- ground_2: some additions

- basic_2/grammar: added missing files

diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/ceq.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/ceq.ma
new file mode 100644 (file)
index 0000000..abd6b25
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/ceq.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2/grammar/lenv.ma".
+
+(* CONTEXT-SENSITIVE EQUIVALENCES FOR TERMS *********************************)
+
+definition ceq: relation3 lenv term term ≝ λL,T1,T2. T1 = T2.
+
+definition cfull: relation3 lenv term term ≝ λL,T1,T2. ⊤.
+
+(* Basic properties *********************************************************)
+
+lemma ceq_refl (L): reflexive … (ceq L).
+// qed.
+
+lemma cfull_refl (L): reflexive … (cfull L).
+// qed.
+
+lemma ceq_sym (L): symmetric … (ceq L).
+// qed-.
+
+lemma cfull_sym (L): symmetric … (cfull L).
+// qed-.
+
+lemma cfull_top (R:relation3 lenv term term) (L) (T1) (T2):
+                R L T1 T2 → cfull L T1 T2.
+// qed-.
+
+lemma ceq_cfull (L) (T1) (T2): ceq L T1 T2 → cfull L T1 T2.
+// qed.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/ceq_ceq.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/ceq_ceq.ma
new file mode 100644 (file)
index 0000000..142f3b8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/ceq_ceq.ma
@@ -0,0 +1,37 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2/grammar/ceq.ma".
+
+(* CONTEXT-SENSITIVE EQUIVALENCES FOR TERMS *********************************)
+
+(* Main properties **********************************************************)
+
+theorem ceq_trans (L): Transitive … (ceq L).
+// qed-.
+
+lemma ceq_canc_sn (L): left_cancellable … (ceq L).
+// qed-.
+
+lemma ceq_canc_dx (L): right_cancellable … (ceq L).
+// qed-.
+
+theorem cfull_trans (L): Transitive … (cfull L).
+// qed-.
+
+lemma cfull_canc_sn (L): left_cancellable … (cfull L).
+// qed-.
+
+lemma cfull_canc_dx (L): right_cancellable … (cfull L).
+// qed-.
\ No newline at end of file

diff --git a/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/runion_3.etc b/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/runion_3.etc
deleted file mode 100644 (file)
index 16120c0..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/runion_3.etc
+++ /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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* GENERAL NOTATION USED BY THE FORMAL SYSTEM λδ ****************************)
-
-notation "hvbox( L1 ⋓ break term 46 L2 ≡ break term 46 L )"
-   non associative with precedence 45
-   for @{ 'RUnion $L1 $L2 $L }.

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma
index 9bbecddca520c86382874012b3765a2169167635..bf7f3b11f4d13410e142e063b4e5f2c99a740756 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma
@@ -21,6 +21,12 @@ definition Decidable: Prop → Prop ≝ λR. R ∨ (R → ⊥).
 
 definition Transitive: ∀A. ∀R: relation A. Prop ≝ λA,R.
                        ∀a1,a0. R a1 a0 → ∀a2. R a0 a2 → R a1 a2.
+                       
+definition left_cancellable: ∀A. ∀R: relation A. Prop ≝ λA,R.
+                             ∀a0,a1. R a0 a1 → ∀a2. R a0 a2 → R a1 a2.
+
+definition right_cancellable: ∀A. ∀R: relation A. Prop ≝ λA,R.
+                              ∀a1,a0. R a1 a0 → ∀a2. R a2 a0 → R a1 a2.
 
 definition confluent2: ∀A. ∀R1,R2: relation A. Prop ≝ λA,R1,R2.
                        ∀a0,a1. R1 a0 a1 → ∀a2. R2 a0 a2 →

diff --git a/matita/matita/contribs/lambdadelta/ground_2/notation/relations/runion_3.ma b/matita/matita/contribs/lambdadelta/ground_2/notation/relations/runion_3.ma
new file mode 100644 (file)
index 0000000..16120c0
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/notation/relations/runion_3.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* GENERAL NOTATION USED BY THE FORMAL SYSTEM λδ ****************************)
+
+notation "hvbox( L1 ⋓ break term 46 L2 ≡ break term 46 L )"
+   non associative with precedence 45
+   for @{ 'RUnion $L1 $L2 $L }.

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma
index 85ad506a26f5582c2b84737104f65691fdeac26c..5f707a57108e0977b31e20eea65d9efec3dbe870 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma
@@ -25,6 +25,52 @@ coinductive sand: relation3 rtmap rtmap rtmap ≝
 interpretation "intersection (rtmap)"
    'RIntersection f1 f2 f = (sand f1 f2 f).
 
+(* Basic inversion lemmas ***************************************************)
+
+lemma sand_inv_ppx: ∀g1,g2,g. g1 ⋒ g2 ≡ g → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 →
+                    ∃∃f. f1 ⋒ f2 ≡ f & ↑f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma sand_inv_npx: ∀g1,g2,g. g1 ⋒ g2 ≡ g → ∀f1,f2. ⫯f1 = g1 → ↑f2 = g2 →
+                    ∃∃f. f1 ⋒ f2 ≡ f & ↑f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma sand_inv_pnx: ∀g1,g2,g. g1 ⋒ g2 ≡ g → ∀f1,f2. ↑f1 = g1 → ⫯f2 = g2 →
+                    ∃∃f. f1 ⋒ f2 ≡ f & ↑f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma sand_inv_nnx: ∀g1,g2,g. g1 ⋒ g2 ≡ g → ∀f1,f2. ⫯f1 = g1 → ⫯f2 = g2 →
+                    ∃∃f. f1 ⋒ f2 ≡ f & ⫯f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
 (* Basic properties *********************************************************)
 
 let corec sand_refl: ∀f. f ⋒ f ≡ f ≝ ?.

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma
new file mode 100644 (file)
index 0000000..7b43709
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma
@@ -0,0 +1,85 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2/notation/relations/runion_3.ma".
+include "ground_2/relocation/rtmap_sle.ma".
+
+coinductive sor: relation3 rtmap rtmap rtmap ≝
+| sor_pp: ∀f1,f2,f,g1,g2,g. sor f1 f2 f → ↑f1 = g1 → ↑f2 = g2 → ↑f = g → sor g1 g2 g
+| sor_np: ∀f1,f2,f,g1,g2,g. sor f1 f2 f → ⫯f1 = g1 → ↑f2 = g2 → ⫯f = g → sor g1 g2 g
+| sor_pn: ∀f1,f2,f,g1,g2,g. sor f1 f2 f → ↑f1 = g1 → ⫯f2 = g2 → ⫯f = g → sor g1 g2 g
+| sor_nn: ∀f1,f2,f,g1,g2,g. sor f1 f2 f → ⫯f1 = g1 → ⫯f2 = g2 → ⫯f = g → sor g1 g2 g
+.
+
+interpretation "union (rtmap)"
+   'RUnion f1 f2 f = (sor f1 f2 f).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma sor_inv_ppx: ∀g1,g2,g. g1 ⋓ g2 ≡ g → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 →
+                   ∃∃f. f1 ⋓ f2 ≡ f & ↑f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma sor_inv_npx: ∀g1,g2,g. g1 ⋓ g2 ≡ g → ∀f1,f2. ⫯f1 = g1 → ↑f2 = g2 →
+                   ∃∃f. f1 ⋓ f2 ≡ f & ⫯f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma sor_inv_pnx: ∀g1,g2,g. g1 ⋓ g2 ≡ g → ∀f1,f2. ↑f1 = g1 → ⫯f2 = g2 →
+                   ∃∃f. f1 ⋓ f2 ≡ f & ⫯f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma sor_inv_nnx: ∀g1,g2,g. g1 ⋓ g2 ≡ g → ∀f1,f2. ⫯f1 = g1 → ⫯f2 = g2 →
+                   ∃∃f. f1 ⋓ f2 ≡ f & ⫯f = g.
+#g1 #g2 #g * -g1 -g2 -g
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
+try (>(injective_push … Hx1) -x1) try (>(injective_next … Hx1) -x1)
+try elim (discr_push_next … Hx1) try elim (discr_next_push … Hx1)
+try (>(injective_push … Hx2) -x2) try (>(injective_next … Hx2) -x2)
+try elim (discr_push_next … Hx2) try elim (discr_next_push … Hx2)
+/2 width=3 by ex2_intro/
+qed-.
+
+(* Basic properties *********************************************************)
+
+let corec sor_refl: ∀f. f ⋓ f ≡ f ≝ ?.
+#f cases (pn_split f) * #g #H
+[ @(sor_pp … H H H) | @(sor_nn … H H H) ] -H //
+qed.
+
+let corec sor_sym: ∀f1,f2,f. f1 ⋓ f2 ≡ f → f2 ⋓ f1 ≡ f ≝ ?.
+#f1 #f2 #f * -f1 -f2 -f
+#f1 #f2 #f #g1 #g2 #g #Hf * * * -g1 -g2 -g
+[ @sor_pp | @sor_pn | @sor_np | @sor_nn ] /2 width=7 by/
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl b/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
index cbff64690523cfb9bb2ff1a54593a09ce69d90af..cfbe19cf3af16db6f5737b7aa074cfea4aeffde7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
@@ -23,8 +23,8 @@ table {
    class "grass"
    [ { "multiple relocation" * } {
         [ { "" * } {
-             [ "rtmap" "rtmap_eq ( ? ≗ ? )" "rtmap_tl ( ⫱? )" "rtmap_tls ( ⫱*[?]? )" "rtmap_isid ( 𝐈⦃?⦄ )" "rtmap_id" "rtmap_sle ( ? ⊆ ? )" "rtmap_sand ( ? ⋒ ? ≡ ? )" "rtmap_at ( @⦃?,?⦄ ≡ ? )" "rtmap_istot ( 𝐓⦃?⦄ )" "rtmap_after ( ? ⊚ ? ≡ ? )" * ]
-             [ "nstream ( ↑? ) ( ⫯? )" "nstream_eq" "" "" "nstream_isid" "nstream_id ( 𝐈𝐝 )" "" "nstream_sand" "" "nstream_istot ( ?@❴?❵ )" "nstream_after ( ? ∘ ? )" * ]
+             [ "rtmap" "rtmap_eq ( ? ≗ ? )" "rtmap_tl ( ⫱? )" "rtmap_tls ( ⫱*[?]? )" "rtmap_isid ( 𝐈⦃?⦄ )" "rtmap_id" "rtmap_sle ( ? ⊆ ? )" "rtmap_sand ( ? ⋒ ? ≡ ? )" "rtmap_sor ( ? ⋓ ? ≡ ? )" "rtmap_at ( @⦃?,?⦄ ≡ ? )" "rtmap_istot ( 𝐓⦃?⦄ )" "rtmap_after ( ? ⊚ ? ≡ ? )" * ]
+             [ "nstream ( ↑? ) ( ⫯? )" "nstream_eq" "" "" "nstream_isid" "nstream_id ( 𝐈𝐝 )" "" "nstream_sand" "" "" "nstream_istot ( ?@❴?❵ )" "nstream_after ( ? ∘ ? )" * ]
 (*
              [ "trace ( ∥?∥ )" "trace_at ( @⦃?,?⦄ ≡ ? )" "trace_after ( ? ⊚ ? ≡ ? )" "trace_isid ( 𝐈⦃?⦄ )" "trace_isun ( 𝐔⦃?⦄ )"
                "trace_sle ( ? ⊆ ? )" "trace_sor ( ? ⋓ ? ≡ ? )" "trace_snot ( ∁ ? )" * ]