update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma
index 6df83d988795ee7be8d9750d9ed6e280c68327b3..50d1bd0e531208f79ce50045ed3c0cd92b8dd656 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma
@@ -19,8 +19,8 @@ include "basic_2/dynamic/cnv.ma".
 
 inductive lsubv (h) (a) (G): relation lenv ≝
 | lsubv_atom: lsubv h a G (⋆) (⋆)
-| lsubv_bind: ∀I,L1,L2. lsubv h a G L1 L2 → lsubv h a G (L1.ⓘ{I}) (L2.ⓘ{I})
-| lsubv_beta: â\88\80L1,L2,W,V. â¦\83G,L1â¦\84 ⊢ ⓝW.V ![h,a] →
+| lsubv_bind: ∀I,L1,L2. lsubv h a G L1 L2 → lsubv h a G (L1.ⓘ[I]) (L2.ⓘ[I])
+| lsubv_beta: â\88\80L1,L2,W,V. â\9dªG,L1â\9d« ⊢ ⓝW.V ![h,a] →
               lsubv h a G L1 L2 → lsubv h a G (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
@@ -45,9 +45,9 @@ lemma lsubv_inv_atom_sn (h) (a) (G):
 /2 width=6 by lsubv_inv_atom_sn_aux/ qed-.
 
 fact lsubv_inv_bind_sn_aux (h) (a) (G): ∀L1,L2. G ⊢ L1 ⫃![h,a] L2 →
-     ∀I,K1. L1 = K1.ⓘ{I} →
-     ∨∨ ∃∃K2. G ⊢ K1 ⫃![h,a] K2 & L2 = K2.ⓘ{I}
-      | â\88\83â\88\83K2,W,V. â¦\83G,K1â¦\84 ⊢ ⓝW.V ![h,a] & G ⊢ K1 ⫃![h,a] K2
+     ∀I,K1. L1 = K1.ⓘ[I] →
+     ∨∨ ∃∃K2. G ⊢ K1 ⫃![h,a] K2 & L2 = K2.ⓘ[I]
+      | â\88\83â\88\83K2,W,V. â\9dªG,K1â\9d« ⊢ ⓝW.V ![h,a] & G ⊢ K1 ⫃![h,a] K2
                 & I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
 #h #a #G #L1 #L2 * -L1 -L2
 [ #J #K1 #H destruct
@@ -58,9 +58,9 @@ qed-.
 
 (* Basic_2A1: uses: lsubsv_inv_pair1 *)
 lemma lsubv_inv_bind_sn (h) (a) (G):
-      ∀I,K1,L2. G ⊢ K1.ⓘ{I} ⫃![h,a] L2 →
-      ∨∨ ∃∃K2. G ⊢ K1 ⫃![h,a] K2 & L2 = K2.ⓘ{I}
-       | â\88\83â\88\83K2,W,V. â¦\83G,K1â¦\84 ⊢ ⓝW.V ![h,a] & G ⊢ K1 ⫃![h,a] K2
+      ∀I,K1,L2. G ⊢ K1.ⓘ[I] ⫃![h,a] L2 →
+      ∨∨ ∃∃K2. G ⊢ K1 ⫃![h,a] K2 & L2 = K2.ⓘ[I]
+       | â\88\83â\88\83K2,W,V. â\9dªG,K1â\9d« ⊢ ⓝW.V ![h,a] & G ⊢ K1 ⫃![h,a] K2
                  & I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
 /2 width=3 by lsubv_inv_bind_sn_aux/ qed-.
 
@@ -80,9 +80,9 @@ lemma lsubv_inv_atom_dx (h) (a) (G):
 
 fact lsubv_inv_bind_dx_aux (h) (a) (G):
      ∀L1,L2. G ⊢ L1 ⫃![h,a] L2 →
-     ∀I,K2. L2 = K2.ⓘ{I} →
-     ∨∨ ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & L1 = K1.ⓘ{I}
-      | â\88\83â\88\83K1,W,V. â¦\83G,K1â¦\84 ⊢ ⓝW.V ![h,a] &
+     ∀I,K2. L2 = K2.ⓘ[I] →
+     ∨∨ ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & L1 = K1.ⓘ[I]
+      | â\88\83â\88\83K1,W,V. â\9dªG,K1â\9d« ⊢ ⓝW.V ![h,a] &
                   G ⊢ K1 ⫃![h,a] K2 & I = BPair Abst W & L1 = K1.ⓓⓝW.V.
 #h #a #G #L1 #L2 * -L1 -L2
 [ #J #K2 #H destruct
@@ -93,9 +93,9 @@ qed-.
 
 (* Basic_2A1: uses: lsubsv_inv_pair2 *)
 lemma lsubv_inv_bind_dx (h) (a) (G):
-      ∀I,L1,K2. G ⊢ L1 ⫃![h,a] K2.ⓘ{I} →
-      ∨∨ ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & L1 = K1.ⓘ{I}
-       | â\88\83â\88\83K1,W,V. â¦\83G,K1â¦\84 ⊢ ⓝW.V ![h,a] &
+      ∀I,L1,K2. G ⊢ L1 ⫃![h,a] K2.ⓘ[I] →
+      ∨∨ ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & L1 = K1.ⓘ[I]
+       | â\88\83â\88\83K1,W,V. â\9dªG,K1â\9d« ⊢ ⓝW.V ![h,a] &
                    G ⊢ K1 ⫃![h,a] K2 & I = BPair Abst W & L1 = K1.ⓓⓝW.V.
 /2 width=3 by lsubv_inv_bind_dx_aux/ qed-.