- one axiom removed from sd

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/lsubc.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/lsubc.ma
index d7094600ce83377310f2832f851ac9e079e43332..bcf6c771431c79b07e956c8316ee8d0512b32723 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/lsubc.ma
@@ -20,7 +20,7 @@ include "basic_2/computation/acp_cr.ma".
 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⦄ [RP] ϵ 〚A〛 → L2 ⊢ W ÷ A →
+| lsubc_abbr: ∀L1,L2,V,W,A. ⦃L1, V⦄ ϵ[RP] 〚A〛 → L2 ⊢ W ⁝ A →
               lsubc RP L1 L2 → lsubc RP (L1. ⓓV) (L2. ⓛW)
 .
 
@@ -30,7 +30,7 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
 #RP #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -39,13 +39,13 @@ fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → L1 = ⋆ → L2 = ⋆.
 qed.
 
 (* Basic_1: was: csubc_gen_sort_r *)
-lemma lsubc_inv_atom1: ∀RP,L2. ⋆ [RP] ⊑ L2 → L2 = ⋆.
+lemma lsubc_inv_atom1: ∀RP,L2. ⋆ ⊑[RP] L2 → L2 = ⋆.
 /2 width=4/ qed-.
 
-fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀I,K1,V. L1 = K1. ⓑ{I} V →
-                          (∃∃K2. K1 [RP] ⊑ K2 & L2 = K2. ⓑ{I} V) ∨
-                          ∃∃K2,W,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                    K1 [RP] ⊑ K2 &
+fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀I,K1,V. L1 = K1. ⓑ{I} V →
+                          (∃∃K2. K1 ⊑[RP] K2 & L2 = K2. ⓑ{I} V) ∨
+                          ∃∃K2,W,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
+                                    K1 ⊑[RP] K2 &
                                     L2 = K2. ⓛW & I = Abbr.
 #RP #L1 #L2 * -L1 -L2
 [ #I #K1 #V #H destruct
@@ -55,14 +55,14 @@ fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀I,K1,V. L1 = K1. 
 qed.
 
 (* Basic_1: was: csubc_gen_head_r *)
-lemma lsubc_inv_pair1: ∀RP,I,K1,L2,V. K1. ⓑ{I} V [RP] ⊑ L2 →
-                       (∃∃K2. K1 [RP] ⊑ K2 & L2 = K2. ⓑ{I} V) ∨
-                       ∃∃K2,W,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                 K1 [RP] ⊑ K2 &
+lemma lsubc_inv_pair1: ∀RP,I,K1,L2,V. K1. ⓑ{I} V ⊑[RP] L2 →
+                       (∃∃K2. K1 ⊑[RP] K2 & L2 = K2. ⓑ{I} V) ∨
+                       ∃∃K2,W,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
+                                 K1 ⊑[RP] K2 &
                                  L2 = K2. ⓛW & I = Abbr.
 /2 width=3/ qed-.
 
-fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → L2 = ⋆ → L1 = ⋆.
+fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L2 = ⋆ → L1 = ⋆.
 #RP #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -71,13 +71,13 @@ fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → L2 = ⋆ → L1 = ⋆.
 qed.
 
 (* Basic_1: was: csubc_gen_sort_l *)
-lemma lsubc_inv_atom2: ∀RP,L1. L1 [RP] ⊑ ⋆ → L1 = ⋆.
+lemma lsubc_inv_atom2: ∀RP,L1. L1 ⊑[RP] ⋆ → L1 = ⋆.
 /2 width=4/ 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⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                    K1 [RP] ⊑ K2 &
+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〛 & K2 ⊢ W ⁝ A &
+                                    K1 ⊑[RP] K2 &
                                     L1 = K1. ⓓV & I = Abst.
 #RP #L1 #L2 * -L1 -L2
 [ #I #K2 #W #H destruct
@@ -87,18 +87,20 @@ fact lsubc_inv_pair2_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀I,K2,W. L2 = K2. 
 qed.
 
 (* Basic_1: was: 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⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                 K1 [RP] ⊑ K2 &
+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〛 & K2 ⊢ W ⁝ A &
+                                 K1 ⊑[RP] K2 &
                                  L1 = K1. ⓓV & I = Abst.
 /2 width=3/ qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: csubc_refl *)
-lemma lsubc_refl: ∀RP,L. L [RP] ⊑ L.
+lemma lsubc_refl: ∀RP,L. L ⊑[RP] L.
 #RP #L elim L -L // /2 width=1/
 qed.
 
-(* Basic_1: removed theorems 2: csubc_clear_conf csubc_getl_conf *)
+(* Basic_1: removed theorems 3:
+            csubc_clear_conf csubc_getl_conf csubc_csuba
+*)