partial commit: "computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsubc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
index 0af4368e39a6b59f271b7e80fffd1f5329f45219..854a79ce6a73bc44514ab01619152415e3d54c28 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
@@ -12,27 +12,27 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lrsubeq_3.ma".
+include "basic_2/notation/relations/lrsubeq_4.ma".
 include "basic_2/static/aaa.ma".
 include "basic_2/computation/acp_cr.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
 
-inductive lsubc (RP:lenv→predicate term): relation lenv ≝
-| lsubc_atom: lsubc RP (⋆) (⋆)
-| lsubc_pair: ∀I,L1,L2,V. lsubc RP L1 L2 → lsubc RP (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubc_abbr: ∀L1,L2,V,W,A. ⦃L1, V⦄ ϵ[RP] 〚A〛 → ⦃L1, W⦄ ϵ[RP] 〚A〛 → L2 ⊢ W ⁝ A →
-              lsubc RP L1 L2 → lsubc RP (L1. ⓓⓝW.V) (L2.ⓛW)
+inductive lsubc (RP) (G): relation lenv ≝
+| lsubc_atom: lsubc RP G (⋆) (⋆)
+| lsubc_pair: ∀I,L1,L2,V. lsubc RP G L1 L2 → lsubc RP G (L1.ⓑ{I}V) (L2.ⓑ{I}V)
+| lsubc_abbr: ∀L1,L2,V,W,A. ⦃G, L1, V⦄ ϵ[RP] 〚A〛 → ⦃G, L1, W⦄ ϵ[RP] 〚A〛 → ⦃G, L2⦄ ⊢ W ⁝ A →
+              lsubc RP G L1 L2 → lsubc RP G (L1. ⓓⓝW.V) (L2.ⓛW)
 .
 
 interpretation
   "local environment refinement (abstract candidates of reducibility)"
-  'LRSubEq RP L1 L2 = (lsubc RP L1 L2).
+  'LRSubEq RP G L1 L2 = (lsubc RP G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
-#RP #L1 #L2 * -L1 -L2
+fact lsubc_inv_atom1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
+#RP #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
 | #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
@@ -40,15 +40,15 @@ fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
 qed-.
 
 (* Basic_1: was just: csubc_gen_sort_r *)
-lemma lsubc_inv_atom1: ∀RP,L2. ⋆ ⊑[RP] L2 → L2 = ⋆.
-/2 width=4 by lsubc_inv_atom1_aux/ qed-.
+lemma lsubc_inv_atom1: ∀RP,G,L2. G ⊢ ⋆ ⊑[RP] L2 → L2 = ⋆.
+/2 width=5 by lsubc_inv_atom1_aux/ qed-.
 
-fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (∃∃K2. K1 ⊑[RP] K2 & L2 = K2.ⓑ{I}X) ∨
-                          ∃∃K2,V,W,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                      K1 ⊑[RP] K2 &
+fact lsubc_inv_pair1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+                          (∃∃K2. G ⊢ K1 ⊑[RP] K2 & L2 = K2.ⓑ{I}X) ∨
+                          ∃∃K2,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+                                      G ⊢ K1 ⊑[RP] K2 &
                                       L2 = K2. ⓛW & X = ⓝW.V & I = Abbr.
-#RP #L1 #L2 * -L1 -L2
+#RP #G #L1 #L2 * -L1 -L2
 [ #I #K1 #V #H destruct
 | #J #L1 #L2 #V #HL12 #I #K1 #W #H destruct /3 width=3/
 | #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K1 #V #H destruct /3 width=10/
@@ -56,15 +56,15 @@ fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{
 qed-.
 
 (* Basic_1: was: csubc_gen_head_r *)
-lemma lsubc_inv_pair1: ∀RP,I,K1,L2,X. K1.ⓑ{I}X ⊑[RP] L2 →
-                       (∃∃K2. K1 ⊑[RP] K2 & L2 = K2.ⓑ{I}X) ∨
-                       ∃∃K2,V,W,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                   K1 ⊑[RP] K2 &
+lemma lsubc_inv_pair1: ∀RP,I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ⊑[RP] L2 →
+                       (∃∃K2. G ⊢ K1 ⊑[RP] K2 & L2 = K2.ⓑ{I}X) ∨
+                       ∃∃K2,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+                                   G ⊢ K1 ⊑[RP] K2 &
                                    L2 = K2.ⓛW & X = ⓝW.V & I = Abbr.
 /2 width=3 by lsubc_inv_pair1_aux/ qed-.
 
-fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L2 = ⋆ → L1 = ⋆.
-#RP #L1 #L2 * -L1 -L2
+fact lsubc_inv_atom2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → L2 = ⋆ → L1 = ⋆.
+#RP #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
 | #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
@@ -72,15 +72,15 @@ fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L2 = ⋆ → L1 = ⋆.
 qed-.
 
 (* Basic_1: was just: csubc_gen_sort_l *)
-lemma lsubc_inv_atom2: ∀RP,L1. L1 ⊑[RP] ⋆ → L1 = ⋆.
-/2 width=4 by lsubc_inv_atom2_aux/ qed-.
+lemma lsubc_inv_atom2: ∀RP,G,L1. G ⊢ L1 ⊑[RP] ⋆ → L1 = ⋆.
+/2 width=5 by lsubc_inv_atom2_aux/ qed-.
 
-fact lsubc_inv_pair2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀I,K2,W. L2 = K2.ⓑ{I} W →
-                          (∃∃K1. K1 ⊑[RP] K2 & L1 = K1. ⓑ{I} W) ∨
-                          ∃∃K1,V,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                    K1 ⊑[RP] K2 &
+fact lsubc_inv_pair2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → ∀I,K2,W. L2 = K2.ⓑ{I} W →
+                          (∃∃K1. G ⊢ K1 ⊑[RP] K2 & L1 = K1. ⓑ{I} W) ∨
+                          ∃∃K1,V,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+                                    G ⊢ K1 ⊑[RP] K2 &
                                     L1 = K1.ⓓⓝW.V & I = Abst.
-#RP #L1 #L2 * -L1 -L2
+#RP #G #L1 #L2 * -L1 -L2
 [ #I #K2 #W #H destruct
 | #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3/
 | #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K2 #W #H destruct /3 width=8/
@@ -88,18 +88,18 @@ fact lsubc_inv_pair2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀I,K2,W. L2 = K2.ⓑ{
 qed-.
 
 (* Basic_1: was just: csubc_gen_head_l *)
-lemma lsubc_inv_pair2: ∀RP,I,L1,K2,W. L1 ⊑[RP] K2.ⓑ{I} W →
-                       (∃∃K1. K1 ⊑[RP] K2 & L1 = K1.ⓑ{I} W) ∨
-                       ∃∃K1,V,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                 K1 ⊑[RP] K2 &
+lemma lsubc_inv_pair2: ∀RP,I,G,L1,K2,W. G ⊢ L1 ⊑[RP] K2.ⓑ{I} W →
+                       (∃∃K1. G ⊢ K1 ⊑[RP] K2 & L1 = K1.ⓑ{I} W) ∨
+                       ∃∃K1,V,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+                                 G ⊢ K1 ⊑[RP] K2 &
                                  L1 = K1.ⓓⓝW.V & I = Abst.
 /2 width=3 by lsubc_inv_pair2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was just: csubc_refl *)
-lemma lsubc_refl: ∀RP,L. L ⊑[RP] L.
-#RP #L elim L -L // /2 width=1/
+lemma lsubc_refl: ∀RP,G,L. G ⊢ L ⊑[RP] L.
+#RP #G #L elim L -L // /2 width=1/
 qed.
 
 (* Basic_1: removed theorems 3: