- new extendedd beta-reductum involving native type annotation

[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 bcf6c771431c79b07e956c8316ee8d0512b32723..a3cc36b24dc0465539348458c456ad3b323be051 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
@@ -20,8 +20,8 @@ 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⦄ ϵ[RP] 〚A〛 → L2 ⊢ W ⁝ A →
-              lsubc RP L1 L2 → lsubc RP (L1. ⓓV) (L2. ⓛW)
+| 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)
 .
 
 interpretation
@@ -34,69 +34,69 @@ fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
 #RP #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #A #_ #_ #_ #H destruct
+| #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
 ]
-qed.
+qed-.
 
-(* Basic_1: was: csubc_gen_sort_r *)
+(* Basic_1: was just: csubc_gen_sort_r *)
 lemma lsubc_inv_atom1: ∀RP,L2. ⋆ ⊑[RP] L2 → L2 = ⋆.
-/2 width=4/ qed-.
+/2 width=4 by lsubc_inv_atom1_aux/ 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⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                    K1 ⊑[RP] K2 &
-                                    L2 = K2. ⓛW & I = Abbr.
+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 &
+                                      L2 = K2. ⓛW & X = ⓝW.V & I = Abbr.
 #RP #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 #HW2 #HL12 #I #K1 #V #H destruct /3 width=7/
+| #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K1 #V #H destruct /3 width=10/
 ]
-qed.
+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⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                 K1 ⊑[RP] K2 &
-                                 L2 = K2. ⓛW & I = Abbr.
-/2 width=3/ qed-.
+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 &
+                                   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
 [ //
 | #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #A #_ #_ #_ #H destruct
+| #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
 ]
-qed.
+qed-.
 
-(* Basic_1: was: csubc_gen_sort_l *)
+(* Basic_1: was just: csubc_gen_sort_l *)
 lemma lsubc_inv_atom2: ∀RP,L1. L1 ⊑[RP] ⋆ → L1 = ⋆.
-/2 width=4/ qed-.
+/2 width=4 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〛 & K2 ⊢ W ⁝ A &
+                          ∃∃K1,V,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
                                     K1 ⊑[RP] K2 &
-                                    L1 = K1. ⓓV & I = Abst.
+                                    L1 = K1. ⓓⓝW.V & I = Abst.
 #RP #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 #HW2 #HL12 #I #K2 #W #H destruct /3 width=7/
+| #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K2 #W #H destruct /3 width=8/
 ]
-qed.
+qed-.
 
-(* Basic_1: was: csubc_gen_head_l *)
+(* 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〛 & K2 ⊢ W ⁝ A &
+                       (∃∃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 &
-                                 L1 = K1. ⓓV & I = Abst.
-/2 width=3/ qed-.
+                                 L1 = K1.ⓓⓝW.V & I = Abst.
+/2 width=3 by lsubc_inv_pair2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
-(* Basic_1: was: csubc_refl *)
+(* Basic_1: was just: csubc_refl *)
 lemma lsubc_refl: ∀RP,L. L ⊑[RP] L.
 #RP #L elim L -L // /2 width=1/
 qed.