X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flpxs.ma;h=ade37fde5a7aa19e2b53c0be3824591792928263;hp=d532c62bfaeb65a7021d757a10b0c3b620f055c7;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
index d532c62bf..ade37fde5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
@@ -28,13 +28,13 @@ interpretation
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: uses: lpxs_pair_refl *)
-lemma lpxs_bind_refl_dx (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 →
-                                 ∀I. ⦃G,L1.ⓘ{I}⦄ ⊢ ⬈*[h] L2.ⓘ{I}.
+lemma lpxs_bind_refl_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ⬈*[h] L2 →
+                                 ∀I. ❪G,L1.ⓘ[I]❫ ⊢ ⬈*[h] L2.ⓘ[I].
 /2 width=1 by lex_bind_refl_dx/ qed.
 
-lemma lpxs_pair (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 →
-                         ∀V1,V2. ⦃G,L1⦄ ⊢ V1 ⬈*[h] V2 →
-                         ∀I. ⦃G,L1.ⓑ{I}V1⦄ ⊢ ⬈*[h] L2.ⓑ{I}V2.
+lemma lpxs_pair (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ⬈*[h] L2 →
+                         ∀V1,V2. ❪G,L1❫ ⊢ V1 ⬈*[h] V2 →
+                         ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈*[h] L2.ⓑ[I]V2.
 /2 width=1 by lex_pair/ qed.
 
 lemma lpxs_refl (h) (G): reflexive … (lpxs h G).
@@ -43,25 +43,25 @@ lemma lpxs_refl (h) (G): reflexive … (lpxs h G).
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: was: lpxs_inv_atom1 *)
-lemma lpxs_inv_atom_sn (h) (G): ∀L2. ⦃G,⋆⦄ ⊢ ⬈*[h] L2 → L2 = ⋆.
+lemma lpxs_inv_atom_sn (h) (G): ∀L2. ❪G,⋆❫ ⊢ ⬈*[h] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
-lemma lpxs_inv_bind_sn (h) (G): ∀I1,L2,K1. ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬈*[h] L2 →
-                                ∃∃I2,K2. ⦃G,K1⦄ ⊢ ⬈*[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬈*[h] I2 & L2 = K2.ⓘ{I2}.
+lemma lpxs_inv_bind_sn (h) (G): ∀I1,L2,K1. ❪G,K1.ⓘ[I1]❫ ⊢ ⬈*[h] L2 →
+                                ∃∃I2,K2. ❪G,K1❫ ⊢ ⬈*[h] K2 & ❪G,K1❫ ⊢ I1 ⬈*[h] I2 & L2 = K2.ⓘ[I2].
 /2 width=1 by lex_inv_bind_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_inv_pair1 *)
-lemma lpxs_inv_pair_sn (h) (G): ∀I,L2,K1,V1. ⦃G,K1.ⓑ{I}V1⦄ ⊢ ⬈*[h] L2 →
-                                ∃∃K2,V2. ⦃G,K1⦄ ⊢ ⬈*[h] K2 & ⦃G,K1⦄ ⊢ V1 ⬈*[h] V2 & L2 = K2.ⓑ{I}V2.
+lemma lpxs_inv_pair_sn (h) (G): ∀I,L2,K1,V1. ❪G,K1.ⓑ[I]V1❫ ⊢ ⬈*[h] L2 →
+                                ∃∃K2,V2. ❪G,K1❫ ⊢ ⬈*[h] K2 & ❪G,K1❫ ⊢ V1 ⬈*[h] V2 & L2 = K2.ⓑ[I]V2.
 /2 width=1 by lex_inv_pair_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_inv_atom2 *)
-lemma lpxs_inv_atom_dx (h) (G): ∀L1. ⦃G,L1⦄ ⊢ ⬈*[h] ⋆ → L1 = ⋆.
+lemma lpxs_inv_atom_dx (h) (G): ∀L1. ❪G,L1❫ ⊢ ⬈*[h] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
 (* Basic_2A1: was: lpxs_inv_pair2 *)
-lemma lpxs_inv_pair_dx (h) (G): ∀I,L1,K2,V2. ⦃G,L1⦄ ⊢ ⬈*[h] K2.ⓑ{I}V2 →
-                                ∃∃K1,V1. ⦃G,K1⦄ ⊢ ⬈*[h] K2 & ⦃G,K1⦄ ⊢ V1 ⬈*[h] V2 & L1 = K1.ⓑ{I}V1.
+lemma lpxs_inv_pair_dx (h) (G): ∀I,L1,K2,V2. ❪G,L1❫ ⊢ ⬈*[h] K2.ⓑ[I]V2 →
+                                ∃∃K1,V1. ❪G,K1❫ ⊢ ⬈*[h] K2 & ❪G,K1❫ ⊢ V1 ⬈*[h] V2 & L1 = K1.ⓑ[I]V1.
 /2 width=1 by lex_inv_pair_dx/ qed-.
 
 (* Basic eliminators ********************************************************)
@@ -70,12 +70,12 @@ lemma lpxs_inv_pair_dx (h) (G): ∀I,L1,K2,V2. ⦃G,L1⦄ ⊢ ⬈*[h] K2.ⓑ{I}V
 lemma lpxs_ind (h) (G): ∀Q:relation lenv.
                         Q (⋆) (⋆) → (
                           ∀I,K1,K2.
-                          ⦃G,K1⦄ ⊢ ⬈*[h] K2 →
-                          Q K1 K2 → Q (K1.ⓘ{I}) (K2.ⓘ{I})
+                          ❪G,K1❫ ⊢ ⬈*[h] K2 →
+                          Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
                         ) → (
                           ∀I,K1,K2,V1,V2.
-                          ⦃G,K1⦄ ⊢ ⬈*[h] K2 → ⦃G,K1⦄ ⊢ V1 ⬈*[h] V2 →
-                          Q K1 K2 → Q (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
+                          ❪G,K1❫ ⊢ ⬈*[h] K2 → ❪G,K1❫ ⊢ V1 ⬈*[h] V2 →
+                          Q K1 K2 → Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
                         ) →
-                        ∀L1,L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → Q L1 L2.
+                        ∀L1,L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → Q L1 L2.
 /3 width=4 by lex_ind/ qed-.