X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Flsubc.ma;h=0a5f81c00287b347d33acade529c7e01ad6b267a;hb=68b4f2490c12139c03760b39895619e63b0f38c9;hp=d7d1c565a4a93e8ca3568c4b2c67d60ca9a4e339;hpb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubc.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubc.ma
index d7d1c565a..0a5f81c00 100644
--- a/matita/matita/contribs/lambdadelta/static_2/static/lsubc.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubc.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground/xoa/ex_6_4.ma".
 include "static_2/notation/relations/lrsubeqc_4.ma".
 include "static_2/static/aaa.ma".
 include "static_2/static/gcp_cr.ma".
@@ -20,8 +21,8 @@ include "static_2/static/gcp_cr.ma".
 
 inductive lsubc (RP) (G): relation lenv ≝
 | lsubc_atom: lsubc RP G (⋆) (⋆)
-| lsubc_bind: ∀I,L1,L2. lsubc RP G L1 L2 → lsubc RP G (L1.ⓘ{I}) (L2.ⓘ{I})
-| lsubc_beta: ∀L1,L2,V,W,A. ⦃G, L1, V⦄ ϵ[RP] 〚A〛 → ⦃G, L1, W⦄ ϵ[RP] 〚A〛 → ⦃G, L2⦄ ⊢ W ⁝ A →
+| lsubc_bind: ∀I,L1,L2. lsubc RP G L1 L2 → lsubc RP G (L1.ⓘ[I]) (L2.ⓘ[I])
+| lsubc_beta: ∀L1,L2,V,W,A. ❪G,L1,V❫ ϵ ⟦A⟧[RP] → ❪G,L1,W❫ ϵ ⟦A⟧[RP] → ❪G,L2❫ ⊢ W ⁝ A →
               lsubc RP G L1 L2 → lsubc RP G (L1. ⓓⓝW.V) (L2.ⓛW)
 .
 
@@ -43,9 +44,9 @@ qed-.
 lemma lsubc_inv_atom1: ∀RP,G,L2. G ⊢ ⋆ ⫃[RP] L2 → L2 = ⋆.
 /2 width=5 by lsubc_inv_atom1_aux/ qed-.
 
-fact lsubc_inv_bind1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K1. L1 = K1.ⓘ{I} →
-                          (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓘ{I}) ∨
-                          ∃∃K2,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+fact lsubc_inv_bind1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K1. L1 = K1.ⓘ[I] →
+                          (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓘ[I]) ∨
+                          ∃∃K2,V,W,A. ❪G,K1,V❫ ϵ ⟦A⟧[RP] & ❪G,K1,W❫ ϵ ⟦A⟧[RP] & ❪G,K2❫ ⊢ W ⁝ A &
                                       G ⊢ K1 ⫃[RP] K2 &
                                       L2 = K2. ⓛW & I = BPair Abbr (ⓝW.V).
 #RP #G #L1 #L2 * -L1 -L2
@@ -57,9 +58,9 @@ fact lsubc_inv_bind1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K1. L1 = K
 qed-.
 
 (* Basic_1: was: csubc_gen_head_r *)
-lemma lsubc_inv_bind1: ∀RP,I,G,K1,L2. G ⊢ K1.ⓘ{I} ⫃[RP] L2 →
-                       (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓘ{I}) ∨
-                       ∃∃K2,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+lemma lsubc_inv_bind1: ∀RP,I,G,K1,L2. G ⊢ K1.ⓘ[I] ⫃[RP] L2 →
+                       (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓘ[I]) ∨
+                       ∃∃K2,V,W,A. ❪G,K1,V❫ ϵ ⟦A⟧[RP] & ❪G,K1,W❫ ϵ ⟦A⟧[RP] & ❪G,K2❫ ⊢ W ⁝ A &
                                    G ⊢ K1 ⫃[RP] K2 &
                                    L2 = K2.ⓛW & I = BPair Abbr (ⓝW.V).
 /2 width=3 by lsubc_inv_bind1_aux/ qed-.
@@ -76,9 +77,9 @@ qed-.
 lemma lsubc_inv_atom2: ∀RP,G,L1. G ⊢ L1 ⫃[RP] ⋆ → L1 = ⋆.
 /2 width=5 by lsubc_inv_atom2_aux/ qed-.
 
-fact lsubc_inv_bind2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K2. L2 = K2.ⓘ{I} →
-                          (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1. ⓘ{I}) ∨
-                          ∃∃K1,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+fact lsubc_inv_bind2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K2. L2 = K2.ⓘ[I] →
+                          (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1. ⓘ[I]) ∨
+                          ∃∃K1,V,W,A. ❪G,K1,V❫ ϵ ⟦A⟧[RP] & ❪G,K1,W❫ ϵ ⟦A⟧[RP] & ❪G,K2❫ ⊢ W ⁝ A &
                                       G ⊢ K1 ⫃[RP] K2 &
                                       L1 = K1.ⓓⓝW.V & I = BPair Abst W.
 #RP #G #L1 #L2 * -L1 -L2
@@ -90,9 +91,9 @@ fact lsubc_inv_bind2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K2. L2 = K
 qed-.
 
 (* Basic_1: was just: csubc_gen_head_l *)
-lemma lsubc_inv_bind2: ∀RP,I,G,L1,K2. G ⊢ L1 ⫃[RP] K2.ⓘ{I} →
-                       (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1.ⓘ{I}) ∨
-                       ∃∃K1,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
+lemma lsubc_inv_bind2: ∀RP,I,G,L1,K2. G ⊢ L1 ⫃[RP] K2.ⓘ[I] →
+                       (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1.ⓘ[I]) ∨
+                       ∃∃K1,V,W,A. ❪G,K1,V❫ ϵ ⟦A⟧[RP] & ❪G,K1,W❫ ϵ ⟦A⟧[RP] & ❪G,K2❫ ⊢ W ⁝ A &
                                    G ⊢ K1 ⫃[RP] K2 &
                                    L1 = K1.ⓓⓝW.V & I = BPair Abst W.
 /2 width=3 by lsubc_inv_bind2_aux/ qed-.