2 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct

-/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, sle_push, ex4_4_intro/
+/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, pr_sle_push, ex4_4_intro/

 qed.
 
 (* Advanced inversion lemmas ************************************************)
 qed.
 
 (* Advanced inversion lemmas ************************************************)


@@ -68,9 +68,9 @@ lemma fsle_inv_lifts_sn: ∀T1,U1. ⇧[1] T1 ≘ U1 →
 * #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p
 elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct
 elim (frees_total L2 V2) #g1 #Hg1
 * #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p
 elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct
 elim (frees_total L2 V2) #g1 #Hg1

-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_

 lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1)
 [1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2
 lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1)
 [1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2

-lapply (sor_inv_sle_dx … Hg) #H0g
-/5 width=10 by frees_bind, sle_tl, sle_trans, ex4_4_intro/
+lapply (pr_sor_inv_sle_dx … Hg) #H0g
+/5 width=10 by frees_bind, pr_sle_tl, pr_sle_trans, ex4_4_intro/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma
index 7965876e204ea4a774c57adec546bdbbbabb8bc2..c49ebe63da3cc3ac04532974a51ad3b20f0f00cc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma
@@ -22,7 +22,7 @@ include "static_2/static/fsle_length.ma".
 lemma fsle_refl: bi_reflexive … fsle.
 #L #T
 elim (frees_total L T) #f #Hf
 lemma fsle_refl: bi_reflexive … fsle.
 #L #T
 elim (frees_total L T) #f #Hf

-/2 width=8 by sle_refl, ex4_4_intro/
+/2 width=8 by pr_sle_refl, ex4_4_intro/

 qed.
 
 lemma fsle_shift: ∀L1,L2. |L1| = |L2| →
 qed.
 
 lemma fsle_shift: ∀L1,L2. |L1| = |L2| →


@@ -33,47 +33,47 @@ lemma fsle_shift: ∀L1,L2. |L1| = |L2| →
 elim (lveq_inj_length … H2L) // -H1L #H1 #H2 destruct
 lapply (lveq_inv_bind_O … H2L) -H2L #HL
 elim (frees_total L2 V) #g1 #Hg1
 elim (lveq_inj_length … H2L) // -H1L #H1 #H2 destruct
 lapply (lveq_inv_bind_O … H2L) -H2L #HL
 elim (frees_total L2 V) #g1 #Hg1

-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-lapply (sor_inv_sle_dx … Hg) #H0g
-/4 width=10 by frees_bind, lveq_void_sn, sle_tl, sle_trans, ex4_4_intro/
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
+lapply (pr_sor_inv_sle_dx … Hg) #H0g
+/4 width=10 by frees_bind, lveq_void_sn, pr_sle_tl, pr_sle_trans, ex4_4_intro/

 qed.
 
 lemma fsle_bind_dx_sn: ∀L1,L2,V1,V2. ❪L1,V1❫ ⊆ ❪L2,V2❫ →
                        ∀p,I,T2. ❪L1,V1❫ ⊆ ❪L2,ⓑ[p,I]V2.T2❫.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #p #I #T2
 elim (frees_total (L2.ⓧ) T2) #g2 #Hg2
 qed.
 
 lemma fsle_bind_dx_sn: ∀L1,L2,V1,V2. ❪L1,V1❫ ⊆ ❪L2,V2❫ →
                        ∀p,I,T2. ❪L1,V1❫ ⊆ ❪L2,ⓑ[p,I]V2.T2❫.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #p #I #T2
 elim (frees_total (L2.ⓧ) T2) #g2 #Hg2

-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_

 @(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)
 @(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)

-/4 width=5 by frees_bind_void, sor_inv_sle_sn, sor_tls, sle_trans/
+/4 width=5 by frees_bind_void, pr_sor_inv_sle_sn, pr_sor_tls, pr_sle_trans/

 qed.
 
 lemma fsle_bind_dx_dx: ∀L1,L2,T1,T2. ❪L1,T1❫ ⊆ ❪L2.ⓧ,T2❫ → |L1| ≤ |L2| →
                        ∀p,I,V2. ❪L1,T1❫ ⊆ ❪L2,ⓑ[p,I]V2.T2❫.
 #L1 #L2 #T1 #T2 * #n1 #x1 #f2 #g2 #Hf2 #Hg2 #H #Hfg2 #HL12 #p #I #V2
 elim (lveq_inv_void_dx_length … H HL12) -H -HL12 #m1 #HL12 #H1 #H2 destruct
 qed.
 
 lemma fsle_bind_dx_dx: ∀L1,L2,T1,T2. ❪L1,T1❫ ⊆ ❪L2.ⓧ,T2❫ → |L1| ≤ |L2| →
                        ∀p,I,V2. ❪L1,T1❫ ⊆ ❪L2,ⓑ[p,I]V2.T2❫.
 #L1 #L2 #T1 #T2 * #n1 #x1 #f2 #g2 #Hf2 #Hg2 #H #Hfg2 #HL12 #p #I #V2
 elim (lveq_inv_void_dx_length … H HL12) -H -HL12 #m1 #HL12 #H1 #H2 destruct

-<tls_xn in Hfg2; #Hfg2
+<pr_tls_swap in Hfg2; #Hfg2

 elim (frees_total L2 V2) #g1 #Hg1
 elim (frees_total L2 V2) #g1 #Hg1

-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_

 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)
 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)

-/4 width=5 by frees_bind_void, sor_inv_sle_dx, sor_tls, sle_trans/
+/4 width=5 by frees_bind_void, pr_sor_inv_sle_dx, pr_sor_tls, pr_sle_trans/

 qed.
 
 lemma fsle_flat_dx_sn: ∀L1,L2,V1,V2. ❪L1,V1❫ ⊆ ❪L2,V2❫ →
                        ∀I,T2. ❪L1,V1❫ ⊆ ❪L2,ⓕ[I]V2.T2❫.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #I #T2
 elim (frees_total L2 T2) #g2 #Hg2
 qed.
 
 lemma fsle_flat_dx_sn: ∀L1,L2,V1,V2. ❪L1,V1❫ ⊆ ❪L2,V2❫ →
                        ∀I,T2. ❪L1,V1❫ ⊆ ❪L2,ⓕ[I]V2.T2❫.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #I #T2
 elim (frees_total L2 T2) #g2 #Hg2

-elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
+elim (pr_sor_isf_bi g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_

 @(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)
 @(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)

-/4 width=5 by frees_flat, sor_inv_sle_sn, sor_tls, sle_trans/
+/4 width=5 by frees_flat, pr_sor_inv_sle_sn, pr_sor_tls, pr_sle_trans/

 qed.
 
 lemma fsle_flat_dx_dx: ∀L1,L2,T1,T2. ❪L1,T1❫ ⊆ ❪L2,T2❫ →
                        ∀I,V2. ❪L1,T1❫ ⊆ ❪L2,ⓕ[I]V2.T2❫.
 #L1 #L2 #T1 #T2 * #n1 #m1 #f2 #g2 #Hf2 #Hg2 #HL12 #Hfg2 #I #V2
 elim (frees_total L2 V2) #g1 #Hg1
 qed.
 
 lemma fsle_flat_dx_dx: ∀L1,L2,T1,T2. ❪L1,T1❫ ⊆ ❪L2,T2❫ →
                        ∀I,V2. ❪L1,T1❫ ⊆ ❪L2,ⓕ[I]V2.T2❫.
 #L1 #L2 #T1 #T2 * #n1 #m1 #f2 #g2 #Hf2 #Hg2 #HL12 #Hfg2 #I #V2
 elim (frees_total L2 V2) #g1 #Hg1

-elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
+elim (pr_sor_isf_bi g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_

 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)
 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)

-/4 width=5 by frees_flat, sor_inv_sle_dx, sor_tls, sle_trans/
+/4 width=5 by frees_flat, pr_sor_inv_sle_dx, pr_sor_tls, pr_sle_trans/

 qed.
 
 (* Advanced forward lemmas ***************************************************)
 qed.
 
 (* Advanced forward lemmas ***************************************************)


@@ -85,5 +85,5 @@ lemma fsle_fwd_pair_sn: ∀I1,I2,L1,L2,V1,V2,T1,T2. ❪L1.ⓑ[I1]V1,T1❫ ⊆ 
 elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
 elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
 lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1
 elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
 elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
 lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1

-/5 width=10 by lsubf_fwd_sle, lveq_bind, sle_trans, ex4_4_intro/ (**) (* full auto too slow *)
+/5 width=10 by lsubf_fwd_sle, lveq_bind, pr_sle_trans, ex4_4_intro/ (**) (* full auto too slow *)

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
index e9ebfb3811409c5865dd46c5f61bf3ec2bcb51d7..7dafa423bfc2e97ccc46766c90ca3cffc06d9458 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
@@ -25,8 +25,8 @@ lemma fsle_frees_trans:
       ∃∃n1,n2,f1. L1 ⊢ 𝐅+❪T1❫ ≘ f1 & L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #f1 #g2 #Hf1 #Hg2 #HL #Hn #f2 #Hf2
 lapply (frees_mono … Hg2 … Hf2) -Hg2 -Hf2 #Hgf2
       ∃∃n1,n2,f1. L1 ⊢ 𝐅+❪T1❫ ≘ f1 & L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #f1 #g2 #Hf1 #Hg2 #HL #Hn #f2 #Hf2
 lapply (frees_mono … Hg2 … Hf2) -Hg2 -Hf2 #Hgf2

-lapply (tls_eq_repl n2 … Hgf2) -Hgf2 #Hgf2
-lapply (sle_eq_repl_back2 … Hn … Hgf2) -g2
+lapply (pr_tls_eq_repl n2 … Hgf2) -Hgf2 #Hgf2
+lapply (pr_sle_eq_repl_back_dx … Hn … Hgf2) -g2

 /2 width=6 by ex3_3_intro/
 qed-.
 
 /2 width=6 by ex3_3_intro/
 qed-.
 


@@ -47,7 +47,7 @@ lemma fsle_inv_frees_eq:
       f1 ⊆ f2.
 #L1 #L2 #H1L #T1 #T2 #H2L #f1 #Hf1 #f2 #Hf2
 elim (fsle_frees_trans_eq … H2L … Hf2) // -L2 -T2
       f1 ⊆ f2.
 #L1 #L2 #H1L #T1 #T2 #H2L #f1 #Hf1 #f2 #Hf2
 elim (fsle_frees_trans_eq … H2L … Hf2) // -L2 -T2

-/3 width=6 by frees_mono, sle_eq_repl_back1/
+/3 width=6 by frees_mono, pr_sle_eq_repl_back_sn/

 qed-.
 
 lemma fsle_frees_conf:
 qed-.
 
 lemma fsle_frees_conf:


@@ -56,8 +56,8 @@ lemma fsle_frees_conf:
       ∃∃n1,n2,f2. L2 ⊢ 𝐅+❪T2❫ ≘ f2 & L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #g1 #g2 #Hg1 #Hg2 #HL #Hn #f1 #Hf1
 lapply (frees_mono … Hg1 … Hf1) -Hg1 -Hf1 #Hgf1
       ∃∃n1,n2,f2. L2 ⊢ 𝐅+❪T2❫ ≘ f2 & L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #g1 #g2 #Hg1 #Hg2 #HL #Hn #f1 #Hf1
 lapply (frees_mono … Hg1 … Hf1) -Hg1 -Hf1 #Hgf1

-lapply (tls_eq_repl n1 … Hgf1) -Hgf1 #Hgf1
-lapply (sle_eq_repl_back1 … Hn … Hgf1) -g1
+lapply (pr_tls_eq_repl n1 … Hgf1) -Hgf1 #Hgf1
+lapply (pr_sle_eq_repl_back_sn … Hn … Hgf1) -g1

 /2 width=6 by ex3_3_intro/
 qed-.
 
 /2 width=6 by ex3_3_intro/
 qed-.
 


@@ -82,8 +82,8 @@ theorem fsle_trans_sn:
 * #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
 lapply (frees_mono … Hf0 … Hg0) -Hf0 -Hg0 #Hfg0
 elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct
 * #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
 lapply (frees_mono … Hf0 … Hg0) -Hf0 -Hg0 #Hfg0
 elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct

-lapply (sle_eq_repl_back1 … Hf … Hfg0) -f0
-/4 width=10 by sle_tls, sle_trans, ex4_4_intro/
+lapply (pr_sle_eq_repl_back_sn … Hf … Hfg0) -f0
+/4 width=10 by pr_sle_tls, pr_sle_trans, ex4_4_intro/

 qed-.
 
 theorem fsle_trans_dx:
 qed-.
 
 theorem fsle_trans_dx:


@@ -95,8 +95,8 @@ theorem fsle_trans_dx:
 * #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
 lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
 elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct
 * #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
 lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
 elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct

-lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
-/4 width=10 by sle_tls, sle_trans, ex4_4_intro/
+lapply (pr_sle_eq_repl_back_dx … Hg … Hgf0) -g0
+/4 width=10 by pr_sle_tls, pr_sle_trans, ex4_4_intro/

 qed-.
 
 theorem fsle_trans_rc:
 qed-.
 
 theorem fsle_trans_rc:


@@ -109,8 +109,8 @@ theorem fsle_trans_rc:
 lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
 elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct
 elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct
 lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
 elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct
 elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct

-lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
-/3 width=10 by lveq_length_eq, sle_trans, ex4_4_intro/
+lapply (pr_sle_eq_repl_back_dx … Hg … Hgf0) -g0
+/3 width=10 by lveq_length_eq, pr_sle_trans, ex4_4_intro/

 qed-.
 
 theorem fsle_bind_sn_ge:
 qed-.
 
 theorem fsle_bind_sn_ge:


@@ -120,9 +120,9 @@ theorem fsle_bind_sn_ge:
 #L1 #L2 #HL #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #p #I
 elim (fsle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
 elim (lveq_inj_void_sn_ge … H1n1 … H1n2) -H1n2 // #H1 #H2 #H3 destruct
 #L1 #L2 #HL #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #p #I
 elim (fsle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
 elim (lveq_inj_void_sn_ge … H1n1 … H1n2) -H1n2 // #H1 #H2 #H3 destruct

-elim (sor_isfin_ex f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-<tls_xn in H2n2; #H2n2
-/4 width=12 by frees_bind_void, sor_inv_sle, sor_tls, ex4_4_intro/
+elim (pr_sor_isf_bi f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #f #Hf #_
+<pr_tls_swap in H2n2; #H2n2
+/4 width=12 by frees_bind_void, pr_sor_inv_sle_bi, pr_sor_tls, ex4_4_intro/

 qed.
 
 theorem fsle_flat_sn:
 qed.
 
 theorem fsle_flat_sn:


@@ -131,8 +131,8 @@ theorem fsle_flat_sn:
 #L1 #L2 #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #I
 elim (fsle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
 elim (lveq_inj … H1n1 … H1n2) -H1n2 #H1 #H2 destruct
 #L1 #L2 #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #I
 elim (fsle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
 elim (lveq_inj … H1n1 … H1n2) -H1n2 #H1 #H2 destruct

-elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
-/4 width=12 by frees_flat, sor_inv_sle, sor_tls, ex4_4_intro/
+elim (pr_sor_isf_bi f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+/4 width=12 by frees_flat, pr_sor_inv_sle_bi, pr_sor_tls, ex4_4_intro/

 qed.
 
 theorem fsle_bind_eq:
 qed.
 
 theorem fsle_bind_eq:


@@ -144,9 +144,9 @@ theorem fsle_bind_eq:
 * #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p #I1
 elim (lveq_inj_length … H1L) // #H1 #H2 destruct
 elim (lveq_inj_length … H2L) // -HL -H2L #H1 #H2 destruct
 * #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p #I1
 elim (lveq_inj_length … H1L) // #H1 #H2 destruct
 elim (lveq_inj_length … H2L) // -HL -H2L #H1 #H2 destruct

-elim (sor_isfin_ex f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-/4 width=15 by frees_bind_void, frees_bind, monotonic_sle_sor, sle_tl, ex4_4_intro/
+elim (pr_sor_isf_bi f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #f #Hf #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
+/4 width=15 by frees_bind_void, frees_bind, pr_sor_monotonic_sle, pr_sle_tl, ex4_4_intro/

 qed.
 
 theorem fsle_bind:
 qed.
 
 theorem fsle_bind:


@@ -158,9 +158,9 @@ theorem fsle_bind:
 * #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p
 elim (lveq_inv_pair_pair … H2L) -H2L #H2L #H1 #H2 destruct
 elim (lveq_inj … H2L … H1L) -H1L #H1 #H2 destruct
 * #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p
 elim (lveq_inv_pair_pair … H2L) -H2L #H2L #H1 #H2 destruct
 elim (lveq_inj … H2L … H1L) -H1L #H1 #H2 destruct

-elim (sor_isfin_ex f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-/4 width=15 by frees_bind, monotonic_sle_sor, sle_tl, ex4_4_intro/
+elim (pr_sor_isf_bi f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #f #Hf #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
+/4 width=15 by frees_bind, pr_sor_monotonic_sle, pr_sle_tl, ex4_4_intro/

 qed.
 
 theorem fsle_flat:
 qed.
 
 theorem fsle_flat:

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_length.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_length.ma
index d2968d82a1d040107aaf55223d12dba0357f6c0d..9fc1cc54b0bf6dc77fe28e68ded5bd94e8c216aa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_length.ma
@@ -20,10 +20,10 @@ include "static_2/static/fsle.ma".
 (* Properties with length for local environments ****************************)
 
 lemma fsle_sort_bi: ∀L1,L2,s1,s2. |L1| = |L2| → ❪L1,⋆s1❫ ⊆ ❪L2,⋆s2❫.
 (* Properties with length for local environments ****************************)
 
 lemma fsle_sort_bi: ∀L1,L2,s1,s2. |L1| = |L2| → ❪L1,⋆s1❫ ⊆ ❪L2,⋆s2❫.

-/3 width=8 by lveq_length_eq, frees_sort, sle_refl, ex4_4_intro/ qed.
+/3 width=8 by lveq_length_eq, frees_sort, pr_sle_refl, ex4_4_intro/ qed.

 
 lemma fsle_gref_bi: ∀L1,L2,l1,l2. |L1| = |L2| → ❪L1,§l1❫ ⊆ ❪L2,§l2❫.
 
 lemma fsle_gref_bi: ∀L1,L2,l1,l2. |L1| = |L2| → ❪L1,§l1❫ ⊆ ❪L2,§l2❫.

-/3 width=8 by lveq_length_eq, frees_gref, sle_refl, ex4_4_intro/ qed.
+/3 width=8 by lveq_length_eq, frees_gref, pr_sle_refl, ex4_4_intro/ qed.

 
 lemma fsle_pair_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ❪K1,V1❫ ⊆ ❪K2,V2❫ →
                     ∀I1,I2. ❪K1.ⓑ[I1]V1,#O❫ ⊆ ❪K2.ⓑ[I2]V2,#O❫.
 
 lemma fsle_pair_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ❪K1,V1❫ ⊆ ❪K2,V2❫ →
                     ∀I1,I2. ❪K1.ⓑ[I1]V1,#O❫ ⊆ ❪K2.ⓑ[I2]V2,#O❫.


@@ -31,10 +31,10 @@ lemma fsle_pair_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ❪K1,V1❫ ⊆ ❪K2,V2
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct

-/3 width=12 by frees_pair, lveq_bind, sle_next, ex4_4_intro/
+/3 width=12 by frees_pair, lveq_bind, pr_sle_next, ex4_4_intro/

 qed.
 
 lemma fsle_unit_bi: ∀K1,K2. |K1| = |K2| →
                     ∀I1,I2. ❪K1.ⓤ[I1],#O❫ ⊆ ❪K2.ⓤ[I2],#O❫.
 qed.
 
 lemma fsle_unit_bi: ∀K1,K2. |K1| = |K2| →
                     ∀I1,I2. ❪K1.ⓤ[I1],#O❫ ⊆ ❪K2.ⓤ[I2],#O❫.

-/3 width=8 by frees_unit, lveq_length_eq, sle_refl, ex4_4_intro/
+/3 width=8 by frees_unit, lveq_length_eq, pr_sle_refl, ex4_4_intro/

 qed.
 qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma b/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma
index 750c3a538c19a2c41b938ac5af2ae8e4b84bfcb2..40e757ad62b4c9bd4445c6e82a1cfd5b492ace06 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma
@@ -37,7 +37,7 @@ theorem acr_aaa_lsubc_lifts (RR) (RS) (RP):
   elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
   lapply (acr_gcr … H1RP H2RP A) #HA
   lapply (drops_trans … HL01 … HLK1 ??) -HL01 [3: |*: // ] #H
   elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
   lapply (acr_gcr … H1RP H2RP A) #HA
   lapply (drops_trans … HL01 … HLK1 ??) -HL01 [3: |*: // ] #H

-  elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK0 #HY
+  elim (drops_split_trans … H) -H [ |*: /2 width=6 by pr_after_nat_uni/ ] #Y #HLK0 #HY

   lapply (drops_tls_at … Hf … HY) -Hf -HY #HY
   elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK01 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #V0 #HV10 #H destruct
   lapply (drops_tls_at … Hf … HY) -Hf -HY #HY
   elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK01 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #V0 #HV10 #H destruct

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma b/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
index a064c7e1f1d65d4d9cc3ae1214f2885309c6dd2f..e1b88f5b682d1f8ce0689e7556e3cb31c4311c41 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
@@ -119,13 +119,13 @@ lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
   elim (lifts_inv_applv1 … H) -H #V0s #X0 #HV0s #H0 #H destruct
   elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
   lapply (drops_trans … HL0 … HLK ??) [3: |*: // ] -HLK #H
   elim (lifts_inv_applv1 … H) -H #V0s #X0 #HV0s #H0 #H destruct
   elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
   lapply (drops_trans … HL0 … HLK ??) [3: |*: // ] -HLK #H

-  elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK0 #HY
+  elim (drops_split_trans … H) -H [ |*: /2 width=6 by pr_after_nat_uni/ ] #Y #HLK0 #HY

   lapply (drops_tls_at … Hf … HY) -HY #HY
   elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK0 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #W1 #HVW1 #H destruct
   elim (lifts_total W1 (𝐔❨↑j❩)) #W2 #HW12
   lapply (lifts_trans … HVW1 … HW12 ??) -HVW1 [3: |*: // ] #H
   lapply (drops_tls_at … Hf … HY) -HY #HY
   elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK0 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #W1 #HVW1 #H destruct
   elim (lifts_total W1 (𝐔❨↑j❩)) #W2 #HW12
   lapply (lifts_trans … HVW1 … HW12 ??) -HVW1 [3: |*: // ] #H

-  lapply (lifts_conf … HV12 … H f ?) -V1 [ /2 width=3 by after_uni_succ_sn/ ] #HVW2
+  lapply (lifts_conf … HV12 … H f ?) -V1 [ /2 width=3 by pr_pat_after_uni_tls/ ] #HVW2

   @(s5 … IHA … (V0⨮V0s) … HW12) /3 width=4 by drops_inv_gen, lifts_applv/
 | #G #L #V1s #V2s #HV12s #p #V #T #HA #HV #f #L0 #V10 #X #HL0 #H #HB
   elim (lifts_inv_applv1 … H) -H #V10s #X0 #HV10s #H0 #H destruct
   @(s5 … IHA … (V0⨮V0s) … HW12) /3 width=4 by drops_inv_gen, lifts_applv/
 | #G #L #V1s #V2s #HV12s #p #V #T #HA #HV #f #L0 #V10 #X #HL0 #H #HB
   elim (lifts_inv_applv1 … H) -H #V10s #X0 #HV10s #H0 #H destruct


@@ -136,7 +136,7 @@ lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
   @(HA … (⫯f)) /3 width=2 by drops_skip, ext2_pair/
   [ @lifts_applv //
     lapply (liftsv_trans … HV10s … HV120s ??) -V10s [3: |*: // ] #H
   @(HA … (⫯f)) /3 width=2 by drops_skip, ext2_pair/
   [ @lifts_applv //
     lapply (liftsv_trans … HV10s … HV120s ??) -V10s [3: |*: // ] #H

-    elim (liftsv_split_trans … H (𝐔❨1❩) (⫯f)) /2 width=1 by after_uni_one_sn/ #V10s #HV10s #HV120s
+    elim (liftsv_split_trans … H (𝐔❨1❩) (⫯f)) /2 width=1 by pr_after_unit_sn/ #V10s #HV10s #HV120s

     >(liftsv_mono … HV12s … HV10s) -V1s //
   | @(acr_lifts … H1RP … HB … HV120) /3 width=2 by drops_refl, drops_drop/
   ]
     >(liftsv_mono … HV12s … HV10s) -V1s //
   | @(acr_lifts … H1RP … HB … HV120) /3 width=2 by drops_refl, drops_drop/
   ]

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubf.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubf.ma
index 8e63f58d2731c9390fe1ae767dca6e9ad6effec5..be342a26bd8ba9c31df6b3341a301bd67d4d5022 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/lsubf.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubf.ma
@@ -24,7 +24,7 @@ include "static_2/static/frees.ma".
 
 (* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
 
 
 (* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
 

-inductive lsubf: relation4 lenv rtmap lenv rtmap ≝
+inductive lsubf: relation4 lenv pr_map lenv pr_map ≝

 | lsubf_atom: ∀f1,f2. f1 ≡ f2 → lsubf (⋆) f1 (⋆) f2
 | lsubf_push: ∀f1,f2,I1,I2,L1,L2. lsubf L1 (f1) L2 (f2) →
               lsubf (L1.ⓘ[I1]) (⫯f1) (L2.ⓘ[I2]) (⫯f2)
 | lsubf_atom: ∀f1,f2. f1 ≡ f2 → lsubf (⋆) f1 (⋆) f2
 | lsubf_push: ∀f1,f2,I1,I2,L1,L2. lsubf L1 (f1) L2 (f2) →
               lsubf (L1.ⓘ[I1]) (⫯f1) (L2.ⓘ[I2]) (⫯f2)


@@ -64,10 +64,10 @@ fact lsubf_inv_push1_aux:
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J1 #K1 #_ #H destruct
 | #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g1 #J1 #K1 #H1 #H2 destruct
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J1 #K1 #_ #H destruct
 | #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g1 #J1 #K1 #H1 #H2 destruct

-  <(injective_push … H1) -g1 /2 width=6 by ex3_3_intro/
-| #f1 #f2 #I #L1 #L2 #_ #g1 #J1 #K1 #H elim (discr_next_push … H)
-| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g1 #J1 #K1 #H elim (discr_next_push … H)
-| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g1 #J1 #K1 #H elim (discr_next_push … H)
+  <(eq_inv_pr_push_bi … H1) -g1 /2 width=6 by ex3_3_intro/
+| #f1 #f2 #I #L1 #L2 #_ #g1 #J1 #K1 #H elim (eq_inv_pr_next_push … H)
+| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g1 #J1 #K1 #H elim (eq_inv_pr_next_push … H)
+| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g1 #J1 #K1 #H elim (eq_inv_pr_next_push … H)

 ]
 qed-.
 
 ]
 qed-.
 


@@ -87,13 +87,13 @@ fact lsubf_inv_pair1_aux:
           K1 ⊢ 𝐅+❪X❫ ≘ g & g0 ⋓ g ≘ g1 & f2 = ↑g2 & L2 = K2.ⓤ[J].
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J #K1 #X #_ #H destruct
           K1 ⊢ 𝐅+❪X❫ ≘ g & g0 ⋓ g ≘ g1 & f2 = ↑g2 & L2 = K2.ⓤ[J].
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J #K1 #X #_ #H destruct

-| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g1 #J #K1 #X #H elim (discr_push_next … H)
+| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g1 #J #K1 #X #H elim (eq_inv_pr_push_next … H)

 | #f1 #f2 #I #L1 #L2 #H12 #g1 #J #K1 #X #H1 #H2 destruct
 | #f1 #f2 #I #L1 #L2 #H12 #g1 #J #K1 #X #H1 #H2 destruct

-  <(injective_next … H1) -g1 /3 width=5 by or3_intro0, ex3_2_intro/
+  <(eq_inv_pr_next_bi … H1) -g1 /3 width=5 by or3_intro0, ex3_2_intro/

 | #f #f0 #f1 #f2 #L1 #L2 #W #V #Hf #Hf1 #H12 #g1 #J #K1 #X #H1 #H2 destruct
 | #f #f0 #f1 #f2 #L1 #L2 #W #V #Hf #Hf1 #H12 #g1 #J #K1 #X #H1 #H2 destruct

-  <(injective_next … H1) -g1 /3 width=12 by or3_intro1, ex7_6_intro/
+  <(eq_inv_pr_next_bi … H1) -g1 /3 width=12 by or3_intro1, ex7_6_intro/

 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #Hf #Hf1 #H12 #g1 #J #K1 #X #H1 #H2 destruct
 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #Hf #Hf1 #H12 #g1 #J #K1 #X #H1 #H2 destruct

-  <(injective_next … H1) -g1 /3 width=10 by or3_intro2, ex5_5_intro/
+  <(eq_inv_pr_next_bi … H1) -g1 /3 width=10 by or3_intro2, ex5_5_intro/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -113,9 +113,9 @@ fact lsubf_inv_unit1_aux:
      ∃∃g2,K2. ❪K1,g1❫ ⫃𝐅+ ❪K2,g2❫ & f2 = ↑g2 & L2 = K2.ⓤ[I].
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J #K1 #_ #H destruct
      ∃∃g2,K2. ❪K1,g1❫ ⫃𝐅+ ❪K2,g2❫ & f2 = ↑g2 & L2 = K2.ⓤ[I].
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J #K1 #_ #H destruct

-| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g1 #J #K1 #H elim (discr_push_next … H)
+| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g1 #J #K1 #H elim (eq_inv_pr_push_next … H)

 | #f1 #f2 #I #L1 #L2 #H12 #g1 #J #K1 #H1 #H2 destruct
 | #f1 #f2 #I #L1 #L2 #H12 #g1 #J #K1 #H1 #H2 destruct

-  <(injective_next … H1) -g1 /2 width=5 by ex3_2_intro/
+  <(eq_inv_pr_next_bi … H1) -g1 /2 width=5 by ex3_2_intro/

 | #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g1 #J #K1 #_ #H destruct
 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g1 #J #K1 #_ #H destruct
 ]
 | #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g1 #J #K1 #_ #H destruct
 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g1 #J #K1 #_ #H destruct
 ]


@@ -148,10 +148,10 @@ fact lsubf_inv_push2_aux:
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J2 #K2 #_ #H destruct
 | #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g2 #J2 #K2 #H1 #H2 destruct
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J2 #K2 #_ #H destruct
 | #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g2 #J2 #K2 #H1 #H2 destruct

-  <(injective_push … H1) -g2 /2 width=6 by ex3_3_intro/
-| #f1 #f2 #I #L1 #L2 #_ #g2 #J2 #K2 #H elim (discr_next_push … H)
-| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g2 #J2 #K2 #H elim (discr_next_push … H)
-| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g2 #J2 #K2 #H elim (discr_next_push … H)
+  <(eq_inv_pr_push_bi … H1) -g2 /2 width=6 by ex3_3_intro/
+| #f1 #f2 #I #L1 #L2 #_ #g2 #J2 #K2 #H elim (eq_inv_pr_next_push … H)
+| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g2 #J2 #K2 #H elim (eq_inv_pr_next_push … H)
+| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g2 #J2 #K2 #H elim (eq_inv_pr_next_push … H)

 ]
 qed-.
 
 ]
 qed-.
 


@@ -169,11 +169,11 @@ fact lsubf_inv_pair2_aux:
           I = Abst & L1 = K1.ⓓⓝW.V.
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J #K2 #X #_ #H destruct
           I = Abst & L1 = K1.ⓓⓝW.V.
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J #K2 #X #_ #H destruct

-| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g2 #J #K2 #X #H elim (discr_push_next … H)
+| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g2 #J #K2 #X #H elim (eq_inv_pr_push_next … H)

 | #f1 #f2 #I #L1 #L2 #H12 #g2 #J #K2 #X #H1 #H2 destruct
 | #f1 #f2 #I #L1 #L2 #H12 #g2 #J #K2 #X #H1 #H2 destruct

-  <(injective_next … H1) -g2 /3 width=5 by ex3_2_intro, or_introl/
+  <(eq_inv_pr_next_bi … H1) -g2 /3 width=5 by ex3_2_intro, or_introl/

 | #f #f0 #f1 #f2 #L1 #L2 #W #V #Hf #Hf1 #H12 #g2 #J #K2 #X #H1 #H2 destruct
 | #f #f0 #f1 #f2 #L1 #L2 #W #V #Hf #Hf1 #H12 #g2 #J #K2 #X #H1 #H2 destruct

-  <(injective_next … H1) -g2 /3 width=10 by ex6_5_intro, or_intror/
+  <(eq_inv_pr_next_bi … H1) -g2 /3 width=10 by ex6_5_intro, or_intror/

 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g2 #J #K2 #X #_ #H destruct
 ]
 qed-.
 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #g2 #J #K2 #X #_ #H destruct
 ]
 qed-.


@@ -194,12 +194,12 @@ fact lsubf_inv_unit2_aux:
           K1 ⊢ 𝐅+❪V❫ ≘ g & g0 ⋓ g ≘ g1 & f1 = ↑g1 & L1 = K1.ⓑ[J]V.
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J #K2 #_ #H destruct
           K1 ⊢ 𝐅+❪V❫ ≘ g & g0 ⋓ g ≘ g1 & f1 = ↑g1 & L1 = K1.ⓑ[J]V.
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J #K2 #_ #H destruct

-| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g2 #J #K2 #H elim (discr_push_next … H)
+| #f1 #f2 #I1 #I2 #L1 #L2 #H12 #g2 #J #K2 #H elim (eq_inv_pr_push_next … H)

 | #f1 #f2 #I #L1 #L2 #H12 #g2 #J #K2 #H1 #H2 destruct
 | #f1 #f2 #I #L1 #L2 #H12 #g2 #J #K2 #H1 #H2 destruct

-  <(injective_next … H1) -g2 /3 width=5 by ex3_2_intro, or_introl/
+  <(eq_inv_pr_next_bi … H1) -g2 /3 width=5 by ex3_2_intro, or_introl/

 | #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g2 #J #K2 #_ #H destruct
 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #Hf #Hf1 #H12 #g2 #J #K2 #H1 #H2 destruct
 | #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #g2 #J #K2 #_ #H destruct
 | #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #Hf #Hf1 #H12 #g2 #J #K2 #H1 #H2 destruct

-  <(injective_next … H1) -g2 /3 width=11 by ex5_6_intro, or_intror/
+  <(eq_inv_pr_next_bi … H1) -g2 /3 width=11 by ex5_6_intro, or_intror/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -262,9 +262,9 @@ qed-.
 lemma lsubf_inv_refl: ∀L,f1,f2. ❪L,f1❫ ⫃𝐅+ ❪L,f2❫ → f1 ≡ f2.
 #L elim L -L /2 width=1 by lsubf_inv_atom/
 #L #I #IH #f1 #f2 #H12
 lemma lsubf_inv_refl: ∀L,f1,f2. ❪L,f1❫ ⫃𝐅+ ❪L,f2❫ → f1 ≡ f2.
 #L elim L -L /2 width=1 by lsubf_inv_atom/
 #L #I #IH #f1 #f2 #H12

-elim (pn_split f1) * #g1 #H destruct
+elim (pr_map_split_tl f1) * #g1 #H destruct

 [ elim (lsubf_inv_push_sn … H12) | elim (lsubf_inv_bind_sn … H12) ] -H12
 [ elim (lsubf_inv_push_sn … H12) | elim (lsubf_inv_bind_sn … H12) ] -H12

-#g2 #H12 #H destruct /3 width=5 by eq_next, eq_push/
+#g2 #H12 #H destruct /3 width=5 by pr_eq_next, pr_eq_push/

 qed-.
 
 (* Basic forward lemmas *****************************************************)
 qed-.
 
 (* Basic forward lemmas *****************************************************)


@@ -272,42 +272,42 @@ qed-.
 lemma lsubf_fwd_bind_tl:
       ∀f1,f2,I,L1,L2. ❪L1.ⓘ[I],f1❫ ⫃𝐅+ ❪L2.ⓘ[I],f2❫ → ❪L1,⫰f1❫ ⫃𝐅+ ❪L2,⫰f2❫.
 #f1 #f2 #I #L1 #L2 #H
 lemma lsubf_fwd_bind_tl:
       ∀f1,f2,I,L1,L2. ❪L1.ⓘ[I],f1❫ ⫃𝐅+ ❪L2.ⓘ[I],f2❫ → ❪L1,⫰f1❫ ⫃𝐅+ ❪L2,⫰f2❫.
 #f1 #f2 #I #L1 #L2 #H

-elim (pn_split f1) * #g1 #H0 destruct
+elim (pr_map_split_tl f1) * #g1 #H0 destruct

 [ elim (lsubf_inv_push_sn … H) | elim (lsubf_inv_bind_sn … H) ] -H
 #g2 #H12 #H destruct //
 qed-.
 
 lemma lsubf_fwd_isid_dx: ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → 𝐈❪f2❫ → 𝐈❪f1❫.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2
 [ elim (lsubf_inv_push_sn … H) | elim (lsubf_inv_bind_sn … H) ] -H
 #g2 #H12 #H destruct //
 qed-.
 
 lemma lsubf_fwd_isid_dx: ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → 𝐈❪f2❫ → 𝐈❪f1❫.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2

-[ /2 width=3 by isid_eq_repl_fwd/
-| /4 width=3 by isid_inv_push, isid_push/
-| #f1 #f2 #I #L1 #L2 #_ #_ #H elim (isid_inv_next … H) -H //
-| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #_ #H elim (isid_inv_next … H) -H //
-| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #_ #H elim (isid_inv_next … H) -H //
+[ /2 width=3 by pr_isi_eq_repl_fwd/
+| /4 width=3 by pr_isi_inv_push, pr_isi_push/
+| #f1 #f2 #I #L1 #L2 #_ #_ #H elim (pr_isi_inv_next … H) -H //
+| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #_ #H elim (pr_isi_inv_next … H) -H //
+| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #_ #H elim (pr_isi_inv_next … H) -H //

 ]
 qed-.
 
 lemma lsubf_fwd_isid_sn: ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → 𝐈❪f1❫ → 𝐈❪f2❫.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2
 ]
 qed-.
 
 lemma lsubf_fwd_isid_sn: ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → 𝐈❪f1❫ → 𝐈❪f2❫.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2

-[ /2 width=3 by isid_eq_repl_back/
-| /4 width=3 by isid_inv_push, isid_push/
-| #f1 #f2 #I #L1 #L2 #_ #_ #H elim (isid_inv_next … H) -H //
-| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #_ #H elim (isid_inv_next … H) -H //
-| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #_ #H elim (isid_inv_next … H) -H //
+[ /2 width=3 by pr_isi_eq_repl_back/
+| /4 width=3 by pr_isi_inv_push, pr_isi_push/
+| #f1 #f2 #I #L1 #L2 #_ #_ #H elim (pr_isi_inv_next … H) -H //
+| #f #f0 #f1 #f2 #L1 #L2 #W #V #_ #_ #_ #_ #H elim (pr_isi_inv_next … H) -H //
+| #f #f0 #f1 #f2 #I1 #I2 #L1 #L2 #V #_ #_ #_ #_ #H elim (pr_isi_inv_next … H) -H //

 ]
 qed-.
 
 lemma lsubf_fwd_sle: ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → f2 ⊆ f1.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2
 ]
 qed-.
 
 lemma lsubf_fwd_sle: ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → f2 ⊆ f1.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2

-/3 width=5 by sor_inv_sle_sn_trans, sle_next, sle_push, sle_refl_eq, eq_sym/
+/3 width=5 by pr_sor_inv_sle_sn_trans, pr_sle_next, pr_sle_push, pr_sle_refl_eq, pr_eq_sym/

 qed-.
 
 (* Basic properties *********************************************************)
 
 qed-.
 
 (* Basic properties *********************************************************)
 

-lemma lsubf_eq_repl_back1: ∀f2,L1,L2. eq_repl_back … (λf1. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).
+lemma lsubf_eq_repl_back1: ∀f2,L1,L2. pr_eq_repl_back … (λf1. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).

 #f2 #L1 #L2 #f #H elim H -f -f2 -L1 -L2
 [ #f1 #f2 #Hf12 #g1 #Hfg1
 #f2 #L1 #L2 #f #H elim H -f -f2 -L1 -L2
 [ #f1 #f2 #Hf12 #g1 #Hfg1

-  /3 width=3 by lsubf_atom, eq_canc_sn/
+  /3 width=3 by lsubf_atom, pr_eq_canc_sn/

 | #f1 #f2 #I1 #I2 #K1 #K2 #_ #IH #g #H
   elim (eq_inv_px … H) -H [|*: // ] #g1 #Hfg1 #H destruct
   /3 width=1 by lsubf_push/
 | #f1 #f2 #I1 #I2 #K1 #K2 #_ #IH #g #H
   elim (eq_inv_px … H) -H [|*: // ] #g1 #Hfg1 #H destruct
   /3 width=1 by lsubf_push/


@@ -316,21 +316,21 @@ lemma lsubf_eq_repl_back1: ∀f2,L1,L2. eq_repl_back … (λf1. ❪L1,f1❫ ⫃
   /3 width=1 by lsubf_bind/
 | #f #f0 #f1 #f2 #K1 #L2 #W #V #Hf #Hf1 #_ #IH #g #H
   elim (eq_inv_nx … H) -H [|*: // ] #g1 #Hfg1 #H destruct
   /3 width=1 by lsubf_bind/
 | #f #f0 #f1 #f2 #K1 #L2 #W #V #Hf #Hf1 #_ #IH #g #H
   elim (eq_inv_nx … H) -H [|*: // ] #g1 #Hfg1 #H destruct

-  /3 width=5 by lsubf_beta, sor_eq_repl_back3/
+  /3 width=5 by lsubf_beta, pr_sor_eq_repl_back/

 | #f #f0 #f1 #f2 #I1 #I2 #K1 #K2 #V #Hf #Hf1 #_ #IH #g #H
   elim (eq_inv_nx … H) -H [|*: // ] #g1 #Hfg1 #H destruct
 | #f #f0 #f1 #f2 #I1 #I2 #K1 #K2 #V #Hf #Hf1 #_ #IH #g #H
   elim (eq_inv_nx … H) -H [|*: // ] #g1 #Hfg1 #H destruct

-  /3 width=5 by lsubf_unit, sor_eq_repl_back3/
+  /3 width=5 by lsubf_unit, pr_sor_eq_repl_back/

 ]
 qed-.
 
 ]
 qed-.
 

-lemma lsubf_eq_repl_fwd1: ∀f2,L1,L2. eq_repl_fwd … (λf1. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).
-#f2 #L1 #L2 @eq_repl_sym /2 width=3 by lsubf_eq_repl_back1/
+lemma lsubf_eq_repl_fwd1: ∀f2,L1,L2. pr_eq_repl_fwd … (λf1. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).
+#f2 #L1 #L2 @pr_eq_repl_sym /2 width=3 by lsubf_eq_repl_back1/

 qed-.
 
 qed-.
 

-lemma lsubf_eq_repl_back2: ∀f1,L1,L2. eq_repl_back … (λf2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).
+lemma lsubf_eq_repl_back2: ∀f1,L1,L2. pr_eq_repl_back … (λf2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).

 #f1 #L1 #L2 #f #H elim H -f1 -f -L1 -L2
 [ #f1 #f2 #Hf12 #g2 #Hfg2
 #f1 #L1 #L2 #f #H elim H -f1 -f -L1 -L2
 [ #f1 #f2 #Hf12 #g2 #Hfg2

-  /3 width=3 by lsubf_atom, eq_trans/
+  /3 width=3 by lsubf_atom, pr_eq_trans/

 | #f1 #f2 #I1 #I2 #K1 #K2 #_ #IH #g #H
   elim (eq_inv_px … H) -H [|*: // ] #g2 #Hfg2 #H destruct
   /3 width=1 by lsubf_push/
 | #f1 #f2 #I1 #I2 #K1 #K2 #_ #IH #g #H
   elim (eq_inv_px … H) -H [|*: // ] #g2 #Hfg2 #H destruct
   /3 width=1 by lsubf_push/


@@ -346,13 +346,13 @@ lemma lsubf_eq_repl_back2: ∀f1,L1,L2. eq_repl_back … (λf2. ❪L1,f1❫ ⫃
 ]
 qed-.
 
 ]
 qed-.
 

-lemma lsubf_eq_repl_fwd2: ∀f1,L1,L2. eq_repl_fwd … (λf2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).
-#f1 #L1 #L2 @eq_repl_sym /2 width=3 by lsubf_eq_repl_back2/
+lemma lsubf_eq_repl_fwd2: ∀f1,L1,L2. pr_eq_repl_fwd … (λf2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫).
+#f1 #L1 #L2 @pr_eq_repl_sym /2 width=3 by lsubf_eq_repl_back2/

 qed-.
 
 lemma lsubf_refl: bi_reflexive … lsubf.
 qed-.
 
 lemma lsubf_refl: bi_reflexive … lsubf.

-#L elim L -L /2 width=1 by lsubf_atom, eq_refl/
-#L #I #IH #f elim (pn_split f) * #g #H destruct
+#L elim L -L /2 width=1 by lsubf_atom, pr_eq_refl/
+#L #I #IH #f elim (pr_map_split_tl f) * #g #H destruct

 /2 width=1 by lsubf_push, lsubf_bind/
 qed.
 
 /2 width=1 by lsubf_push, lsubf_bind/
 qed.
 


@@ -363,7 +363,7 @@ lemma lsubf_bind_tl_dx:
       ∀g1,f2,I,L1,L2. ❪L1,g1❫ ⫃𝐅+ ❪L2,⫰f2❫ →
       ∃∃f1. ❪L1.ⓘ[I],f1❫ ⫃𝐅+ ❪L2.ⓘ[I],f2❫ & g1 = ⫰f1.
 #g1 #f2 #I #L1 #L2 #H
       ∀g1,f2,I,L1,L2. ❪L1,g1❫ ⫃𝐅+ ❪L2,⫰f2❫ →
       ∃∃f1. ❪L1.ⓘ[I],f1❫ ⫃𝐅+ ❪L2.ⓘ[I],f2❫ & g1 = ⫰f1.
 #g1 #f2 #I #L1 #L2 #H

-elim (pn_split f2) * #g2 #H2 destruct
+elim (pr_map_split_tl f2) * #g2 #H2 destruct

 @ex2_intro [1,2,4,5: /2 width=2 by lsubf_push, lsubf_bind/ ] // (**) (* constructor needed *)
 qed-.
 
 @ex2_intro [1,2,4,5: /2 width=2 by lsubf_push, lsubf_bind/ ] // (**) (* constructor needed *)
 qed-.
 


@@ -372,8 +372,8 @@ lemma lsubf_beta_tl_dx:
       ∀f2,L2,W. ❪L1,f0❫ ⫃𝐅+ ❪L2,⫰f2❫ →
       ∃∃f1. ❪L1.ⓓⓝW.V,f1❫ ⫃𝐅+ ❪L2.ⓛW,f2❫ & ⫰f1 ⊆ g1.
 #f #f0 #g1 #L1 #V #Hf #Hg1 #f2
       ∀f2,L2,W. ❪L1,f0❫ ⫃𝐅+ ❪L2,⫰f2❫ →
       ∃∃f1. ❪L1.ⓓⓝW.V,f1❫ ⫃𝐅+ ❪L2.ⓛW,f2❫ & ⫰f1 ⊆ g1.
 #f #f0 #g1 #L1 #V #Hf #Hg1 #f2

-elim (pn_split f2) * #x2 #H2 #L2 #W #HL12 destruct
-[ /3 width=4 by lsubf_push, sor_inv_sle_sn, ex2_intro/
+elim (pr_map_split_tl f2) * #x2 #H2 #L2 #W #HL12 destruct
+[ /3 width=4 by lsubf_push, pr_sor_inv_sle_sn, ex2_intro/

 | @(ex2_intro … (↑g1)) /2 width=5 by lsubf_beta/ (**) (* full auto fails *)
 ]
 qed-.
 | @(ex2_intro … (↑g1)) /2 width=5 by lsubf_beta/ (**) (* full auto fails *)
 ]
 qed-.


@@ -384,32 +384,32 @@ lemma lsubf_inv_sor_dx:
       ∀f2l,f2r. f2l⋓f2r ≘ f2 →
       ∃∃f1l,f1r. ❪L1,f1l❫ ⫃𝐅+ ❪L2,f2l❫ & ❪L1,f1r❫ ⫃𝐅+ ❪L2,f2r❫ & f1l⋓f1r ≘ f1.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2
       ∀f2l,f2r. f2l⋓f2r ≘ f2 →
       ∃∃f1l,f1r. ❪L1,f1l❫ ⫃𝐅+ ❪L2,f2l❫ & ❪L1,f1r❫ ⫃𝐅+ ❪L2,f2r❫ & f1l⋓f1r ≘ f1.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2

-[ /3 width=7 by sor_eq_repl_fwd3, ex3_2_intro/
+[ /3 width=7 by pr_sor_eq_repl_fwd, ex3_2_intro/

 | #g1 #g2 #I1 #I2 #L1 #L2 #_ #IH #f2l #f2r #H
 | #g1 #g2 #I1 #I2 #L1 #L2 #_ #IH #f2l #f2r #H

-  elim (sor_inv_xxp … H) -H [|*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct
-  elim (IH … Hg2) -g2 /3 width=11 by lsubf_push, sor_pp, ex3_2_intro/
+  elim (pr_sor_inv_push … H) -H [|*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct
+  elim (IH … Hg2) -g2 /3 width=11 by lsubf_push, pr_sor_push_bi, ex3_2_intro/

 | #g1 #g2 #I #L1 #L2 #_ #IH #f2l #f2r #H
 | #g1 #g2 #I #L1 #L2 #_ #IH #f2l #f2r #H

-  elim (sor_inv_xxn … H) -H [1,3,4: * |*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct
-  elim (IH … Hg2) -g2 /3 width=11 by lsubf_push, lsubf_bind, sor_np, sor_pn, sor_nn, ex3_2_intro/
+  elim (pr_sor_inv_next … H) -H [1,3,4: * |*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct
+  elim (IH … Hg2) -g2 /3 width=11 by lsubf_push, lsubf_bind, pr_sor_next_push, pr_sor_push_next, pr_sor_next_bi, ex3_2_intro/

 | #g #g0 #g1 #g2 #L1 #L2 #W #V #Hg #Hg1 #_ #IH #f2l #f2r #H
 | #g #g0 #g1 #g2 #L1 #L2 #W #V #Hg #Hg1 #_ #IH #f2l #f2r #H

-  elim (sor_inv_xxn … H) -H [1,3,4: * |*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct
+  elim (pr_sor_inv_next … H) -H [1,3,4: * |*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct

   elim (IH … Hg2) -g2 #g1l #g1r #Hl #Hr #Hg0
   elim (IH … Hg2) -g2 #g1l #g1r #Hl #Hr #Hg0

-  [ lapply (sor_comm_23 … Hg0 Hg1 ?) -g0 [3: |*: // ] #Hg1
-    /3 width=11 by lsubf_push, lsubf_beta, sor_np, ex3_2_intro/
-  | lapply (sor_assoc_dx … Hg1 … Hg0 ??) -g0 [3: |*: // ] #Hg1
-    /3 width=11 by lsubf_push, lsubf_beta, sor_pn, ex3_2_intro/
-  | lapply (sor_distr_dx … Hg0 … Hg1) -g0 [5: |*: // ] #Hg1
-    /3 width=11 by lsubf_beta, sor_nn, ex3_2_intro/
+  [ lapply (pr_sor_comm_23 … Hg0 Hg1 ?) -g0 [3: |*: // ] #Hg1
+    /3 width=11 by lsubf_push, lsubf_beta, pr_sor_next_push, ex3_2_intro/
+  | lapply (pr_sor_assoc_dx … Hg1 … Hg0 ??) -g0 [3: |*: // ] #Hg1
+    /3 width=11 by lsubf_push, lsubf_beta, pr_sor_push_next, ex3_2_intro/
+  | lapply (pr_sor_distr_dx … Hg0 … Hg1) -g0 [5: |*: // ] #Hg1
+    /3 width=11 by lsubf_beta, pr_sor_next_bi, ex3_2_intro/

   ]
 | #g #g0 #g1 #g2 #I1 #I2 #L1 #L2 #V #Hg #Hg1 #_ #IH #f2l #f2r #H
   ]
 | #g #g0 #g1 #g2 #I1 #I2 #L1 #L2 #V #Hg #Hg1 #_ #IH #f2l #f2r #H

-  elim (sor_inv_xxn … H) -H [1,3,4: * |*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct
+  elim (pr_sor_inv_next … H) -H [1,3,4: * |*: // ] #g2l #g2r #Hg2 #Hl #Hr destruct

   elim (IH … Hg2) -g2 #g1l #g1r #Hl #Hr #Hg0
   elim (IH … Hg2) -g2 #g1l #g1r #Hl #Hr #Hg0

-  [ lapply (sor_comm_23 … Hg0 Hg1 ?) -g0 [3: |*: // ] #Hg1
-    /3 width=11 by lsubf_push, lsubf_unit, sor_np, ex3_2_intro/
-  | lapply (sor_assoc_dx … Hg1 … Hg0 ??) -g0 [3: |*: // ] #Hg1
-    /3 width=11 by lsubf_push, lsubf_unit, sor_pn, ex3_2_intro/
-  | lapply (sor_distr_dx … Hg0 … Hg1) -g0 [5: |*: // ] #Hg1
-    /3 width=11 by lsubf_unit, sor_nn, ex3_2_intro/
+  [ lapply (pr_sor_comm_23 … Hg0 Hg1 ?) -g0 [3: |*: // ] #Hg1
+    /3 width=11 by lsubf_push, lsubf_unit, pr_sor_next_push, ex3_2_intro/
+  | lapply (pr_sor_assoc_dx … Hg1 … Hg0 ??) -g0 [3: |*: // ] #Hg1
+    /3 width=11 by lsubf_push, lsubf_unit, pr_sor_push_next, ex3_2_intro/
+  | lapply (pr_sor_distr_dx … Hg0 … Hg1) -g0 [5: |*: // ] #Hg1
+    /3 width=11 by lsubf_unit, pr_sor_next_bi, ex3_2_intro/

   ]
 ]
 qed-.
   ]
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma
index de32a2f006af60383aa4c1c062b612c6c942441b..e36bc6729a3973a630ef35609dbab14eac26960a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma
@@ -25,9 +25,9 @@ lemma lsubf_frees_trans:
 [ /3 width=5 by lsubf_fwd_isid_dx, frees_sort/
 | #f2 #i #Hf2 #g1 #Y1 #H
   elim (lsubf_inv_atom2 … H) -H #Hg1 #H destruct
 [ /3 width=5 by lsubf_fwd_isid_dx, frees_sort/
 | #f2 #i #Hf2 #g1 #Y1 #H
   elim (lsubf_inv_atom2 … H) -H #Hg1 #H destruct

-  elim (eq_inv_pushs_dx … Hg1) -Hg1 #g #Hg #H destruct
+  elim (pr_eq_inv_pushs_dx … Hg1) -Hg1 #g #Hg #H destruct

   elim (eq_inv_xn … Hg) -Hg
   elim (eq_inv_xn … Hg) -Hg

-  /3 width=3 by frees_atom, isid_eq_repl_fwd/
+  /3 width=3 by frees_atom, pr_isi_eq_repl_fwd/

 | #f2 #I #K2 #W #_ #IH #g1 #Y1 #H elim (lsubf_inv_pair2 … H) -H *
   [ #f1 #K1 #H12 #H1 #H2 destruct /3 width=1 by frees_pair/
   | #f #f0 #f1 #K1 #V #H12 #Hf #Hf1 #H1 #H2 #H3 destruct
 | #f2 #I #K2 #W #_ #IH #g1 #Y1 #H elim (lsubf_inv_pair2 … H) -H *
   [ #f1 #K1 #H12 #H1 #H2 destruct /3 width=1 by frees_pair/
   | #f #f0 #f1 #K1 #V #H12 #Hf #Hf1 #H1 #H2 #H3 destruct


@@ -37,7 +37,7 @@ lemma lsubf_frees_trans:
   [ #f1 #L1 #H12 #H1 #H2 destruct
     /3 width=5 by lsubf_fwd_isid_dx, frees_unit/
   | #f #f0 #f1 #J #L1 #V #H12 #Hf #Hf1 #H1 #H2 destruct
   [ #f1 #L1 #H12 #H1 #H2 destruct
     /3 width=5 by lsubf_fwd_isid_dx, frees_unit/
   | #f #f0 #f1 #J #L1 #V #H12 #Hf #Hf1 #H1 #H2 destruct

-    /5 width=9 by lsubf_fwd_isid_dx, frees_eq_repl_back, frees_pair, sor_isid_inv_sn/
+    /5 width=9 by lsubf_fwd_isid_dx, frees_eq_repl_back, frees_pair, pr_sor_inv_isi_sn/

   ]
 | #f2 #I #L2 #i #_ #IH #g1 #L1 #H elim (lsubf_inv_push2 … H) -H
   /3 width=1 by frees_lref/
   ]
 | #f2 #I #L2 #i #_ #IH #g1 #L1 #H elim (lsubf_inv_push2 … H) -H
   /3 width=1 by frees_lref/

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma
index 7d162a58ed9fdc7c84dffe124c4e4c353de6fdd3..8ad9f517d929336cd921b0fe86e8f7fe0801563c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma
@@ -27,16 +27,16 @@ theorem lsubf_sor:
 [ #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
   elim (lsubf_inv_atom1 … H1) -H1 #H1 #H destruct
   lapply (lsubf_inv_atom … H2) -H2 #H2
 [ #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
   elim (lsubf_inv_atom1 … H1) -H1 #H1 #H destruct
   lapply (lsubf_inv_atom … H2) -H2 #H2

-  /5 width=4 by lsubf_atom, sor_mono, sor_eq_repl_back2, sor_eq_repl_back1/
+  /5 width=4 by lsubf_atom, pr_sor_mono, pr_sor_eq_repl_back_dx, pr_sor_eq_repl_back_sn/

 | #K #J #IH #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
 | #K #J #IH #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf

-  elim (pn_split g1) * #y1 #H destruct
-  elim (pn_split g2) * #y2 #H destruct
-  [ elim (sor_inv_ppx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+  elim (pr_map_split_tl g1) * #y1 #H destruct
+  elim (pr_map_split_tl g2) * #y2 #H destruct
+  [ elim (pr_sor_inv_push_bi … Hg) -Hg [|*: // ] #y #Hy #H destruct

     elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
     elim (lsubf_inv_push_sn … H2) -H2 #x2 #H2 #H destruct
     elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
     elim (lsubf_inv_push_sn … H2) -H2 #x2 #H2 #H destruct

-    elim (sor_inv_ppx … Hf) -Hf [|*: // ] #x #Hx #H destruct
+    elim (pr_sor_inv_push_bi … Hf) -Hf [|*: // ] #x #Hx #H destruct

     /3 width=8 by lsubf_push/
     /3 width=8 by lsubf_push/

-  | elim (sor_inv_pnx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+  | elim (pr_sor_inv_push_next … Hg) -Hg [|*: // ] #y #Hy #H destruct

     elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
     generalize in match H2; -H2 cases J -J #J [| #V ] #H2
     [ elim (lsubf_inv_unit1 … H2) -H2 #x2 #Y2 #H2 #H #H0 destruct
     elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
     generalize in match H2; -H2 cases J -J #J [| #V ] #H2
     [ elim (lsubf_inv_unit1 … H2) -H2 #x2 #Y2 #H2 #H #H0 destruct


@@ -46,9 +46,9 @@ theorem lsubf_sor:
       | #y3 #y4 #x2 #Z2 #Y2 #H2 #Hy3 #Hy2 #H #H0 destruct
       ]
     ]
       | #y3 #y4 #x2 #Z2 #Y2 #H2 #Hy3 #Hy2 #H #H0 destruct
       ]
     ]

-    elim (sor_inv_pnx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
-    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_assoc_sn/
-  | elim (sor_inv_npx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (pr_sor_inv_push_next … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, pr_sor_assoc_sn/
+  | elim (pr_sor_inv_next_push … Hg) -Hg [|*: // ] #y #Hy #H destruct

     elim (lsubf_inv_push1 … H2) -H2 #x2 #Z2 #Y2 #H2 #H #H0 destruct
     generalize in match H1; -H1 cases J -J #J [| #V ] #H1
     [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
     elim (lsubf_inv_push1 … H2) -H2 #x2 #Z2 #Y2 #H2 #H #H0 destruct
     generalize in match H1; -H1 cases J -J #J [| #V ] #H1
     [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct


@@ -58,9 +58,9 @@ theorem lsubf_sor:
       | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
       ]
     ]
       | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
       ]
     ]

-    elim (sor_inv_npx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
-    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_comm_23/
-  | elim (sor_inv_nnx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (pr_sor_inv_next_push … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, pr_sor_comm_23/
+  | elim (pr_sor_inv_next_bi … Hg) -Hg [|*: // ] #y #Hy #H destruct

     generalize in match H2; generalize in match H1; -H1 -H2 cases J -J #J [| #V ] #H1 #H2
     [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
       elim (lsubf_inv_bind_sn … H2) -H2 #x2 #H2 #H destruct
     generalize in match H2; generalize in match H1; -H1 -H2 cases J -J #J [| #V ] #H1 #H2
     [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
       elim (lsubf_inv_bind_sn … H2) -H2 #x2 #H2 #H destruct


@@ -70,15 +70,15 @@ theorem lsubf_sor:
       | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
         elim (lsubf_inv_beta_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
         lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3
       | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
         elim (lsubf_inv_beta_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
         lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3

-        lapply (sor_eq_repl_back2 … Hy2 … H3) -z3 #Hy2
+        lapply (pr_sor_eq_repl_back_dx … Hy2 … H3) -z3 #Hy2

       | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
         elim (lsubf_inv_unit_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
         lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3
       | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
         elim (lsubf_inv_unit_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
         lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3

-        lapply (sor_eq_repl_back2 … Hy2 … H3) -z3 #Hy2
+        lapply (pr_sor_eq_repl_back_dx … Hy2 … H3) -z3 #Hy2

       ]
     ]
       ]
     ]

-    elim (sor_inv_nnx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
-    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_coll_dx/
+    elim (pr_sor_inv_next_bi … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, pr_sor_coll_dx/

   ]
 ]
 qed-.
   ]
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubr.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubr.ma
index 3e0ce90bac2bd904bfd82808972c1818c8c6101f..3d4448a68811cf0c3f1c18b105d794ccce90a48e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubr.ma
@@ -22,11 +22,11 @@ include "static_2/static/lsubf_lsubf.ma".
 lemma lsubf_fwd_lsubr_isdiv:
       ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → 𝛀❪f1❫ → 𝛀❪f2❫ → L1 ⫃ L2.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2
 lemma lsubf_fwd_lsubr_isdiv:
       ∀f1,f2,L1,L2. ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫ → 𝛀❪f1❫ → 𝛀❪f2❫ → L1 ⫃ L2.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2

-/4 width=3 by lsubr_bind, isdiv_inv_next/
+/4 width=3 by lsubr_bind, pr_isd_inv_next/

 [ #f1 #f2 #I1 #I2 #L1 #L2 #_ #_ #H
 [ #f1 #f2 #I1 #I2 #L1 #L2 #_ #_ #H

-  elim (isdiv_inv_push … H) //
-| /5 width=5 by lsubf_fwd_sle, lsubr_beta, sle_inv_isdiv_sn, isdiv_inv_next/
-| /5 width=5 by lsubf_fwd_sle, lsubr_unit, sle_inv_isdiv_sn, isdiv_inv_next/
+  elim (pr_isd_inv_push … H) //
+| /5 width=5 by lsubf_fwd_sle, lsubr_beta, pr_sle_inv_isd_sn, pr_isd_inv_next/
+| /5 width=5 by lsubf_fwd_sle, lsubr_unit, pr_sle_inv_isd_sn, pr_isd_inv_next/

 ]
 qed-.
 
 ]
 qed-.
 


@@ -35,12 +35,12 @@ qed-.
 lemma lsubr_lsubf_isid:
       ∀L1,L2. L1 ⫃ L2 → ∀f1,f2. 𝐈❪f1❫ → 𝐈❪f2❫ → ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫.
 #L1 #L2 #H elim H -L1 -L2
 lemma lsubr_lsubf_isid:
       ∀L1,L2. L1 ⫃ L2 → ∀f1,f2. 𝐈❪f1❫ → 𝐈❪f2❫ → ❪L1,f1❫ ⫃𝐅+ ❪L2,f2❫.
 #L1 #L2 #H elim H -L1 -L2

-[ /3 width=1 by lsubf_atom, isid_inv_eq_repl/
+[ /3 width=1 by lsubf_atom, pr_isi_inv_eq_repl/

 | #I #L1 #L2 | #L1 #L2 #V #W | #I1 #I2 #L1 #L2 #V
 ]
 #_ #IH #f1 #f2 #Hf1 #Hf2
 | #I #L1 #L2 | #L1 #L2 #V #W | #I1 #I2 #L1 #L2 #V
 ]
 #_ #IH #f1 #f2 #Hf1 #Hf2

-elim (isid_inv_gen … Hf1) -Hf1 #g1 #Hg1 #H destruct
-elim (isid_inv_gen … Hf2) -Hf2 #g2 #Hg2 #H destruct
+elim (pr_isi_inv_gen … Hf1) -Hf1 #g1 #Hg1 #H destruct
+elim (pr_isi_inv_gen … Hf2) -Hf2 #g2 #Hg2 #H destruct

 /3 width=1 by lsubf_push/
 qed.
 
 /3 width=1 by lsubf_push/
 qed.
 


@@ -53,7 +53,7 @@ lemma lsubr_lsubf:
 | #f2 #i #Hf2 #Y1 #HY1
   >(lsubr_inv_atom2 … HY1) -Y1 #g1 #Hg1
   elim (frees_inv_atom … Hg1) -Hg1 #f1 #Hf1 #H destruct
 | #f2 #i #Hf2 #Y1 #HY1
   >(lsubr_inv_atom2 … HY1) -Y1 #g1 #Hg1
   elim (frees_inv_atom … Hg1) -Hg1 #f1 #Hf1 #H destruct

-  /5 width=5 by lsubf_atom, isid_inv_eq_repl, pushs_eq_repl, eq_next/
+  /5 width=5 by lsubf_atom, pr_isi_inv_eq_repl, pr_pushs_eq_repl, pr_eq_next/

 | #f2 #Z #L2 #W #_ #IH #Y1 #HY1 #g1 #Hg1 elim (lsubr_inv_pair2 … HY1) -HY1 *
   [ #L1 #HL12 #H destruct
     elim (frees_inv_pair … Hg1) -Hg1 #f1 #Hf1 #H destruct
 | #f2 #Z #L2 #W #_ #IH #Y1 #HY1 #g1 #Hg1 elim (lsubr_inv_pair2 … HY1) -HY1 *
   [ #L1 #HL12 #H destruct
     elim (frees_inv_pair … Hg1) -Hg1 #f1 #Hf1 #H destruct


@@ -68,7 +68,7 @@ lemma lsubr_lsubf:
     /3 width=1 by lsubf_bind, lsubr_lsubf_isid/
   | #I #L1 #V #HL12 #H destruct
     elim (frees_inv_pair … Hg1) -Hg1 #f1 #Hf1 #H destruct
     /3 width=1 by lsubf_bind, lsubr_lsubf_isid/
   | #I #L1 #V #HL12 #H destruct
     elim (frees_inv_pair … Hg1) -Hg1 #f1 #Hf1 #H destruct

-    /3 width=5 by lsubf_unit, sor_isid_sn, lsubr_lsubf_isid/
+    /3 width=5 by lsubf_unit, pr_sor_isi_sn, lsubr_lsubf_isid/

   ]
 | #f2 #I2 #L2 #i #_ #IH #Y1 #HY1 #g1 #Hg1
   elim (lsubr_fwd_bind2 … HY1) -HY1 #I1 #L1 #HL12 #H destruct
   ]
 | #f2 #I2 #L2 #i #_ #IH #Y1 #HY1 #g1 #Hg1
   elim (lsubr_fwd_bind2 … HY1) -HY1 #I1 #L1 #HL12 #H destruct

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/req.ma b/matita/matita/contribs/lambdadelta/static_2/static/req.ma
index 59efd1af8f640cbc0d1d2b43902467c7c75fe214..93aaafbb476cce6360568ec5ef210f98357bcb23 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/req.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/req.ma
@@ -20,7 +20,7 @@ include "static_2/static/reqg.ma".
 
 (* Basic_2A1: was: lleq *)
 definition req: relation3 term lenv lenv ≝
 
 (* Basic_2A1: was: lleq *)
 definition req: relation3 term lenv lenv ≝

-           reqg (eq …).
+           reqg (pr_eq …).

 
 interpretation
   "syntactic equivalence on referred entries (local environment)"
 
 interpretation
   "syntactic equivalence on referred entries (local environment)"

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqg.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqg.ma
index 1c5d5ed9074426338777e671831f42b7d0ed6f8f..93f10a93d4a2359ea0b16e54243cff51b75ea663 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/reqg.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/reqg.ma
@@ -59,10 +59,10 @@ lemma frees_teqg_conf_seqg (S):
   >(teqg_inv_gref1 … H1) -X /2 width=1 by frees_gref/
 | #f1V #f1T #f1 #p #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #X #H1
   elim (teqg_inv_pair1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H1 #L2 #HL12 destruct
   >(teqg_inv_gref1 … H1) -X /2 width=1 by frees_gref/
 | #f1V #f1T #f1 #p #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #X #H1
   elim (teqg_inv_pair1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H1 #L2 #HL12 destruct

-  /6 width=5 by frees_bind, sex_inv_tl, ext2_pair, sle_sex_trans, sor_inv_sle_dx, sor_inv_sle_sn/
+  /6 width=5 by frees_bind, sex_inv_tl, ext2_pair, sle_sex_trans, pr_sor_inv_sle_dx, pr_sor_inv_sle_sn/

 | #f1V #f1T #f1 #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #X #H1
   elim (teqg_inv_pair1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H1 #L2 #HL12 destruct
 | #f1V #f1T #f1 #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #X #H1
   elim (teqg_inv_pair1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H1 #L2 #HL12 destruct

-  /5 width=5 by frees_flat, sle_sex_trans, sor_inv_sle_dx, sor_inv_sle_sn/
+  /5 width=5 by frees_flat, sle_sex_trans, pr_sor_inv_sle_dx, pr_sor_inv_sle_sn/

 ]
 qed-.
 
 ]
 qed-.
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqg_reqg.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqg_reqg.ma
index cb01ec66296453a6a5401902b3e8fa481670e78e..c5ad7a7b7f7b92ec0b337ed82b503f05ff35a985 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/reqg_reqg.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/reqg_reqg.ma
@@ -33,7 +33,7 @@ lemma reqg_fsle_comp (S):
       rex_fsle_compatible (ceqg S).
 #S #HS #L1 #L2 #T #HL12
 elim (frees_total L1 T) #f #Hf
       rex_fsle_compatible (ceqg S).
 #S #HS #L1 #L2 #T #HL12
 elim (frees_total L1 T) #f #Hf

-/4 width=8 by frees_reqg_conf, rex_fwd_length, lveq_length_eq, sle_refl, ex4_4_intro/
+/4 width=8 by frees_reqg_conf, rex_fwd_length, lveq_length_eq, pr_sle_refl, ex4_4_intro/

 qed.
 
 (* Advanced properties ******************************************************)
 qed.
 
 (* Advanced properties ******************************************************)

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex.ma
index 0eb1164eb652cf0b626e63d5b3dcd3ae95e6f2b7..45e9028d70ff7668af576eca059b5e9bb3fdbbd6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex.ma
@@ -80,7 +80,7 @@ lemma rex_inv_sort (R):
 #R * [ | #Y1 #I1 ] #Y2 #s * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | lapply (frees_inv_sort … H1) -H1 #Hf
 #R * [ | #Y1 #I1 ] #Y2 #s * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | lapply (frees_inv_sort … H1) -H1 #Hf

-  elim (isid_inv_gen … Hf) -Hf #g #Hg #H destruct
+  elim (pr_isi_inv_gen … Hf) -Hf #g #Hg #H destruct

   elim (sex_inv_push1 … H2) -H2 #I2 #L2 #H12 #_ #H destruct
   /5 width=7 by frees_sort, ex3_4_intro, ex2_intro, or_intror/
 ]
   elim (sex_inv_push1 … H2) -H2 #I2 #L2 #H12 #_ #H destruct
   /5 width=7 by frees_sort, ex3_4_intro, ex2_intro, or_intror/
 ]


@@ -122,7 +122,7 @@ lemma rex_inv_gref (R):
 #R * [ | #Y1 #I1 ] #Y2 #l * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | lapply (frees_inv_gref … H1) -H1 #Hf
 #R * [ | #Y1 #I1 ] #Y2 #l * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | lapply (frees_inv_gref … H1) -H1 #Hf

-  elim (isid_inv_gen … Hf) -Hf #g #Hg #H destruct
+  elim (pr_isi_inv_gen … Hf) -Hf #g #Hg #H destruct

   elim (sex_inv_push1 … H2) -H2 #I2 #L2 #H12 #_ #H destruct
   /5 width=7 by frees_gref, ex3_4_intro, ex2_intro, or_intror/
 ]
   elim (sex_inv_push1 … H2) -H2 #I2 #L2 #H12 #_ #H destruct
   /5 width=7 by frees_gref, ex3_4_intro, ex2_intro, or_intror/
 ]


@@ -133,7 +133,7 @@ lemma rex_inv_bind (R):
       ∀p,I,L1,L2,V1,V2,T. L1 ⪤[R,ⓑ[p,I]V1.T] L2 → R L1 V1 V2 →
       ∧∧ L1 ⪤[R,V1] L2 & L1.ⓑ[I]V1 ⪤[R,T] L2.ⓑ[I]V2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f #Hf #HL #HV elim (frees_inv_bind … Hf) -Hf
       ∀p,I,L1,L2,V1,V2,T. L1 ⪤[R,ⓑ[p,I]V1.T] L2 → R L1 V1 V2 →
       ∧∧ L1 ⪤[R,V1] L2 & L1.ⓑ[I]V1 ⪤[R,T] L2.ⓑ[I]V2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f #Hf #HL #HV elim (frees_inv_bind … Hf) -Hf

-/6 width=6 by sle_sex_trans, sex_inv_tl, ext2_pair, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
+/6 width=6 by sle_sex_trans, sex_inv_tl, ext2_pair, pr_sor_inv_sle_dx, pr_sor_inv_sle_sn, ex2_intro, conj/

 qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_flat *)
 qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_flat *)


@@ -141,7 +141,7 @@ lemma rex_inv_flat (R):
       ∀I,L1,L2,V,T. L1 ⪤[R,ⓕ[I]V.T] L2 →
       ∧∧ L1 ⪤[R,V] L2 & L1 ⪤[R,T] L2.
 #R #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_flat … Hf) -Hf
       ∀I,L1,L2,V,T. L1 ⪤[R,ⓕ[I]V.T] L2 →
       ∧∧ L1 ⪤[R,V] L2 & L1 ⪤[R,T] L2.
 #R #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_flat … Hf) -Hf

-/5 width=6 by sle_sex_trans, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
+/5 width=6 by sle_sex_trans, pr_sor_inv_sle_dx, pr_sor_inv_sle_sn, ex2_intro, conj/

 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 qed-.
 
 (* Advanced inversion lemmas ************************************************)


@@ -255,7 +255,7 @@ lemma rex_fwd_pair_sn (R):
       ∀I,L1,L2,V,T. L1 ⪤[R,②[I]V.T] L2 → L1 ⪤[R,V] L2.
 #R * [ #p ] #I #L1 #L2 #V #T * #f #Hf #HL
 [ elim (frees_inv_bind … Hf) | elim (frees_inv_flat … Hf) ] -Hf
       ∀I,L1,L2,V,T. L1 ⪤[R,②[I]V.T] L2 → L1 ⪤[R,V] L2.
 #R * [ #p ] #I #L1 #L2 #V #T * #f #Hf #HL
 [ elim (frees_inv_bind … Hf) | elim (frees_inv_flat … Hf) ] -Hf

-/4 width=6 by sle_sex_trans, sor_inv_sle_sn, ex2_intro/
+/4 width=6 by sle_sex_trans, pr_sor_inv_sle_sn, ex2_intro/

 qed-.
 
 (* Basic_2A1: uses: llpx_sn_fwd_bind_dx llpx_sn_fwd_bind_O_dx *)
 qed-.
 
 (* Basic_2A1: uses: llpx_sn_fwd_bind_dx llpx_sn_fwd_bind_O_dx *)


@@ -274,7 +274,7 @@ qed-.
 lemma rex_fwd_dx (R):
       ∀I2,L1,K2,T. L1 ⪤[R,T] K2.ⓘ[I2] →
       ∃∃I1,K1. L1 = K1.ⓘ[I1].
 lemma rex_fwd_dx (R):
       ∀I2,L1,K2,T. L1 ⪤[R,T] K2.ⓘ[I2] →
       ∃∃I1,K1. L1 = K1.ⓘ[I1].

-#R #I2 #L1 #K2 #T * #f elim (pn_split f) * #g #Hg #_ #Hf destruct
+#R #I2 #L1 #K2 #T * #f elim (pr_map_split_tl f) * #g #Hg #_ #Hf destruct

 [ elim (sex_inv_push2 … Hf) | elim (sex_inv_next2 … Hf) ] -Hf #I1 #K1 #_ #_ #H destruct
 /2 width=3 by ex1_2_intro/
 qed-.
 [ elim (sex_inv_push2 … Hf) | elim (sex_inv_next2 … Hf) ] -Hf #I1 #K1 #_ #_ #H destruct
 /2 width=3 by ex1_2_intro/
 qed-.


@@ -290,7 +290,7 @@ lemma rex_sort (R):
       ∀I1,I2,L1,L2,s. L1 ⪤[R,⋆s] L2 → L1.ⓘ[I1] ⪤[R,⋆s] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #s * #f #Hf #H12
 lapply (frees_inv_sort … Hf) -Hf
       ∀I1,I2,L1,L2,s. L1 ⪤[R,⋆s] L2 → L1.ⓘ[I1] ⪤[R,⋆s] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #s * #f #Hf #H12
 lapply (frees_inv_sort … Hf) -Hf

-/4 width=3 by frees_sort, sex_push, isid_push, ex2_intro/
+/4 width=3 by frees_sort, sex_push, pr_isi_push, ex2_intro/

 qed.
 
 lemma rex_pair (R):
 qed.
 
 lemma rex_pair (R):


@@ -314,7 +314,7 @@ lemma rex_gref (R):
       ∀I1,I2,L1,L2,l. L1 ⪤[R,§l] L2 → L1.ⓘ[I1] ⪤[R,§l] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #l * #f #Hf #H12
 lapply (frees_inv_gref … Hf) -Hf
       ∀I1,I2,L1,L2,l. L1 ⪤[R,§l] L2 → L1.ⓘ[I1] ⪤[R,§l] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #l * #f #Hf #H12
 lapply (frees_inv_gref … Hf) -Hf

-/4 width=3 by frees_gref, sex_push, isid_push, ex2_intro/
+/4 width=3 by frees_gref, sex_push, pr_isi_push, ex2_intro/

 qed.
 
 lemma rex_bind_repl_dx (R):
 qed.
 
 lemma rex_bind_repl_dx (R):

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.ma
index 0638328413af4dde3459582c0a94e59d2df9ab22..5454bc0325ca121227266112eea5744798e26033 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.ma
@@ -30,7 +30,7 @@ lemma rex_pair_refl (R):
       ∀L,V1,V2. R L V1 V2 → ∀I,T. L.ⓑ[I]V1 ⪤[R,T] L.ⓑ[I]V2.
 #R #HR #L #V1 #V2 #HV12 #I #T
 elim (frees_total (L.ⓑ[I]V1) T) #f #Hf
       ∀L,V1,V2. R L V1 V2 → ∀I,T. L.ⓑ[I]V1 ⪤[R,T] L.ⓑ[I]V2.
 #R #HR #L #V1 #V2 #HV12 #I #T
 elim (frees_total (L.ⓑ[I]V1) T) #f #Hf

-elim (pn_split f) * #g #H destruct
+elim (pr_map_split_tl f) * #g #H destruct

 /5 width=3 by sex_refl, sex_next, sex_push, ext2_refl, ext2_pair, ex2_intro/
 qed.
 
 /5 width=3 by sex_refl, sex_next, sex_push, ext2_refl, ext2_pair, ex2_intro/
 qed.
 


@@ -39,7 +39,7 @@ qed.
 lemma rex_inv_bind_void (R):
       ∀p,I,L1,L2,V,T. L1 ⪤[R,ⓑ[p,I]V.T] L2 → L1 ⪤[R,V] L2 ∧ L1.ⓧ ⪤[R,T] L2.ⓧ.
 #R #p #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_bind_void … Hf) -Hf
 lemma rex_inv_bind_void (R):
       ∀p,I,L1,L2,V,T. L1 ⪤[R,ⓑ[p,I]V.T] L2 → L1 ⪤[R,V] L2 ∧ L1.ⓧ ⪤[R,T] L2.ⓧ.
 #R #p #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_bind_void … Hf) -Hf

-/6 width=6 by sle_sex_trans, sex_inv_tl, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
+/6 width=6 by sle_sex_trans, sex_inv_tl, pr_sor_inv_sle_dx, pr_sor_inv_sle_sn, ex2_intro, conj/

 qed-.
 
 (* Advanced forward lemmas **************************************************)
 qed-.
 
 (* Advanced forward lemmas **************************************************)

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma
index e3914f23a90f243dd61350a1d8b6de9c4cebe4d2..8e1fbedef5d969f9c58dbb1082a8c6824c39ba07 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma
@@ -83,8 +83,8 @@ lemma rex_pair_sn_split (R1) (R2):
   elim (frees_inv_flat … Hg) #y1 #y2 #H #_ #Hy
 ]
 lapply(frees_mono … H … Hf) -H #H1
   elim (frees_inv_flat … Hg) #y1 #y2 #H #_ #Hy
 ]
 lapply(frees_mono … H … Hf) -H #H1

-lapply (sor_eq_repl_back1 … Hy … H1) -y1 #Hy
-lapply (sor_inv_sle_sn … Hy) -y2 #Hfg
+lapply (pr_sor_eq_repl_back_sn … Hy … H1) -y1 #Hy
+lapply (pr_sor_inv_sle_sn … Hy) -y2 #Hfg

 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2
 lapply (sle_sex_trans … HL1 … Hfg) // #H
 elim (frees_sex_conf_fsge … Hf … H) -Hf -H
 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2
 lapply (sle_sex_trans … HL1 … Hfg) // #H
 elim (frees_sex_conf_fsge … Hf … H) -Hf -H


@@ -100,8 +100,8 @@ lemma rex_flat_dx_split (R1) (R2):
 elim (frees_total L1 (ⓕ[I]V.T)) #g #Hg
 elim (frees_inv_flat … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 elim (frees_total L1 (ⓕ[I]V.T)) #g #Hg
 elim (frees_inv_flat … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2

-lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy
-lapply (sor_inv_sle_dx … Hy) -y1 #Hfg
+lapply (pr_sor_eq_repl_back_dx … Hy … H2) -y2 #Hy
+lapply (pr_sor_inv_sle_dx … Hy) -y1 #Hfg

 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2
 lapply (sle_sex_trans … HL1 … Hfg) // #H
 elim (frees_sex_conf_fsge … Hf … H) -Hf -H
 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2
 lapply (sle_sex_trans … HL1 … Hfg) // #H
 elim (frees_sex_conf_fsge … Hf … H) -Hf -H


@@ -117,10 +117,10 @@ lemma rex_bind_dx_split (R1) (R2):
 elim (frees_total L1 (ⓑ[p,I]V1.T)) #g #Hg
 elim (frees_inv_bind … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 elim (frees_total L1 (ⓑ[p,I]V1.T)) #g #Hg
 elim (frees_inv_bind … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2

-lapply (tl_eq_repl … H2) -H2 #H2
-lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy
-lapply (sor_inv_sle_dx … Hy) -y1 #Hfg
-lapply (sle_inv_tl_sn … Hfg) -Hfg #Hfg
+lapply (pr_tl_eq_repl … H2) -H2 #H2
+lapply (pr_sor_eq_repl_back_dx … Hy … H2) -y2 #Hy
+lapply (pr_sor_inv_sle_dx … Hy) -y1 #Hfg
+lapply (pr_sle_inv_tl_sn … Hfg) -Hfg #Hfg

 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #Y #H #HL2
 lapply (sle_sex_trans … H … Hfg) // #H0
 elim (sex_inv_next1 … H) -H #Z #L #HL1 #H
 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #Y #H #HL2
 lapply (sle_sex_trans … H … Hfg) // #H0
 elim (sex_inv_next1 … H) -H #Z #L #HL1 #H


@@ -138,10 +138,10 @@ lemma rex_bind_dx_split_void (R1) (R2):
 elim (frees_total L1 (ⓑ[p,I]V.T)) #g #Hg
 elim (frees_inv_bind_void … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 elim (frees_total L1 (ⓑ[p,I]V.T)) #g #Hg
 elim (frees_inv_bind_void … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2

-lapply (tl_eq_repl … H2) -H2 #H2
-lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy
-lapply (sor_inv_sle_dx … Hy) -y1 #Hfg
-lapply (sle_inv_tl_sn … Hfg) -Hfg #Hfg
+lapply (pr_tl_eq_repl … H2) -H2 #H2
+lapply (pr_sor_eq_repl_back_dx … Hy … H2) -y2 #Hy
+lapply (pr_sor_inv_sle_dx … Hy) -y1 #Hfg
+lapply (pr_sle_inv_tl_sn … Hfg) -Hfg #Hfg

 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #Y #H #HL2
 lapply (sle_sex_trans … H … Hfg) // #H0
 elim (sex_inv_next1 … H) -H #Z #L #HL1 #H
 elim (sex_sle_split_sn (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #Y #H #HL2
 lapply (sle_sex_trans … H … Hfg) // #H0
 elim (sex_inv_next1 … H) -H #Z #L #HL1 #H

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
index e43cd5459c428d767a8f8596c26c37da0c3dc2fc..3fb780bb8159b0d91f367a749d90ea55405184e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
@@ -24,7 +24,7 @@ lemma rex_lex (R):
       ∀L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤[R,T] L2.
 #R #L1 #L2 * #f #Hf #HL12 #T
 elim (frees_total L1 T) #g #Hg
       ∀L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤[R,T] L2.
 #R #L1 #L2 * #f #Hf #HL12 #T
 elim (frees_total L1 T) #g #Hg

-/4 width=5 by sex_sdj, sdj_isid_sn, ex2_intro/
+/4 width=5 by sex_sdj, pr_sdj_isi_sn, ex2_intro/

 qed.
 
 (* Inversion lemmas with generic extension of a context sensitive relation **)
 qed.
 
 (* Inversion lemmas with generic extension of a context sensitive relation **)


@@ -36,9 +36,9 @@ lemma rex_inv_req_lex (R):
 #R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
 elim (sex_sdj_split_dx … ceq_ext … HL 𝐢) -HL
 [ #L0 #HL10 #HL02
 #R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
 elim (sex_sdj_split_dx … ceq_ext … HL 𝐢) -HL
 [ #L0 #HL10 #HL02

-  lapply (sex_sdj … HL02 f1 ?) /2 width=1 by sdj_isid_sn/ #H
+  lapply (sex_sdj … HL02 f1 ?) /2 width=1 by pr_sdj_isi_sn/ #H

   /3 width=5 by (* 2x *) ex2_intro/
   /3 width=5 by (* 2x *) ex2_intro/

-|*: /2 width=1 by ext2_refl, sdj_isid_dx/
+|*: /2 width=1 by ext2_refl, pr_sdj_isi_dx/

   #g #I #K #n #HLK #Hg @H2R /width=7 by/ (**) (* no auto with H2R *)
 ]
 qed-.
   #g #I #K #n #HLK #Hg @H2R /width=7 by/ (**) (* no auto with H2R *)
 ]
 qed-.


@@ -51,8 +51,8 @@ lemma rex_fwd_lex_req (R):
       ∃∃L. L1 ⪤[R] L & L ≡[T] L2.
 #R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
 elim (sex_sdj_split_sn … ceq_ext … HL 𝐢 ?) -HL
       ∃∃L. L1 ⪤[R] L & L ≡[T] L2.
 #R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
 elim (sex_sdj_split_sn … ceq_ext … HL 𝐢 ?) -HL

-[ #L0 #HL10 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ] -H1R
-lapply (sex_sdj … HL10 f1 ?) /2 width=1 by sdj_isid_sn/ #H
+[ #L0 #HL10 #HL02 |*: /2 width=1 by ext2_refl, pr_sdj_isi_dx/ ] -H1R
+lapply (sex_sdj … HL10 f1 ?) /2 width=1 by pr_sdj_isi_sn/ #H

 elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01
 /4 width=7 by sle_sex_trans, (* 2x *) ex2_intro/
 qed-.
 elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01
 /4 width=7 by sle_sex_trans, (* 2x *) ex2_intro/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma
index ba250697aa4eb12fcc0a19feb494101870cba3d1..e3d0aee798028727edb627f6db86e6504e38d2a5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_rex.ma
@@ -45,22 +45,22 @@ theorem rex_bind (R) (p) (I):
         ∀L1,L2,V1,V2,T. L1 ⪤[R,V1] L2 → L1.ⓑ[I]V1 ⪤[R,T] L2.ⓑ[I]V2 →
         L1 ⪤[R,ⓑ[p,I]V1.T] L2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
         ∀L1,L2,V1,V2,T. L1 ⪤[R,V1] L2 → L1.ⓑ[I]V1 ⪤[R,T] L2.ⓑ[I]V2 →
         L1 ⪤[R,ⓑ[p,I]V1.T] L2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2

-lapply (sex_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫰f2))
-/3 width=7 by frees_fwd_isfin, frees_bind, sex_join, isfin_tl, ex2_intro/
+lapply (sex_fwd_bind … Hf2) -Hf2 #Hf2 elim (pr_sor_isf_bi f1 (⫰f2))
+/3 width=7 by frees_fwd_isfin, frees_bind, sex_join, pr_isf_tl, ex2_intro/

 qed.
 
 (* Basic_2A1: llpx_sn_flat *)
 theorem rex_flat (R) (I):
         ∀L1,L2,V,T. L1 ⪤[R,V] L2 → L1 ⪤[R,T] L2 → L1 ⪤[R,ⓕ[I]V.T] L2.
 qed.
 
 (* Basic_2A1: llpx_sn_flat *)
 theorem rex_flat (R) (I):
         ∀L1,L2,V,T. L1 ⪤[R,V] L2 → L1 ⪤[R,T] L2 → L1 ⪤[R,ⓕ[I]V.T] L2.

-#R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (sor_isfin_ex f1 f2)
+#R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (pr_sor_isf_bi f1 f2)

 /3 width=7 by frees_fwd_isfin, frees_flat, sex_join, ex2_intro/
 qed.
 
 theorem rex_bind_void (R) (p) (I):
         ∀L1,L2,V,T. L1 ⪤[R,V] L2 → L1.ⓧ ⪤[R,T] L2.ⓧ → L1 ⪤[R,ⓑ[p,I]V.T] L2.
 #R #p #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
 /3 width=7 by frees_fwd_isfin, frees_flat, sex_join, ex2_intro/
 qed.
 
 theorem rex_bind_void (R) (p) (I):
         ∀L1,L2,V,T. L1 ⪤[R,V] L2 → L1.ⓧ ⪤[R,T] L2.ⓧ → L1 ⪤[R,ⓑ[p,I]V.T] L2.
 #R #p #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2

-lapply (sex_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫰f2))
-/3 width=7 by frees_fwd_isfin, frees_bind_void, sex_join, isfin_tl, ex2_intro/
+lapply (sex_fwd_bind … Hf2) -Hf2 #Hf2 elim (pr_sor_isf_bi f1 (⫰f2))
+/3 width=7 by frees_fwd_isfin, frees_bind_void, sex_join, pr_isf_tl, ex2_intro/

 qed.
 
 (* Negated inversion lemmas *************************************************)
 qed.
 
 (* Negated inversion lemmas *************************************************)

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/ac.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/ac.ma
index aa9b4db7b306f4de9c5ed89ecc3ea5f7bc2692f3..2d7d320e886ff7858be14ea5674683a6fa4d4ef1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/ac.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/ac.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
 (*                                                                        *)
 (**************************************************************************)
 

-include "ground/lib/arith.ma".
+include "ground/arith/nat_le.ma".

 include "static_2/notation/functions/one_0.ma".
 include "static_2/notation/functions/two_0.ma".
 include "static_2/notation/functions/omega_0.ma".
 include "static_2/notation/functions/one_0.ma".
 include "static_2/notation/functions/two_0.ma".
 include "static_2/notation/functions/omega_0.ma".


@@ -46,13 +46,13 @@ qed.
 definition ac_eq (k): ac ≝ mk_ac (eq … k).
 
 interpretation "one (applicability domain)"
 definition ac_eq (k): ac ≝ mk_ac (eq … k).
 
 interpretation "one (applicability domain)"

-  'Two = (ac_eq (S O)).
+  'Two = (ac_eq (nsucc nzero)).

 
 interpretation "zero (applicability domain)"
 
 interpretation "zero (applicability domain)"

-  'One = (ac_eq O).
+  'One = (ac_eq nzero).

 
 lemma ac_eq_props (k): ac_props (ac_eq k) ≝ mk_ac_props ….
 
 lemma ac_eq_props (k): ac_props (ac_eq k) ≝ mk_ac_props ….

-#m elim (le_dec m k) #Hm
+#m elim (nle_dec m k) #Hm

 [ /3 width=3 by or_introl, ex2_intro/
 | @or_intror * #n #Hn #Hmn destruct /2 width=1 by/
 ]
 [ /3 width=3 by or_introl, ex2_intro/
 | @or_intror * #n #Hn #Hmn destruct /2 width=1 by/
 ]


@@ -61,9 +61,9 @@ qed.
 definition ac_le (k): ac ≝ mk_ac (λn. n ≤ k).
 
 lemma ac_le_props (k): ac_props (ac_le k) ≝ mk_ac_props ….
 definition ac_le (k): ac ≝ mk_ac (λn. n ≤ k).
 
 lemma ac_le_props (k): ac_props (ac_le k) ≝ mk_ac_props ….

-#m elim (le_dec m k) #Hm
+#m elim (nle_dec m k) #Hm

 [ /3 width=3 by or_introl, ex2_intro/
 | @or_intror * #n #Hn #Hmn
 [ /3 width=3 by or_introl, ex2_intro/
 | @or_intror * #n #Hn #Hmn

-  /3 width=3 by transitive_le/
+  /3 width=3 by nle_trans/

 ]
 qed.
 ]
 qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/acle.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/acle.ma
index 30a025356a5df12ed6f2d26c5a8dd1e7e0a5dca8..52f8e6797b95e45e0da620ae0b513d3aa3824d0e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/acle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/acle.ma
@@ -45,12 +45,12 @@ qed.
 lemma acle_le_monotonic_le (k1) (k2):
       k1 ≤ k2 → (ac_le k1) ⊆ (ac_le k2).
 #k1 #k2 #Hk #m #Hm
 lemma acle_le_monotonic_le (k1) (k2):
       k1 ≤ k2 → (ac_le k1) ⊆ (ac_le k2).
 #k1 #k2 #Hk #m #Hm

-/3 width=3 by acle_refl, transitive_le/
+/3 width=3 by acle_refl, nle_trans/

 qed.
 
 lemma acle_eq_le (k): (ac_eq k) ⊆ (ac_le k).
 #k #m #Hm destruct
 qed.
 
 lemma acle_eq_le (k): (ac_eq k) ⊆ (ac_le k).
 #k #m #Hm destruct

-/2 width=1 by acle_refl, le_n/
+/2 width=1 by nle_refl, acle_refl/

 qed.
 
 lemma acle_le_eq (k): (ac_le k) ⊆ (ac_eq k).
 qed.
 
 lemma acle_le_eq (k): (ac_le k) ⊆ (ac_eq k).

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.ma
index 9b8998900b22a2aa3a213f285c5e2ef26fa3b346..2edee6e4cb75a0638bca51e2fbee9d8eb718c4f7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.ma
@@ -22,5 +22,5 @@ theorem acle_trans: Transitive … acle.
 #a1 #a #Ha1 #a2 #Ha2 #m1 #Hm1
 elim (Ha1 … Hm1) -Ha1 -Hm1 #m #Ha #Hm1
 elim (Ha2 … Ha) -Ha2 -Ha #m2 #Ha2 #Hm2
 #a1 #a #Ha1 #a2 #Ha2 #m1 #Hm1
 elim (Ha1 … Hm1) -Ha1 -Hm1 #m #Ha #Hm1
 elim (Ha2 … Ha) -Ha2 -Ha #m2 #Ha2 #Hm2

-/3 width=5 by transitive_le, ex2_intro/
+/3 width=5 by nle_trans, ex2_intro/

 qed-.
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/append.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/append.ma
index 220944f49e9affca4a26c19131f12d87930a1628..0377292d68b1c4dc04406e0d31bff57f9ddce556 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/append.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/append.ma
@@ -28,7 +28,7 @@ rec definition append L K on K ≝ match K with
 | LBind K I ⇒ (append L K).ⓘ[I]
 ].
 
 | LBind K I ⇒ (append L K).ⓘ[I]
 ].
 

-interpretation "append (local environment)" 'plus L1 L2 = (append L1 L2).
+interpretation "append (local environment)" 'nplus L1 L2 = (append L1 L2).

 
 interpretation "local environment tail binding construction (generic)"
    'SnItem I L = (append (LBind LAtom I) L).
 
 interpretation "local environment tail binding construction (generic)"
    'SnItem I L = (append (LBind LAtom I) L).

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/append_length.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/append_length.ma
index c76a2a6e7a915eaee2a0ac5e8329e8b52c685fee..2222c52ff01876cb6f2f8b675b7e587e92829352 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/append_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/append_length.ma
@@ -72,12 +72,12 @@ lemma append_inj_length_dx: ∀K1,K2,L1,L2. L1 + K1 = L2 + K2 → |L1| = |L2| 
 #K1 elim K1 -K1
 [ * /2 width=1 by conj/
   #K2 #I2 #L1 #L2 >append_atom >append_bind #H destruct
 #K1 elim K1 -K1
 [ * /2 width=1 by conj/
   #K2 #I2 #L1 #L2 >append_atom >append_bind #H destruct

-  >length_bind >append_length >plus_n_Sm
-  #H elim (plus_xSy_x_false … H)
+  >length_bind >append_length >nplus_succ_dx
+  #H elim (succ_nplus_refl_sn … H)

 | #K1 #I1 #IH *
   [ #L1 #L2 >append_bind >append_atom #H destruct
 | #K1 #I1 #IH *
   [ #L1 #L2 >append_bind >append_atom #H destruct

-    >length_bind >append_length >plus_n_Sm #H
-    lapply (discr_plus_x_xy … H) -H #H destruct
+    >length_bind >append_length >nplus_succ_dx #H
+    lapply (nplus_refl_sn … H) -H #H destruct

   | #K2 #I2 #L1 #L2 >append_bind >append_bind #H1 #H2
     elim (destruct_lbind_lbind_aux … H1) -H1 #H1 #H3 destruct (**) (* destruct lemma needed *)
     elim (IH … H1) -IH -H1 /2 width=1 by conj/
   | #K2 #I2 #L1 #L2 >append_bind >append_bind #H1 #H2
     elim (destruct_lbind_lbind_aux … H1) -H1 #H1 #H3 destruct (**) (* destruct lemma needed *)
     elim (IH … H1) -IH -H1 /2 width=1 by conj/


@@ -105,7 +105,7 @@ qed-.
 (* Basic_2A1: was: lenv_ind_alt *)
 lemma lenv_ind_tail: ∀Q:predicate lenv.
                      Q (⋆) → (∀I,L. Q L → Q (ⓘ[I].L)) → ∀L. Q L.
 (* Basic_2A1: was: lenv_ind_alt *)
 lemma lenv_ind_tail: ∀Q:predicate lenv.
                      Q (⋆) → (∀I,L. Q L → Q (ⓘ[I].L)) → ∀L. Q L.

-#Q #IH1 #IH2 #L @(f_ind … length … L) -L #x #IHx * //
+#Q #IH1 #IH2 #L @(wf1_ind_nlt … length … L) -L #x #IHx * //

 #L #I -IH1 #H destruct
 elim (lenv_case_tail … L) [2: * #K #J ]
 #H destruct /3 width=1 by/
 #L #I -IH1 #H destruct
 elim (lenv_case_tail … L) [2: * #K #J ]
 #H destruct /3 width=1 by/

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma
index 8340649d8175b97d27fc17edac191b4d5021022d..62ce9d6fca80fa26e839b01a0fb9b16dc3bba84c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma
@@ -25,11 +25,11 @@ interpretation "weight (restricted closure)" 'Weight L T = (rfw L T).
 
 (* Basic_1: was: flt_shift *)
 lemma rfw_shift: ∀p,I,K,V,T. ♯❨K.ⓑ[I]V,T❩ < ♯❨K,ⓑ[p,I]V.T❩.
 
 (* Basic_1: was: flt_shift *)
 lemma rfw_shift: ∀p,I,K,V,T. ♯❨K.ⓑ[I]V,T❩ < ♯❨K,ⓑ[p,I]V.T❩.

-normalize /2 width=1 by monotonic_le_plus_r/
+normalize /2 width=1 by nle_plus_bi_sn/

 qed.
 
 lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯❨K.ⓤ[I1],T❩ < ♯❨K,ⓑ[p,I2]V.T❩.
 qed.
 
 lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯❨K.ⓤ[I1],T❩ < ♯❨K,ⓑ[p,I2]V.T❩.

-normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
+normalize /4 width=1 by nle_plus_bi_sn, nle_succ_bi/

 qed.
 
 lemma rfw_tpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L,②[I]V.T❩.
 qed.
 
 lemma rfw_tpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L,②[I]V.T❩.


@@ -41,11 +41,11 @@ normalize in ⊢ (?→?→?→?→?%%); //
 qed.
 
 lemma rfw_lpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L.ⓑ[I]V,T❩.
 qed.
 
 lemma rfw_lpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L.ⓑ[I]V,T❩.

-normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
+normalize /3 width=1 by nlt_plus_bi_dx, nle_plus_bi_sn/

 qed.
 
 lemma rfw_lpair_dx: ∀I,L,V,T. ♯❨L,T❩ < ♯❨L.ⓑ[I]V,T❩.
 qed.
 
 lemma rfw_lpair_dx: ∀I,L,V,T. ♯❨L,T❩ < ♯❨L.ⓑ[I]V,T❩.

-normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
+normalize /3 width=1 by nlt_plus_bi_dx, nle_plus_bi_sn/

 qed.
 
 (* Basic_1: removed theorems 7:
 qed.
 
 (* Basic_1: removed theorems 7:

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/cl_weight.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/cl_weight.ma
index ad3f08f93769494f711e92e52ef8228780bab450..e87996c23e7e8835357ce58e0acffdf5b62d0098 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/cl_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/cl_weight.ma
@@ -27,11 +27,11 @@ interpretation "weight (closure)" 'Weight G L T = (fw G L T).
 
 (* Basic_1: was: flt_shift *)
 lemma fw_shift: ∀p,I,G,K,V,T. ♯❨G,K.ⓑ[I]V,T❩ < ♯❨G,K,ⓑ[p,I]V.T❩.
 
 (* Basic_1: was: flt_shift *)
 lemma fw_shift: ∀p,I,G,K,V,T. ♯❨G,K.ⓑ[I]V,T❩ < ♯❨G,K,ⓑ[p,I]V.T❩.

-normalize /2 width=1 by monotonic_le_plus_r/
+normalize /2 width=1 by nle_plus_bi_sn/

 qed.
 
 lemma fw_clear: ∀p,I1,I2,G,K,V,T. ♯❨G,K.ⓤ[I1],T❩ < ♯❨G,K,ⓑ[p,I2]V.T❩.
 qed.
 
 lemma fw_clear: ∀p,I1,I2,G,K,V,T. ♯❨G,K.ⓤ[I1],T❩ < ♯❨G,K,ⓑ[p,I2]V.T❩.

-normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
+normalize /4 width=1 by nle_plus_bi_sn, nle_succ_bi/

 qed.
 
 lemma fw_tpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L,②[I]V.T❩.
 qed.
 
 lemma fw_tpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L,②[I]V.T❩.


@@ -43,7 +43,7 @@ normalize in ⊢ (?→?→?→?→?→?%%); //
 qed.
 
 lemma fw_lpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L.ⓑ[I]V,T❩.
 qed.
 
 lemma fw_lpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L.ⓑ[I]V,T❩.

-normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
+normalize /3 width=1 by nlt_plus_bi_dx, nle_plus_bi_sn/

 qed.
 
 (* Basic_1: removed theorems 7:
 qed.
 
 (* Basic_1: removed theorems 7:

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/fold.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/fold.ma
index 05b86e627cad78d38d74d0c18397f03459475f57..061ef6ed903f17ced947387ed4b37f2020b5d7fc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/fold.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/fold.ma
@@ -24,7 +24,7 @@ rec definition fold L T on L ≝ match L with
   ]
 ].
 
   ]
 ].
 

-interpretation "fold (restricted closure)" 'plus L T = (fold L T).
+interpretation "fold (restricted closure)" 'nplus L T = (fold L T).

 
 (* Basic properties *********************************************************)
 
 
 (* Basic properties *********************************************************)
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/genv_weight.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/genv_weight.ma
index 3dd315e0a6e39d128f6b7c978135db72aa3169e1..88dcbc185f4d2eeba7ccd6a76204d5751a2b0d3f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/genv_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/genv_weight.ma
@@ -27,4 +27,4 @@ interpretation "weight (global environment)" 'Weight G = (gw G).
 (* Basic properties *********************************************************)
 
 lemma gw_pair: ∀I,G,T. ♯❨G❩ < ♯❨G.ⓑ[I]T❩.
 (* Basic properties *********************************************************)
 
 lemma gw_pair: ∀I,G,T. ♯❨G❩ < ♯❨G.ⓑ[I]T❩.

-normalize /2 width=1 by monotonic_le_plus_r/ qed.
+normalize /2 width=1 by nle_plus_bi_sn/ qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/item.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/item.ma
index bcaff1f89d528ca2eb07e0866aee3907fccf3bc1..c2ecea94277238b1414ef8577b1571f9a5c3b36a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/item.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/item.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "ground/lib/bool.ma".
 (**************************************************************************)
 
 include "ground/lib/bool.ma".

-include "ground/lib/arith.ma".
+include "ground/arith/nat.ma".

 
 (* ITEMS ********************************************************************)
 
 
 (* ITEMS ********************************************************************)
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma
index 768105e54ed2de654d7c085d8dbeaacf4c19f4f3..5f4b5dcb71cf718e4d4469c4912ce97ee2e00451 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma
@@ -47,7 +47,7 @@ lemma length_inv_succ_dx: ∀n,L. |L| = ↑n →
                           ∃∃I,K. |K| = n & L = K. ⓘ[I].
 #n *
 [ >length_atom #H destruct
                           ∃∃I,K. |K| = n & L = K. ⓘ[I].
 #n *
 [ >length_atom #H destruct

-| #L #I >length_bind /3 width=4 by ex2_2_intro, injective_S/
+| #L #I >length_bind /3 width=4 by ex2_2_intro, eq_inv_nsucc_bi/

 ]
 qed-.
 
 ]
 qed-.
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_weight.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_weight.ma
index 19a645439a1cd89b829ef508a50e07b2abbd18f3..66d46a41fae7be54262c032febc6732a5d4cc582 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_weight.ma
@@ -28,7 +28,7 @@ interpretation "weight (local environment)" 'Weight L = (lw L).
 
 (* Basic_2A1: uses: lw_pair *)
 lemma lw_bind: ∀I,L. ♯❨L❩ < ♯❨L.ⓘ[I]❩.
 
 (* Basic_2A1: uses: lw_pair *)
 lemma lw_bind: ∀I,L. ♯❨L❩ < ♯❨L.ⓘ[I]❩.

-normalize /2 width=1 by monotonic_le_plus_r/ qed.
+normalize /2 width=1 by nle_plus_bi_sn/ qed.

 
 (* Basic_1: removed theorems 4: clt_cong clt_head clt_thead clt_wf_ind *)
 (* Basic_1: removed local theorems 1: clt_wf__q_ind *)
 
 (* Basic_1: removed theorems 4: clt_cong clt_head clt_thead clt_wf_ind *)
 (* Basic_1: removed local theorems 1: clt_wf__q_ind *)

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_length.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_length.ma
index b97d967fa12da0a03e6617f76b6a084d83e8ec79..da13d1248779501fe85903b5e745e4957ab6b8bc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_length.ma
@@ -32,30 +32,30 @@ qed.
 
 lemma lveq_fwd_length_le_sn: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → n1 ≤ |L1|.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize
 
 lemma lveq_fwd_length_le_sn: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → n1 ≤ |L1|.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize

-/2 width=1 by le_S_S/
+/2 width=1 by nle_succ_bi/

 qed-.
 
 lemma lveq_fwd_length_le_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → n2 ≤ |L2|.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize
 qed-.
 
 lemma lveq_fwd_length_le_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → n2 ≤ |L2|.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize

-/2 width=1 by le_S_S/
+/2 width=1 by nle_succ_bi/

 qed-.
 
 lemma lveq_fwd_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                        ∧∧ |L1|-|L2| = n1 & |L2|-|L1| = n2.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 /2 width=1 by conj/
 qed-.
 
 lemma lveq_fwd_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                        ∧∧ |L1|-|L2| = n1 & |L2|-|L1| = n2.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 /2 width=1 by conj/

-#K1 #K2 #n #_ * #H1 #H2 >length_bind /3 width=1 by minus_Sn_m, conj/
+#K1 #K2 #n #_ * #H1 #H2 >length_bind /3 width=1 by nminus_succ_sn, conj/

 qed-.
 
 lemma lveq_length_fwd_sn: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → |L1| ≤ |L2| → 0 = n1.
 #L1 #L2 #n1 #n2 #H #HL
 elim (lveq_fwd_length … H) -H
 qed-.
 
 lemma lveq_length_fwd_sn: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → |L1| ≤ |L2| → 0 = n1.
 #L1 #L2 #n1 #n2 #H #HL
 elim (lveq_fwd_length … H) -H

->(eq_minus_O … HL) //
+>(nle_inv_eq_zero_minus … HL) //

 qed-.
 
 lemma lveq_length_fwd_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → |L2| ≤ |L1| → 0 = n2.
 #L1 #L2 #n1 #n2 #H #HL
 elim (lveq_fwd_length … H) -H
 qed-.
 
 lemma lveq_length_fwd_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 → |L2| ≤ |L1| → 0 = n2.
 #L1 #L2 #n1 #n2 #H #HL
 elim (lveq_fwd_length … H) -H

->(eq_minus_O … HL) //
+>(nle_inv_eq_zero_minus … HL) //

 qed-.
 
 lemma lveq_inj_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
 qed-.
 
 lemma lveq_inj_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →


@@ -68,15 +68,15 @@ qed-.
 lemma lveq_fwd_length_plus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                             |L1| + n2 = |L2| + n1.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize
 lemma lveq_fwd_length_plus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                             |L1| + n2 = |L2| + n1.
 #L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize

-/2 width=2 by injective_plus_r/
+/2 width=2 by eq_inv_nplus_bi_sn/

 qed-.
 
 lemma lveq_fwd_length_eq: ∀L1,L2. L1 ≋ⓧ*[0,0] L2 → |L1| = |L2|.
 qed-.
 
 lemma lveq_fwd_length_eq: ∀L1,L2. L1 ≋ⓧ*[0,0] L2 → |L1| = |L2|.

-/3 width=2 by lveq_fwd_length_plus, injective_plus_l/ qed-.
+/3 width=2 by lveq_fwd_length_plus, eq_inv_nplus_bi_dx/ qed-.

 
 lemma lveq_fwd_length_minus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                              |L1| - n1 = |L2| - n2.
 
 lemma lveq_fwd_length_minus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                              |L1| - n1 = |L2| - n2.

-/3 width=3 by lveq_fwd_length_plus, lveq_fwd_length_le_dx, lveq_fwd_length_le_sn, plus_to_minus_2/ qed-.
+/3 width=3 by lveq_fwd_length_plus, lveq_fwd_length_le_dx, lveq_fwd_length_le_sn, nminus_plus_swap/ qed-.

 
 lemma lveq_fwd_abst_bind_length_le: ∀I1,I2,L1,L2,V1,n1,n2.
                                     L1.ⓑ[I1]V1 ≋ⓧ*[n1,n2] L2.ⓘ[I2] → |L1| ≤ |L2|.
 
 lemma lveq_fwd_abst_bind_length_le: ∀I1,I2,L1,L2,V1,n1,n2.
                                     L1.ⓑ[I1]V1 ≋ⓧ*[n1,n2] L2.ⓘ[I2] → |L1| ≤ |L2|.


@@ -94,9 +94,9 @@ lemma lveq_fwd_bind_abst_length_le: ∀I1,I2,L1,L2,V2,n1,n2.
 lemma lveq_inv_void_dx_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2.ⓧ → |L1| ≤ |L2| →
                                ∃∃m2. L1 ≋ ⓧ*[n1,m2] L2 & 0 = n1 & ↑m2 = n2.
 #L1 #L2 #n1 #n2 #H #HL12
 lemma lveq_inv_void_dx_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2.ⓧ → |L1| ≤ |L2| →
                                ∃∃m2. L1 ≋ ⓧ*[n1,m2] L2 & 0 = n1 & ↑m2 = n2.
 #L1 #L2 #n1 #n2 #H #HL12

-lapply (lveq_fwd_length_plus … H) normalize >plus_n_Sm #H0
-lapply (plus2_le_sn_sn … H0 HL12) -H0 -HL12 #H0
-elim (le_inv_S1 … H0) -H0 #m2 #_ #H0 destruct
+lapply (lveq_fwd_length_plus … H) normalize >nplus_succ_dx #H0
+lapply (nplus_2_des_le_sn_sn … H0 HL12) -H0 -HL12 #H0
+elim (nle_inv_succ_sn … H0) -H0 #m2 #_ #H0 destruct

 elim (lveq_inv_void_succ_dx … H) -H /2 width=3 by ex3_intro/
 qed-.
 
 elim (lveq_inv_void_succ_dx … H) -H /2 width=3 by ex3_intro/
 qed-.
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_lveq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_lveq.ma
index f3b2d18cd8a98b255331ad25e327493a900f7a7b..6966715c4202ad3fb716de9cd84218785b8aecc9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_lveq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_lveq.ma
@@ -42,8 +42,8 @@ theorem lveq_inj_void_sn_ge: ∀K1,K2. |K2| ≤ |K1| →
 #L1 #L2 #HL #n1 #n2 #Hn #m1 #m2 #Hm
 elim (lveq_fwd_length … Hn) -Hn #H1 #H2 destruct
 elim (lveq_fwd_length … Hm) -Hm #H1 #H2 destruct
 #L1 #L2 #HL #n1 #n2 #Hn #m1 #m2 #Hm
 elim (lveq_fwd_length … Hn) -Hn #H1 #H2 destruct
 elim (lveq_fwd_length … Hm) -Hm #H1 #H2 destruct

->length_bind >eq_minus_S_pred >(eq_minus_O … HL)
-/3 width=4 by plus_minus, and3_intro/
+>length_bind >nminus_succ_dx >(nle_inv_eq_zero_minus … HL)
+/3 width=4 by nminus_plus_comm_23, and3_intro/

 qed-.
 
 theorem lveq_inj_void_dx_le: ∀K1,K2. |K1| ≤ |K2| →
 qed-.
 
 theorem lveq_inj_void_dx_le: ∀K1,K2. |K1| ≤ |K2| →

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sd.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sd.ma
index 533a79e05bc91ce73cce3c3391f94d6088c76f14..cd62fb439da88207b1194c78f9494b5cc3634acd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sd.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sd.ma
@@ -12,7 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
 (*                                                                        *)
 (**************************************************************************)
 

-include "static_2/syntax/sh.ma".
+include "ground/arith/nat_plus.ma".
+include "ground/arith/nat_minus.ma".
+include "ground/arith/nat_lt_pred.ma".
+include "static_2/syntax/sh_nexts.ma".

 
 (* SORT DEGREE **************************************************************)
 
 
 (* SORT DEGREE **************************************************************)
 


@@ -28,41 +31,46 @@ record sd_props (h) (o): Prop ≝ {
    deg_total: ∀s. ∃d. deg o s d;
    deg_mono : ∀s,d1,d2. deg o s d1 → deg o s d2 → d1 = d2;
 (* compatibility condition *)
    deg_total: ∀s. ∃d. deg o s d;
    deg_mono : ∀s,d1,d2. deg o s d1 → deg o s d2 → d1 = d2;
 (* compatibility condition *)

-   deg_next : â\88\80s,d. deg o s d â\86\92 deg o (⫯[h]s) (↓d)
+   deg_next : â\88\80s,d. deg o s d â\86\92 deg o (â\87¡[h]s) (↓d)

 }.
 
 (* Notable specifications ***************************************************)
 
 }.
 
 (* Notable specifications ***************************************************)
 

-definition deg_O: relation nat ≝ λs,d. d = 0.
+definition deg_O: relation nat ≝ λs,d. d = 𝟎.

 
 definition sd_O: sd ≝ mk_sd deg_O.
 
 lemma sd_O_props (h): sd_props h sd_O ≝ mk_sd_props ….
 
 definition sd_O: sd ≝ mk_sd deg_O.
 
 lemma sd_O_props (h): sd_props h sd_O ≝ mk_sd_props ….

-/2 width=2 by le_n_O_to_eq, le_n, ex_intro/ qed.
+/2 width=2 by nle_inv_zero_dx, nle_refl, ex_intro/ qed.

 
 (* Basic inversion lemmas ***************************************************)
 
 lemma deg_inv_pred (h) (o): sd_props h o →
 
 (* Basic inversion lemmas ***************************************************)
 
 lemma deg_inv_pred (h) (o): sd_props h o →

-      â\88\80s,d. deg o (⫯[h]s) (↑d) → deg o s (↑↑d).
+      â\88\80s,d. deg o (â\87¡[h]s) (↑d) → deg o s (↑↑d).

 #h #o #Ho #s #d #H1
 elim (deg_total … Ho s) #d0 #H0
 lapply (deg_next … Ho … H0) #H2
 #h #o #Ho #s #d #H1
 elim (deg_total … Ho s) #d0 #H0
 lapply (deg_next … Ho … H0) #H2

-lapply (deg_mono … Ho … H1 H2) -H1 -H2 #H >H >S_pred
-/2 width=2 by ltn_to_ltO/
+lapply (deg_mono … Ho … H1 H2) -H1 -H2 #H >H <nlt_des_gen
+/2 width=2 by nlt_des_lt_zero_sn/

 qed-.
 
 lemma deg_inv_prec (h) (o): sd_props h o →
 qed-.
 
 lemma deg_inv_prec (h) (o): sd_props h o →

-      ∀s,n,d. deg o ((next h)^n s) (↑d) → deg o s (↑(d+n)).
-#h #o #H0 #s #n elim n -n normalize /3 width=3 by deg_inv_pred/
+      ∀s,n,d. deg o (⇡*[h,n]s) (↑d) → deg o s (↑(d+n)).
+#h #o #H0 #s #n @(nat_ind_succ … n) -n [ // ]
+#n #IH #d <sh_nexts_succ
+#H <nplus_succ_shift
+@IH -IH @(deg_inv_pred … H0) // (**) (* auto fails *)

 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma deg_iter (h) (o): sd_props h o →
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma deg_iter (h) (o): sd_props h o →

-      ∀s,d,n. deg o s d → deg o ((next h)^n s) (d-n).
-#h #o #Ho #s #d #n elim n -n normalize /3 width=1 by deg_next/
+      ∀s,d,n. deg o s d → deg o (⇡*[h,n]s) (d-n).
+#h #o #Ho #s #d #n @(nat_ind_succ … n) -n [ // ]
+#n #IH #H <nminus_succ_dx <sh_nexts_succ
+/3 width=1 by deg_next/

 qed.
 
 lemma deg_next_SO (h) (o): sd_props h o →
 qed.
 
 lemma deg_next_SO (h) (o): sd_props h o →

-      ∀s,d. deg o s (↑d) → deg o (next h s) d.
+      ∀s,d. deg o s (↑d) → deg o (⇡[h]s) d.

 /2 width=1 by deg_next/ qed-.
 /2 width=1 by deg_next/ qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sd_d.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sd_d.ma
index 296322e61a8f173698ce3a0f2a439130d2b91298..7c6f680e84f750f72900f7af7983691fb1b56761 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sd_d.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sd_d.ma
@@ -19,25 +19,25 @@ include "static_2/syntax/sd.ma".
 
 (* Basic_2A1: includes: deg_SO_pos *)
 inductive deg_SO (h) (s) (s0): predicate nat ≝
 
 (* Basic_2A1: includes: deg_SO_pos *)
 inductive deg_SO (h) (s) (s0): predicate nat ≝

-| deg_SO_succ : ∀n. (next h)^n s0 = s → deg_SO h s s0 (↑n)
-| deg_SO_zero: (∀n. (next h)^n s0 = s → ⊥) → deg_SO h s s0 0
+| deg_SO_succ : ∀n. ⇡*[h,n]s0 = s → deg_SO h s s0 (↑n)
+| deg_SO_zero: (∀n. ⇡*[h,n]s0 = s → ⊥) → deg_SO h s s0 𝟎

 .
 
 fact deg_SO_inv_succ_aux (h) (s) (s0):
 .
 
 fact deg_SO_inv_succ_aux (h) (s) (s0):

-     ∀n0. deg_SO h s s0 n0 → ∀n. n0 = ↑n → (next h)^n s0 = s.
+     ∀n0. deg_SO h s s0 n0 → ∀n. n0 = ↑n → ⇡*[h,n]s0 = s.

 #h #s #s0 #n0 * -n0
 [ #n #Hn #x #H destruct //
 #h #s #s0 #n0 * -n0
 [ #n #Hn #x #H destruct //

-| #_ #x #H destruct
+| #_ #x #H elim (eq_inv_zero_nsucc … H)

 ]
 qed-.
 
 (* Basic_2A1: was: deg_SO_inv_pos *)
 lemma deg_SO_inv_succ (h) (s) (s0):
 ]
 qed-.
 
 (* Basic_2A1: was: deg_SO_inv_pos *)
 lemma deg_SO_inv_succ (h) (s) (s0):

-      ∀n. deg_SO h s s0 (↑n) → (next h)^n s0 = s.
+      ∀n. deg_SO h s s0 (↑n) → ⇡*[h,n]s0 = s.

 /2 width=3 by deg_SO_inv_succ_aux/ qed-.
 
 /2 width=3 by deg_SO_inv_succ_aux/ qed-.
 

-lemma deg_SO_refl (h) (s): deg_SO h s s 1.
-#h #s @(deg_SO_succ … 0 ?) //
+lemma deg_SO_refl (h) (s): deg_SO h s s 𝟏.
+#h #s @(deg_SO_succ … 𝟎 ?) //

 qed.
 
 definition sd_SO (h) (s): sd ≝ mk_sd (deg_SO h s).
 qed.
 
 definition sd_SO (h) (s): sd ≝ mk_sd (deg_SO h s).


@@ -47,24 +47,25 @@ lemma sd_SO_props (h) (s): sh_decidable h → sh_acyclic h →
 #h #s #Hhd #Hha
 @mk_sd_props
 [ #s0
 #h #s #Hhd #Hha
 @mk_sd_props
 [ #s0

-  elim (nexts_dec … Hhd s0 s) -Hhd
+  elim (sh_nexts_dec … Hhd s0 s) -Hhd

   [ * /3 width=2 by deg_SO_succ, ex_intro/
   | /5 width=2 by deg_SO_zero, ex_intro/
   ]
 | #s0 #d1 #d2 * [ #n1 ] #H1 * [1,3: #n2 ] #H2
   [ < H2 in H1; -H2 #H
   [ * /3 width=2 by deg_SO_succ, ex_intro/
   | /5 width=2 by deg_SO_zero, ex_intro/
   ]
 | #s0 #d1 #d2 * [ #n1 ] #H1 * [1,3: #n2 ] #H2
   [ < H2 in H1; -H2 #H

-    lapply (nexts_inj … Hha … H) -H #H destruct //
+    lapply (sh_nexts_inj … Hha … H) -H #H destruct //

   | elim H1 /2 width=2 by ex_intro/
   | elim H2 /2 width=2 by ex_intro/
   | //
   ]
 | #s0 #d *
   | elim H1 /2 width=2 by ex_intro/
   | elim H2 /2 width=2 by ex_intro/
   | //
   ]
 | #s0 #d *

-  [ #n #H destruct cases n -n normalize
-    [ @deg_SO_zero #n >iter_n_Sm #H
-      lapply (nexts_inj … Hha … (↑n) 0 H) -H #H destruct
-    | #n @deg_SO_succ >iter_n_Sm //
+  [ #n #H destruct
+    <npred_succ @(nat_ind_succ … n) -n
+    [ @deg_SO_zero #n >(sh_nexts_succ_next h n s0) #H 
+      lapply (sh_nexts_inj … Hha ???) -H #H destruct
+    | #n @deg_SO_succ >sh_nexts_swap //

     ]
     ]

-  | #H0 @deg_SO_zero #n >iter_n_Sm #H destruct
+  | #H0 @deg_SO_zero #n >sh_nexts_swap #H destruct

     /2 width=2 by/
   ]
 ]
     /2 width=2 by/
   ]
 ]


@@ -75,7 +76,7 @@ rec definition sd_d (h:?) (s:?) (d:?) on d: sd ≝
    [ O   ⇒ sd_O
    | S d ⇒ match d with
            [ O ⇒ sd_SO h s
    [ O   ⇒ sd_O
    | S d ⇒ match d with
            [ O ⇒ sd_SO h s

-           | _ ⇒ sd_d h (next h s) d
+           | _ ⇒ sd_d h (pr_next h s) d

            ]
    ].
 
            ]
    ].
 

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma
index 238d1a28b60a5ddae2fb4055dd63971e59e88aa9..23725dba7544c109e848565422f7bd71571cc835 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.ma
@@ -23,10 +23,10 @@ lemma deg_SO_gt (h): sh_lt h →
       ∀s1,s2. s1 < s2 → deg_SO h s1 s2 0.
 #h #Hh #s1 #s2 #Hs12 @deg_SO_zero * normalize
 [ #H destruct
       ∀s1,s2. s1 < s2 → deg_SO h s1 s2 0.
 #h #Hh #s1 #s2 #Hs12 @deg_SO_zero * normalize
 [ #H destruct

-  elim (lt_refl_false … Hs12)
+  elim (nlt_inv_refl … Hs12)

 | #n #H
 | #n #H

-  lapply (next_lt … Hh ((next h)^n s2)) >H -H #H
-  lapply (transitive_lt … H Hs12) -s1 #H1
-  /3 width=5 by lt_le_false, nexts_le/ (* full auto too slow *)
+  lapply (next_lt … Hh ((pr_next h)^n s2)) >H -H #H
+  lapply (nlt_trans … H Hs12) -s1 #H1
+  /3 width=5 by nlt_ge_false, nexts_le/ (* full auto too slow *)

 ]
 qed.
 ]
 qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sh.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sh.ma
index 8129473752d35bd95146f95897f66fe65431a75f..9e9b8adc173d9d572be15726499bf99b27b4c0d0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sh.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sh.ma
@@ -12,18 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
 (*                                                                        *)
 (**************************************************************************)
 

-include "ground/lib/arith.ma".
-include "static_2/notation/functions/upspoon_2.ma".
+include "ground/arith/nat.ma".
+include "static_2/notation/functions/uparrow_1_0.ma".

 
 (* SORT HIERARCHY ***********************************************************)
 
 (* sort hierarchy specification *)
 record sh: Type[0] ≝ {
 
 (* SORT HIERARCHY ***********************************************************)
 
 (* sort hierarchy specification *)
 record sh: Type[0] ≝ {

-  next: nat → nat (* next sort in the hierarchy *)
+  sh_next: nat → nat (* next sort in the hierarchy *)

 }.
 
 interpretation "next sort (sort hierarchy)"
 }.
 
 interpretation "next sort (sort hierarchy)"

-   'UpSpoon h s = (next h s).
+   'UpArrow_1_0 h = (sh_next h).

 
 definition sh_is_next (h): relation nat ≝
 
 definition sh_is_next (h): relation nat ≝

-           λs1,s2. ⫯[h]s1 = s2.
+           λs1,s2. â\87¡[h]s1 = s2.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
index d33515ef80dfb47e04a986bcdf781b1a77e1ebf3..bfeab590553cf8940ef01d581ae2515055da2e60 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
 (*                                                                        *)
 (**************************************************************************)
 

+include "ground/arith/nat_lt_minus.ma".

 include "static_2/syntax/sh_props.ma".
 
 (* SORT HIERARCHY ***********************************************************)
 include "static_2/syntax/sh_props.ma".
 
 (* SORT HIERARCHY ***********************************************************)


@@ -19,38 +20,38 @@ include "static_2/syntax/sh_props.ma".
 (* strict monotonicity condition *)
 record sh_lt (h): Prop ≝
 {
 (* strict monotonicity condition *)
 record sh_lt (h): Prop ≝
 {

-  next_lt: ∀s. s < ⫯[h]s
+  sh_next_lt: ∀s. s < ⇡[h]s

 }.
 
 (* Basic properties *********************************************************)
 
 }.
 
 (* Basic properties *********************************************************)
 

-lemma nexts_le (h): sh_lt h → ∀s,n. s ≤ (next h)^n s.
-#h #Hh #s #n elim n -n [ // ] normalize #n #IH
-lapply (next_lt … Hh ((next h)^n s)) #H
-lapply (le_to_lt_to_lt … IH H) -IH -H /2 width=2 by lt_to_le/
+lemma sh_nexts_le (h): sh_lt h → ∀s,n. s ≤ ⇡*[h,n]s.
+#h #Hh #s #n @(nat_ind_succ … n) -n [ // ] #n #IH <sh_nexts_succ
+lapply (sh_next_lt … Hh ((sh_next h)^n s)) #H
+lapply (nle_nlt_trans … IH H) -IH -H /2 width=2 by nlt_des_le/

 qed.
 
 qed.
 

-lemma nexts_lt (h): sh_lt h → ∀s,n. s < (next h)^(↑n) s.
-#h #Hh #s #n normalize
-lapply (nexts_le … Hh s n) #H
-@(le_to_lt_to_lt … H) /2 width=1 by next_lt/
+lemma sh_nexts_lt (h): sh_lt h → ∀s,n. s < ⇡*[h,↑n]s.
+#h #Hh #s #n <sh_nexts_succ
+lapply (sh_nexts_le … Hh s n) #H
+@(nle_nlt_trans … H) /2 width=1 by sh_next_lt/

 qed.
 
 lemma sh_lt_nexts_inv_lt (h): sh_lt h →
 qed.
 
 lemma sh_lt_nexts_inv_lt (h): sh_lt h →

-      ∀s,n1,n2. (next h)^n1 s < (next h)^n2 s → n1 < n2.
+      ∀s,n1,n2. ⇡*[h,n1]s < ⇡*[h,n2]s → n1 < n2.

 #h #Hh
 @pull_2 #n1
 #h #Hh
 @pull_2 #n1

-elim n1 -n1
-[ #s *
-  [ #H elim (lt_refl_false … H)
-  | #n2 //
+@(nat_ind_succ … n1) -n1
+[ #s #n2 @(nat_ind_succ … n2) -n2
+  [ #H elim (nlt_inv_refl … H)
+  | #n2 #_ //

   ]
   ]

-| #n1 #IH #s *
-  [ >iter_O #H
-    elim (lt_refl_false s)
-    /3 width=3 by nexts_lt, transitive_lt/
-  | #n2 >iter_S >iter_S <(iter_n_Sm … (next h)) <(iter_n_Sm … (next h)) #H
-    /3 width=2 by lt_S_S/
+| #n1 #IH #s #n2 @(nat_ind_succ … n2) -n2
+  [ <sh_nexts_zero #H
+    elim (nlt_inv_refl s)
+    /3 width=3 by sh_nexts_lt, nlt_trans/
+  | #n2 #_ <sh_nexts_succ <sh_nexts_succ >sh_nexts_swap >sh_nexts_swap #H
+    /3 width=2 by nlt_succ_bi/

   ]
 ]
 qed-.
   ]
 ]
 qed-.


@@ -59,16 +60,16 @@ lemma sh_lt_acyclic (h): sh_lt h → sh_acyclic h.
 #h #Hh
 @mk_sh_acyclic
 @pull_2 #n1
 #h #Hh
 @mk_sh_acyclic
 @pull_2 #n1

-elim n1 -n1
-[ #s * [ // ] #n2 >iter_O #H
-  elim (lt_refl_false s) >H in ⊢ (??%); -H
-  /2 width=1 by nexts_lt/
-| #n1 #IH #s *
-  [ >iter_O #H -IH
-    elim (lt_refl_false s) <H in ⊢ (??%); -H
-    /2 width=1 by nexts_lt/
-  | #n2 >iter_S >iter_S <(iter_n_Sm … (next h)) <(iter_n_Sm … (next h)) #H
-    /3 width=2 by eq_f/
+@(nat_ind_succ … n1) -n1
+[ #s #n2 @(nat_ind_succ … n2) -n2 [ // ] #n2 #_ <sh_nexts_zero #H
+  elim (nlt_inv_refl s) >H in ⊢ (??%); -H
+  /2 width=1 by sh_nexts_lt/
+| #n1 #IH #s #n2 @(nat_ind_succ … n2) -n2
+  [ <sh_nexts_zero #H -IH
+    elim (nlt_inv_refl s) <H in ⊢ (??%); -H
+    /2 width=1 by sh_nexts_lt/
+  | #n2 #_ <sh_nexts_succ <sh_nexts_succ >sh_nexts_swap >sh_nexts_swap #H
+    lapply (IH … H) -IH -H //

   ]
 ]
 qed.
   ]
 ]
 qed.


@@ -76,33 +77,33 @@ qed.
 lemma sh_lt_dec (h): sh_lt h → sh_decidable h.
 #h #Hh
 @mk_sh_decidable #s1 #s2
 lemma sh_lt_dec (h): sh_lt h → sh_decidable h.
 #h #Hh
 @mk_sh_decidable #s1 #s2

-elim (lt_or_ge s2 s1) #Hs
+elim (nat_split_lt_ge s2 s1) #Hs

 [ @or_intror * #n #H destruct
 [ @or_intror * #n #H destruct

-  @(lt_le_false … Hs) /2 width=1 by nexts_le/ (**) (* full auto too slow *)
-| @(nat_elim_le_sn … Hs) -s1 -s2 #s1 #s2 #IH #Hs12
-  elim (lt_or_eq_or_gt s2 (⫯[h]s1)) #Hs21 destruct
-  [ elim (le_to_or_lt_eq … Hs12) -Hs12 #Hs12 destruct
+  @(nlt_ge_false … Hs) /2 width=1 by sh_nexts_le/ (**) (* full auto too slow *)
+| @(nle_ind_sn … Hs) -s1 -s2 #s1 #s2 #IH #Hs12
+  elim (nat_split_lt_eq_gt s2 (⇡[h]s1)) #Hs21 destruct
+  [ elim (nle_split_lt_eq … Hs12) -Hs12 #Hs12 destruct

     [ -IH @or_intror * #n #H destruct
       generalize in match Hs21; -Hs21
     [ -IH @or_intror * #n #H destruct
       generalize in match Hs21; -Hs21

-      <(iter_O … (next h) s1) in ⊢ (??%→?); <(iter_S … (next h)) #H
+      >sh_nexts_unit #H

       lapply (sh_lt_nexts_inv_lt … Hh … H) -H #H
       lapply (sh_lt_nexts_inv_lt … Hh … H) -H #H

-      <(le_n_O_to_eq n) in Hs12;
-      /2 width=2 by lt_refl_false, le_S_S_to_le/
+      <(nle_inv_zero_dx n) in Hs12;
+      /2 width=2 by nlt_inv_refl, nle_inv_succ_bi/

     | /3 width=2 by ex_intro, or_introl/
     ]
     | /3 width=2 by ex_intro, or_introl/
     ]

-  | -IH @or_introl @(ex_intro … 1) // (**) (* auto fails *)
-  | lapply (transitive_lt s1 ??? Hs21) [ /2 width=1 by next_lt/ ] -Hs12 #Hs12
-    elim (IH (s2-⫯[h]s1)) -IH
-    [3: /3 width=1 by next_lt, monotonic_lt_minus_r/ ]
-    >minus_minus_m_m [2,4: /2 width=1 by lt_to_le/ ] -Hs21
+  | -IH @or_introl @(ex_intro … 𝟏) // (**) (* auto fails *)
+  | lapply (nlt_trans s1 ??? Hs21) [ /2 width=1 by sh_next_lt/ ] -Hs12 #Hs12
+    elim (IH (s2-â\87¡[h]s1)) -IH
+    [3: /3 width=1 by sh_next_lt, nlt_minus_bi_sn/ ]
+    <nminus_minus_dx_refl_sn [2,4: /2 width=1 by nlt_des_le/ ] -Hs21

     [ * #n #H destruct
     [ * #n #H destruct

-      @or_introl @(ex_intro … (↑n)) >iter_S >iter_n_Sm //
+      @or_introl @(ex_intro … (↑n)) <sh_nexts_succ >sh_nexts_swap //

     | #H1 @or_intror * #n #H2 @H1 -H1 destruct
       generalize in match Hs12; -Hs12
     | #H1 @or_intror * #n #H2 @H1 -H1 destruct
       generalize in match Hs12; -Hs12

-      <(iter_O … (next h) s1) in ⊢ (?%?→?); #H
+      >(sh_nexts_zero h s1) in ⊢ (?%?→?); #H

       lapply (sh_lt_nexts_inv_lt … Hh … H) -H #H
       lapply (sh_lt_nexts_inv_lt … Hh … H) -H #H

-      <(S_pred … H) -H
-      @(ex_intro … (↓n)) >(iter_n_Sm … (next h)) >iter_S //
+      >(nlt_des_gen … H) -H
+      @(ex_intro … (↓n)) <sh_nexts_succ >sh_nexts_swap //

     ]
   ]
 ]
     ]
   ]
 ]

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_nexts.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_nexts.ma
new file mode 100644 (file)
index 0000000..143e2db
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_nexts.ma
@@ -0,0 +1,46 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground/arith/nat_succ_iter.ma".
+include "static_2/notation/functions/uparrowstar_2_0.ma".
+include "static_2/syntax/sh.ma".
+
+(* SORT HIERARCHY ***********************************************************)
+
+definition sh_nexts (h) (n): nat → nat ≝ ⇡[h]^n.
+
+interpretation
+  "iterated next sort (sort hierarchy)"
+  'UpArrowStar_2_0 h n = (sh_nexts h n).
+
+(* Basic constructions *)
+
+lemma sh_nexts_zero (h): ∀s. s = ⇡*[h,𝟎]s.
+// qed.
+
+lemma sh_nexts_unit (h): ⇡[h] ≐ ⇡*[h,𝟏].
+// qed.
+
+lemma sh_nexts_succ (h) (n): ⇡[h] ∘ (⇡*[h,n]) ≐ ⇡*[h,↑n].
+/2 width=1 by niter_succ/ qed.
+
+(* Advanced constructions ****************************)
+
+lemma sh_nexts_swap (h) (n): ⇡[h] ∘ (⇡*[h,n]) ≐ ⇡*[h,n] ∘ ⇡[h].
+/2 width=1 by niter_appl/ qed.
+
+(* Helper constructions *****************************************************)
+
+lemma sh_nexts_succ_next (h) (n): ⇡*[h,n] ∘ (⇡[h]) ≐ ⇡*[h,↑n].
+// qed.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_props.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_props.ma
index 4302026d4db8138d9e778b7aef8748bb7571f36f..53c4cfcfc9367a582f31e616a1a1bca878850bba 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_props.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_props.ma
@@ -12,18 +12,19 @@
 (*                                                                        *)
 (**************************************************************************)
 
 (*                                                                        *)
 (**************************************************************************)
 

-include "static_2/syntax/sh.ma".
+include "static_2/syntax/sh_nexts.ma".

 
 (* SORT HIERARCHY ***********************************************************)
 
 (* acyclicity condition *)
 record sh_acyclic (h): Prop ≝
 {
 
 (* SORT HIERARCHY ***********************************************************)
 
 (* acyclicity condition *)
 record sh_acyclic (h): Prop ≝
 {

-  nexts_inj: ∀s,n1,n2. (next h)^n1 s = (next h)^n2 s → n1 = n2
+(**) (* use extensional equivalence *) 
+  sh_nexts_inj: ∀s,n1,n2. ⇡*[h,n1]s = ⇡*[h,n2]s → n1 = n2

 }.
 
 (* decidability condition *)
 record sh_decidable (h): Prop ≝
 {
 }.
 
 (* decidability condition *)
 record sh_decidable (h): Prop ≝
 {

-  nexts_dec: ∀s1,s2. Decidable (∃n. (next h)^n s1 = s2)
+  sh_nexts_dec: ∀s1,s2. Decidable (∃n. ⇡*[h,n]s1 = s2)

 }.
 }.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/teq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/teq.ma
index 6b4a58e82f9d902c77c75e2c0244d75edc9033b4..c8a82e16b67f6b42a56a395cf1b2ad5778019ba8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/teq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/teq.ma
@@ -18,7 +18,7 @@ include "static_2/syntax/teqg.ma".
 (* SYNTACTIC EQUIVALENCE ON TERMS *******************************************)
 
 definition teq: relation term ≝
 (* SYNTACTIC EQUIVALENCE ON TERMS *******************************************)
 
 definition teq: relation term ≝

-           teqg (eq …).
+           teqg (pr_eq …).

 
 interpretation
   "context-free syntactic equivalence (term)"
 
 interpretation
   "context-free syntactic equivalence (term)"

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/teq_ext.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/teq_ext.ma
index c91f93e93a2cfcbc70b285bd722c22fe42feca9a..c71e77ddc08092f6821addff8855305a9fb15dcc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/teq_ext.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/teq_ext.ma
@@ -19,10 +19,10 @@ include "static_2/syntax/teq.ma".
 (* SYNTACTIC EQUIVALENCE ****************************************************)
 
 definition ceq: relation3 lenv term term ≝
 (* SYNTACTIC EQUIVALENCE ****************************************************)
 
 definition ceq: relation3 lenv term term ≝

-           ceqg (eq …).
+           ceqg (pr_eq …).

 
 definition ceq_ext: lenv → relation bind ≝
 
 definition ceq_ext: lenv → relation bind ≝

-           ceqg_ext (eq …).
+           ceqg_ext (pr_eq …).

 
 interpretation
   "context-dependent syntactic equivalence (term)"
 
 interpretation
   "context-dependent syntactic equivalence (term)"

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/teqg.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/teqg.ma
index 46e9c67b6848850ec22fa52de166f06cfe4c8746..8be52d4a5fb28bc931ec422befeb7fec2f8112b7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/teqg.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/teqg.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
 (*                                                                        *)
 (**************************************************************************)
 

+include "ground/xoa/or_3.ma".

 include "ground/xoa/ex_3_2.ma".
 include "static_2/notation/relations/stareq_3.ma".
 include "static_2/syntax/term.ma".
 include "ground/xoa/ex_3_2.ma".
 include "static_2/notation/relations/stareq_3.ma".
 include "static_2/syntax/term.ma".

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/teqw.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/teqw.ma
index 1412f42b6a35c3ab6a7fe636328f05ef0768c2cc..6758d2f3d24792e06830c19049a85c8c03effd92 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/teqw.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/teqw.ma
@@ -210,7 +210,7 @@ elim (teqw_inv_cast_sn … H) -H #W2 #U2 #HVW #HTU #H destruct
 qed-.
 
 lemma teqw_inv_cast_xy_y: ∀T,V. ⓝV.T ≃ T → ⊥.
 qed-.
 
 lemma teqw_inv_cast_xy_y: ∀T,V. ⓝV.T ≃ T → ⊥.

-@(f_ind … tw) #n #IH #T #Hn #V #H destruct
+@(wf1_ind_nlt … tw) #n #IH #T #Hn #V #H destruct

 elim (teqw_inv_cast_sn … H) -H #X1 #X2 #_ #HX2 #H destruct -V
 /2 width=4 by/
 qed-.
 elim (teqw_inv_cast_sn … H) -H #X1 #X2 #_ #HX2 #H destruct -V
 /2 width=4 by/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/term_vector.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/term_vector.ma
index 2714a1b91cc1abfeadf89e50c02513d18135b26f..25327ed32cab08c0431c30ddfd3e7ec72a5dc95a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/term_vector.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/term_vector.ma
@@ -21,7 +21,7 @@ include "static_2/syntax/term_simple.ma".
 rec definition applv Vs T on Vs ≝
   match Vs with
   [ nil        ⇒ T
 rec definition applv Vs T on Vs ≝
   match Vs with
   [ nil        ⇒ T

-  | cons hd tl ⇒ ⓐhd. (applv tl T)
+  | cons hd pr_tl ⇒ ⓐhd. (applv pr_tl T)

   ].
 
 interpretation "application to vector (term)"
   ].
 
 interpretation "application to vector (term)"

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/term_weight.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/term_weight.ma
index ee53e62e754e8b3f3210c401508dd832dd10cd3a..bcb826bb41bf7477067c229b2116c9d48105f31a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/term_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/term_weight.ma
@@ -32,7 +32,7 @@ lemma tw_pos: ∀T. 1 ≤ ♯❨T❩.
 qed.
 
 lemma tw_le_pair_dx (I): ∀V,T. ♯❨T❩ < ♯❨②[I]V.T❩.
 qed.
 
 lemma tw_le_pair_dx (I): ∀V,T. ♯❨T❩ < ♯❨②[I]V.T❩.

-#I #V #T /2 width=1 by le_S_S/
+#I #V #T /2 width=1 by nle_succ_bi/

 qed.
 
 (* Basic_1: removed theorems 11:
 qed.
 
 (* Basic_1: removed theorems 11: