partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / lex.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma
index cc4bf1797629af644cf4211aee7360f683475da7..02ba4bedc837ea1318c83fb27239cb9456ca0f35 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/pull/pull_4.ma".
-include "ground_2/relocation/rtmap_uni.ma".
+include "ground/pull/pull_4.ma".
+include "ground/relocation/rtmap_uni.ma".
 include "static_2/notation/relations/relation_3.ma".
 include "static_2/syntax/cext2.ma".
 include "static_2/relocation/sex.ma".
@@ -21,7 +21,7 @@ include "static_2/relocation/sex.ma".
 (* GENERIC EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS **************)
 
 definition lex (R): relation lenv ≝
-                    λL1,L2. â\88\83â\88\83f. ð\9d\90\88â¦\83fâ¦\84 & L1 ⪤[cfull,cext2 R,f] L2.
+                    λL1,L2. â\88\83â\88\83f. ð\9d\90\88â\9dªfâ\9d« & L1 ⪤[cfull,cext2 R,f] L2.
 
 interpretation "generic extension (local environment)"
    'Relation R L1 L2 = (lex R L1 L2).
@@ -42,9 +42,9 @@ lemma lex_atom (R): ⋆ ⪤[R] ⋆.
 /2 width=3 by sex_atom, ex2_intro/ qed.
 
 lemma lex_bind (R): ∀I1,I2,K1,K2. K1 ⪤[R] K2 → cext2 R K1 I1 I2 →
-                    K1.ⓘ{I1} ⪤[R] K2.ⓘ{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 *)
@@ -59,15 +59,15 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma lex_bind_refl_dx (R): c_reflexive … R →
-                            ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓘ{I} ⪤[R] K2.ⓘ{I}.
+                            ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓘ[I] ⪤[R] K2.ⓘ[I].
 /3 width=3 by ext2_refl, lex_bind/ qed.
 
-lemma lex_unit (R): ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓤ{I} ⪤[R] K2.ⓤ{I}.
+lemma lex_unit (R): ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓤ[I] ⪤[R] K2.ⓤ[I].
 /3 width=1 by lex_bind, ext2_unit/ qed.
 
 (* Basic_2A1: was: lpx_sn_pair *)
 lemma lex_pair (R): ∀I,K1,K2,V1,V2. K1 ⪤[R] K2 → R K1 V1 V2 →
-                    K1.ⓑ{I}V1 ⪤[R] K2.ⓑ{I}V2.
+                    K1.ⓑ[I]V1 ⪤[R] K2.ⓑ[I]V2.
 /3 width=1 by lex_bind, ext2_pair/ qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -77,10 +77,10 @@ lemma lex_inv_atom_sn (R): ∀L2. ⋆ ⪤[R] L2 → L2 = ⋆.
 #R #L2 * #f #Hf #H >(sex_inv_atom1 … H) -L2 //
 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}.
+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-.
@@ -90,18 +90,18 @@ lemma lex_inv_atom_dx (R): ∀L1. L1 ⪤[R] ⋆ → L1 = ⋆.
 #R #L1 * #f #Hf #H >(sex_inv_atom2 … H) -L1 //
 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}.
+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-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lex_inv_unit_sn (R): ∀I,L2,K1. K1.ⓤ{I} ⪤[R] L2 →
-                           ∃∃K2. K1 ⪤[R] K2 & L2 = K2.ⓤ{I}.
+lemma lex_inv_unit_sn (R): ∀I,L2,K1. K1.ⓤ[I] ⪤[R] L2 →
+                           ∃∃K2. K1 ⪤[R] K2 & L2 = K2.ⓤ[I].
 #R #I #L2 #K1 #H
 elim (lex_inv_bind_sn … H) -H #Z2 #K2 #HK12 #HZ2 #H destruct
 elim (ext2_inv_unit_sn … HZ2) -HZ2
@@ -109,16 +109,16 @@ elim (ext2_inv_unit_sn … HZ2) -HZ2
 qed-.
 
 (* Basic_2A1: was: lpx_sn_inv_pair1 *)
-lemma lex_inv_pair_sn (R): ∀I,L2,K1,V1. K1.ⓑ{I}V1 ⪤[R] L2 →
-                           ∃∃K2,V2. K1 ⪤[R] K2 & R K1 V1 V2 & L2 = K2.ⓑ{I}V2.
+lemma lex_inv_pair_sn (R): ∀I,L2,K1,V1. K1.ⓑ[I]V1 ⪤[R] L2 →
+                           ∃∃K2,V2. K1 ⪤[R] K2 & R K1 V1 V2 & L2 = K2.ⓑ[I]V2.
 #R #I #L2 #K1 #V1 #H
 elim (lex_inv_bind_sn … H) -H #Z2 #K2 #HK12 #HZ2 #H destruct
 elim (ext2_inv_pair_sn … HZ2) -HZ2 #V2 #HV12 #H destruct
 /2 width=5 by ex3_2_intro/
 qed-.
 
-lemma lex_inv_unit_dx (R): ∀I,L1,K2. L1 ⪤[R] K2.ⓤ{I} →
-                           ∃∃K1. K1 ⪤[R] K2 & L1 = K1.ⓤ{I}.
+lemma lex_inv_unit_dx (R): ∀I,L1,K2. L1 ⪤[R] K2.ⓤ[I] →
+                           ∃∃K1. K1 ⪤[R] K2 & L1 = K1.ⓤ[I].
 #R #I #L1 #K2 #H
 elim (lex_inv_bind_dx … H) -H #Z1 #K1 #HK12 #HZ1 #H destruct
 elim (ext2_inv_unit_dx … HZ1) -HZ1
@@ -126,8 +126,8 @@ elim (ext2_inv_unit_dx … HZ1) -HZ1
 qed-.
 
 (* Basic_2A1: was: lpx_sn_inv_pair2 *)
-lemma lex_inv_pair_dx (R): ∀I,L1,K2,V2. L1 ⪤[R] K2.ⓑ{I}V2 →
-                           ∃∃K1,V1. K1 ⪤[R] K2 & R K1 V1 V2 & L1 = K1.ⓑ{I}V1.
+lemma lex_inv_pair_dx (R): ∀I,L1,K2,V2. L1 ⪤[R] K2.ⓑ[I]V2 →
+                           ∃∃K1,V1. K1 ⪤[R] K2 & R K1 V1 V2 & L1 = K1.ⓑ[I]V1.
 #R #I #L1 #K2 #V2 #H
 elim (lex_inv_bind_dx … H) -H #Z1 #K1 #HK12 #HZ1 #H destruct
 elim (ext2_inv_pair_dx … HZ1) -HZ1 #V1 #HV12 #H destruct
@@ -136,7 +136,7 @@ qed-.
 
 (* Basic_2A1: was: lpx_sn_inv_pair *)
 lemma lex_inv_pair (R): ∀I1,I2,L1,L2,V1,V2.
-                        L1.ⓑ{I1}V1 ⪤[R] L2.ⓑ{I2}V2 →
+                        L1.ⓑ[I1]V1 ⪤[R] L2.ⓑ[I2]V2 →
                         ∧∧ L1 ⪤[R] L2 & R L1 V1 V2 & I1 = I2.
 #R #I1 #I2 #L1 #L2 #V1 #V2 #H elim (lex_inv_pair_sn … H) -H
 #L0 #V0 #HL10 #HV10 #H destruct /2 width=1 by and3_intro/
@@ -147,15 +147,15 @@ qed-.
 lemma lex_ind (R) (Q:relation2 …):
               Q (⋆) (⋆) →
               (
-                 ∀I,K1,K2. K1 ⪤[R] K2 → Q K1 K2 → Q (K1.ⓤ{I}) (K2.ⓤ{I})
+                 ∀I,K1,K2. K1 ⪤[R] K2 → Q K1 K2 → Q (K1.ⓤ[I]) (K2.ⓤ[I])
               ) → (
-                 ∀I,K1,K2,V1,V2. K1 ⪤[R] K2 → Q K1 K2 → R K1 V1 V2 →Q (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
+                 ∀I,K1,K2,V1,V2. K1 ⪤[R] K2 → Q K1 K2 → R K1 V1 V2 →Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
               ) →
               ∀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-.