X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbg_fpbs.ma;h=888b969696dba7be6a3e48e8bb058e437dcbace5;hp=f7e3f5b230458c7dcd878185e5c1429851cb5428;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

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 f7e3f5b23..888b96969 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
@@ -22,7 +22,7 @@ include "basic_2/rt_computation/fpbg.ma".
 (* Advanced forward lemmas **************************************************)
 
 lemma fpbg_fwd_fpbs: ∀h,G1,G2,L1,L2,T1,T2.
-                     ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+                     ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
 #h #G1 #G2 #L1 #L2 #T1 #T2 *
 /3 width=5 by fpbs_strap2, fpb_fpbq/
 qed-.
@@ -30,8 +30,8 @@ qed-.
 (* Advanced properties with sort-irrelevant equivalence on closures *********)
 
 (* Basic_2A1: uses: fleq_fpbg_trans *)
-lemma feqx_fpbg_trans: ∀h,G,G2,L,L2,T,T2. ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ →
-                       ∀G1,L1,T1. ⦃G1,L1,T1⦄ ≛ ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+lemma feqx_fpbg_trans: ∀h,G,G2,L,L2,T,T2. ❪G,L,T❫ >[h] ❪G2,L2,T2❫ →
+                       ∀G1,L1,T1. ❪G1,L1,T1❫ ≛ ❪G,L,T❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
 #h #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
 elim (feqx_fpb_trans …  H1 … H0) -G -L -T
 /4 width=9 by fpbs_strap2, fpbq_feqx, ex2_3_intro/
@@ -40,15 +40,15 @@ qed-.
 (* Properties with parallel proper rst-reduction on closures ****************)
 
 lemma fpb_fpbg_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1,L1,T1⦄ ≻[h] ⦃G,L,T⦄ → ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ →
-                      ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+                      ❪G1,L1,T1❫ ≻[h] ❪G,L,T❫ → ❪G,L,T❫ >[h] ❪G2,L2,T2❫ →
+                      ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
 /3 width=5 by fpbg_fwd_fpbs, ex2_3_intro/ qed-.
 
 (* Properties with parallel rst-reduction on closures ***********************)
 
 lemma fpbq_fpbg_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
-                       ⦃G1,L1,T1⦄ ≽[h] ⦃G,L,T⦄ → ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ →
-                       ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+                       ❪G1,L1,T1❫ ≽[h] ❪G,L,T❫ → ❪G,L,T❫ >[h] ❪G2,L2,T2❫ →
+                       ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
 #h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
 elim (fpbq_inv_fpb … H1) -H1
 /2 width=5 by feqx_fpbg_trans, fpb_fpbg_trans/
@@ -56,24 +56,24 @@ qed-.
 
 (* Properties with parallel rst-compuutation on closures ********************)
 
-lemma fpbs_fpbg_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G,L,T⦄ →
-                       ∀G2,L2,T2. ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+lemma fpbs_fpbg_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
+                       ∀G2,L2,T2. ❪G,L,T❫ >[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
 #h #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
 qed-.
 
 (* Advanced properties with plus-iterated structural successor for closures *)
 
 lemma fqup_fpbg_trans (h):
-      ∀G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ⬂+ ⦃G,L,T⦄ →
-      ∀G2,L2,T2. ⦃G,L,T⦄ >[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+      ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ⬂+ ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ >[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
 /3 width=5 by fpbs_fpbg_trans, fqup_fpbs/ qed-.
 
 (* Advanced inversion lemmas of parallel rst-computation on closures ********)
 
 (* Basic_2A1: was: fpbs_fpbg *)
-lemma fpbs_inv_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ →
-                     ∨∨ ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄
-                      | ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
+lemma fpbs_inv_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ →
+                     ∨∨ ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫
+                      | ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
 #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
 [ /2 width=1 by or_introl/
 | #G #G2 #L #L2 #T #T2 #_ #H2 * #H1
@@ -89,9 +89,9 @@ qed-.
 
 (* Advanced properties of parallel rst-computation on closures **************)
 
-lemma fpbs_fpb_trans: ∀h,F1,F2,K1,K2,T1,T2. ⦃F1,K1,T1⦄ ≥[h] ⦃F2,K2,T2⦄ →
-                      ∀G2,L2,U2. ⦃F2,K2,T2⦄ ≻[h] ⦃G2,L2,U2⦄ →
-                      ∃∃G1,L1,U1. ⦃F1,K1,T1⦄ ≻[h] ⦃G1,L1,U1⦄ & ⦃G1,L1,U1⦄ ≥[h] ⦃G2,L2,U2⦄.
+lemma fpbs_fpb_trans: ∀h,F1,F2,K1,K2,T1,T2. ❪F1,K1,T1❫ ≥[h] ❪F2,K2,T2❫ →
+                      ∀G2,L2,U2. ❪F2,K2,T2❫ ≻[h] ❪G2,L2,U2❫ →
+                      ∃∃G1,L1,U1. ❪F1,K1,T1❫ ≻[h] ❪G1,L1,U1❫ & ❪G1,L1,U1❫ ≥[h] ❪G2,L2,U2❫.
 #h #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
 [ #H12 #G2 #L2 #U2 #H2 elim (feqx_fpb_trans … H12 … H2) -F2 -K2 -T2
   /3 width=5 by feqx_fpbs, ex2_3_intro/