- advances in the theory of cofrees

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
index 0755ebf79960759c76b8d4312e356c9b17d042ef..5d7ce1cb342f0b56d17fe9f783c248ef4fce6c10 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
@@ -25,38 +25,38 @@ interpretation "general 'big tree' proper parallel computation (closure)"
 
 (* Basic properties *********************************************************)
 
-lemma fpbc_fpbg: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\89»â\8b\95[h, g] ⦃G2, L2, T2⦄ →
-                 â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄.
+lemma fpbc_fpbg: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\89»â\89¡[h, g] ⦃G2, L2, T2⦄ →
+                 â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 /2 width=1 by tri_inj/ qed.
 
 lemma fpbg_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                   â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\89»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\89¡[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\89»â\89¡[h, g] ⦃G2, L2, T2⦄ →
+                   â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄.
 /2 width=5 by tri_step/ qed.
 
 lemma fpbg_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                   â¦\83G1, L1, T1â¦\84 â\89»â\8b\95[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\89»â\89¡[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⦄.
 /2 width=5 by tri_TC_strap/ qed.
 
 (* Note: this is used in the closure proof *)
-lemma fqup_fpbg: â\88\80h,g,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\8b\95[h, g] ⦃G2, L2, T2⦄.
+lemma fqup_fpbg: â\88\80h,g,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, g] ⦃G2, L2, T2⦄.
 /4 width=1 by fpbc_fpbg, fpbu_fpbc, fpbu_fqup/ qed.
 
 (* Basic eliminators ********************************************************)
 
 lemma fpbg_ind: ∀h,g,G1,L1,T1. ∀R:relation3 ….
-                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\89»â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                (â\88\80G,G2,L,L2,T,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\89»â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
+                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\89»â\89¡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                (â\88\80G,G2,L,L2,T,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\89»â\89¡[h, g] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
+                â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
 #h #g #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
 @(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
 qed-.
 
 lemma fpbg_ind_dx: ∀h,g,G2,L2,T2. ∀R:relation3 ….
-                   (â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\89»â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1) →
-                   (â\88\80G1,G,L1,L,T1,T. â¦\83G1, L1, T1â¦\84 â\89»â\8b\95[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
+                   (â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\89»â\89¡[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1) →
+                   (â\88\80G1,G,L1,L,T1,T. â¦\83G1, L1, T1â¦\84 â\89»â\89¡[h, g] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
+                   â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
 #h #g #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
 @(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
 qed-.