- advances in the theory of cofrees

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / fpbg_fleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
index bb79f4aab341b387f99820c66e1db82329cda230..293e666d528866c8a6f83a05c3b3b3c8dc8dad93 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
@@ -19,16 +19,16 @@ include "basic_2/computation/fpbg.ma".
 
 (* Properties on lazy equivalence for closures ******************************)
 
-lemma fpbg_fleq_trans: â\88\80h,g,G1,G,L1,L,T1,T. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G, L, T⦄ →
-                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 â\8b\95[0] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+lemma fpbg_fleq_trans: â\88\80h,g,G1,G,L1,L,T1,T. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G, L, T⦄ →
+                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 â\89¡[0] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G #L1 #L #T1 #T #H @(fpbg_ind … H) -G -L -T
 [ /3 width=5 by fpbc_fpbg, fpbc_fleq_trans/
 | /4 width=9 by fpbg_strap1, fpbc_fleq_trans/
 ]
 qed-.
 
-lemma fleq_fpbg_trans: â\88\80h,g,G,G2,L,L2,T,T2. â¦\83G, L, Tâ¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ →
-                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\8b\95[0] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+lemma fleq_fpbg_trans: â\88\80h,g,G,G2,L,L2,T,T2. â¦\83G, L, Tâ¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ →
+                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\89¡[0] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G #G2 #L #L2 #T #T2 #H @(fpbg_ind_dx … H) -G -L -T
 [ /3 width=5 by fpbc_fpbg, fleq_fpbc_trans/
 | /4 width=9 by fpbg_strap2, fleq_fpbc_trans/
@@ -36,8 +36,8 @@ lemma fleq_fpbg_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >⋕[h, g] ⦃G2, L2
 qed-.
 
 lemma fpbs_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                 â¦\83G1, L1, T1â¦\84 â\8b\95[0] ⦃G2, L2, T2⦄ ∨
-                 â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+                 â¦\83G1, L1, T1â¦\84 â\89¡[0] ⦃G2, L2, T2⦄ ∨
+                 â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #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 elim (fpb_fpbu … H2) -H2 #H2
@@ -52,27 +52,27 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma fpbg_fpb_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
-                      â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+                      â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
+                      â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fpb_fpbu … H2) -H2
 /3 width=5 by fpbg_fleq_trans, fpbg_strap1, fpbu_fpbc/
 qed-.
 
 
 lemma fpb_fpbg_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      â¦\83G1, L1, T1â¦\84 â\89½[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ →
-                      â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+                      â¦\83G1, L1, T1â¦\84 â\89½[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ →
+                      â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 elim (fpb_fpbu … H1) -H1
 /3 width=5 by fleq_fpbg_trans, fpbg_strap2, fpbu_fpbc/
 qed-.
 
 lemma fpbs_fpbg_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
-                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 >â\8b\95[h, g] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 >â\89¡[h, g] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpb_fpbg_trans/
 qed-.
 
 (* Note: this is used in the closure proof *)
 lemma fpbg_fpbs_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 #h #g #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpb_trans/
 qed-.