- notation change for tdeq and related notions

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fpbg_fpbs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
index df666294c99819a357f0098e6752f60e7f52f9ae..2118c2c16b9ce59b7b296fccb0775d30525b9ee1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
@@ -21,13 +21,13 @@ include "basic_2/computation/fpbg_fleq.ma".
 (* Properties on "qrst" parallel reduction on closures **********************)
 
 lemma fpb_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                      â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄ →
-                      â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄.
+                      â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄ →
+                      â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄.
 /3 width=5 by fpbg_fwd_fpbs, ex2_3_intro/ qed-.
 
 lemma fpbq_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                       â¦\83G1, L1, T1â¦\84 â\89½[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄ →
-                       â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄.
+                       â¦\83G1, L1, T1â¦\84 â\89½[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄ →
+                       â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄.
 #h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fpbq_ind_alt … H1) -H1
 /2 width=5 by fleq_fpbg_trans, fpb_fpbg_trans/
 qed-.
@@ -35,34 +35,34 @@ qed-.
 (* Properties on "qrst" parallel compuutation on closures *******************)
 
 lemma fpbs_fpbg_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 >â\89¡[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄.
+                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 >â\89\9b[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄.
 #h #o #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
 qed-.
 
 (* Note: this is used in the closure proof *)
 lemma fpbg_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄.
+                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄.
 #h #o #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
 qed-.
 
 (* Note: this is used in the closure proof *)
-lemma fqup_fpbg: â\88\80h,o,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄.
+lemma fqup_fpbg: â\88\80h,o,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqup_inv_step_sn … H) -H
 /3 width=5 by fqus_fpbs, fpb_fqu, ex2_3_intro/
 qed.
 
 lemma cpxs_fpbg: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 →
-                 (T1 = T2 â\86\92 â\8a¥) â\86\92 â¦\83G, L, T1â¦\84 >â\89¡[h, o] ⦃G, L, T2⦄.
+                 (T1 = T2 â\86\92 â\8a¥) â\86\92 â¦\83G, L, T1â¦\84 >â\89\9b[h, o] ⦃G, L, T2⦄.
 #h #o #G #L #T1 #T2 #H #H0 elim (cpxs_neq_inv_step_sn … H … H0) -H -H0
 /4 width=5 by cpxs_fpbs, fpb_cpx, ex2_3_intro/
 qed.
 
 lemma lstas_fpbg: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → (T1 = T2 → ⊥) →
-                  â\88\80d1. d2 â\89¤ d1 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T1 â\96ª[h, o] d1 â\86\92 â¦\83G, L, T1â¦\84 >â\89¡[h, o] ⦃G, L, T2⦄.
+                  â\88\80d1. d2 â\89¤ d1 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T1 â\96ª[h, o] d1 â\86\92 â¦\83G, L, T1â¦\84 >â\89\9b[h, o] ⦃G, L, T2⦄.
 /3 width=5 by lstas_cpxs, cpxs_fpbg/ qed.
 
 lemma lpxs_fpbg: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 →
-                 (L1 â\89¡[T, 0] L2 â\86\92 â\8a¥) â\86\92 â¦\83G, L1, Tâ¦\84 >â\89¡[h, o] ⦃G, L2, T⦄.
+                 (L1 â\89¡[T, 0] L2 â\86\92 â\8a¥) â\86\92 â¦\83G, L1, Tâ¦\84 >â\89\9b[h, o] ⦃G, L2, T⦄.
 #h #o #G #L1 #L2 #T #H #H0 elim (lpxs_nlleq_inv_step_sn … H … H0) -H -H0
 /4 width=5 by fpb_lpx, lpxs_lleq_fpbs, ex2_3_intro/
 qed.