X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx.ma;h=9ed838235de6ac14cdd1e7c9d4002efa7d9a0a10;hp=d162f660a984b37fbadc4e8b274881d8207ed719;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
index d162f660a..9ed838235 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
@@ -28,11 +28,11 @@ interpretation
 (* Basic eliminators ********************************************************)
 
 lemma csx_ind: ∀h,G,L. ∀Q:predicate term.
-               (∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-                     (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) →
+               (∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
+                     (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) →
                      Q T1
                ) →
-               ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →  Q T.
+               ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ →  Q T.
 #h #G #L #Q #H0 #T1 #H elim H -T1
 /5 width=1 by SN_intro/
 qed-.
@@ -41,54 +41,54 @@ qed-.
 
 (* Basic_1: was just: sn3_pr2_intro *)
 lemma csx_intro: ∀h,G,L,T1.
-                 (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T2⦄) →
-                 ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄.
+                 (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T2❫) →
+                 ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫.
 /4 width=1 by SN_intro/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-fact csx_fwd_pair_sn_aux: ∀h,G,L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ②{I}V.T → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
+fact csx_fwd_pair_sn_aux: ∀h,G,L,U. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪U❫ →
+                          ∀I,V,T. U = ②[I]V.T → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪V❫.
 #h #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csx_intro #V2 #HLV2 #HV2
-@(IH (②{I}V2.T)) -IH /2 width=3 by cpx_pair_sn/ -HLV2
+@(IH (②[I]V2.T)) -IH /2 width=3 by cpx_pair_sn/ -HLV2
 #H elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 (* Basic_1: was just: sn3_gen_head *)
-lemma csx_fwd_pair_sn: ∀h,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃②{I}V.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
+lemma csx_fwd_pair_sn: ∀h,I,G,L,V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪②[I]V.T❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪V❫.
 /2 width=5 by csx_fwd_pair_sn_aux/ qed-.
 
-fact csx_fwd_bind_dx_aux: ∀h,G,L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                          ∀p,I,V,T. U = ⓑ{p,I}V.T → ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+fact csx_fwd_bind_dx_aux: ∀h,G,L,U. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪U❫ →
+                          ∀p,I,V,T. U = ⓑ[p,I]V.T → ❪G,L.ⓑ[I]V❫ ⊢ ⬈*[h] 𝐒❪T❫.
 #h #G #L #U #H elim H -H #U0 #_ #IH #p #I #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
-@(IH (ⓑ{p, I}V.T2)) -IH /2 width=3 by cpx_bind/ -HLT2
+@(IH (ⓑ[p, I]V.T2)) -IH /2 width=3 by cpx_bind/ -HLT2
 #H elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 (* Basic_1: was just: sn3_gen_bind *)
-lemma csx_fwd_bind_dx: ∀h,p,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ → ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_fwd_bind_dx: ∀h,p,I,G,L,V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓑ[p,I]V.T❫ → ❪G,L.ⓑ[I]V❫ ⊢ ⬈*[h] 𝐒❪T❫.
 /2 width=4 by csx_fwd_bind_dx_aux/ qed-.
 
-fact csx_fwd_flat_dx_aux: ∀h,G,L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ⓕ{I}V.T → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+fact csx_fwd_flat_dx_aux: ∀h,G,L,U. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪U❫ →
+                          ∀I,V,T. U = ⓕ[I]V.T → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
 #h #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
-@(IH (ⓕ{I}V.T2)) -IH /2 width=3 by cpx_flat/ -HLT2
+@(IH (ⓕ[I]V.T2)) -IH /2 width=3 by cpx_flat/ -HLT2
 #H elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 (* Basic_1: was just: sn3_gen_flat *)
-lemma csx_fwd_flat_dx: ∀h,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_fwd_flat_dx: ∀h,I,G,L,V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓕ[I]V.T❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
 /2 width=5 by csx_fwd_flat_dx_aux/ qed-.
 
-lemma csx_fwd_bind: ∀h,p,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                    ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_fwd_bind: ∀h,p,I,G,L,V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓑ[p,I]V.T❫ →
+                    ❪G,L❫ ⊢ ⬈*[h] 𝐒❪V❫ ∧ ❪G,L.ⓑ[I]V❫ ⊢ ⬈*[h] 𝐒❪T❫.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_bind_dx, conj/ qed-.
 
-lemma csx_fwd_flat: ∀h,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ →
-                    ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_fwd_flat: ∀h,I,G,L,V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓕ[I]V.T❫ →
+                    ❪G,L❫ ⊢ ⬈*[h] 𝐒❪V❫ ∧ ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_1: removed theorems 14: