update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / s_computation / fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup.ma b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup.ma
index 1f21d404ef32fbdc70ff20e02bf3863e8d009a06..91a2ab2a914818c4ed9e18f22056e0fe9f3b651f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqup.ma
@@ -30,55 +30,55 @@ interpretation "plus-iterated structural successor (closure)"
 
 (* Basic properties *********************************************************)
 
-lemma fqu_fqup: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+lemma fqu_fqup: â\88\80b,G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d«.
 /2 width=1 by tri_inj/ qed.
 
 lemma fqup_strap1: ∀b,G1,G,G2,L1,L,L2,T1,T,T2.
-                   â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                   â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+                   â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                   â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d«.
 /2 width=5 by tri_step/ qed.
 
 lemma fqup_strap2: ∀b,G1,G,G2,L1,L,L2,T1,T,T2.
-                   â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 →
-                   â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+                   â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d« →
+                   â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d«.
 /2 width=5 by tri_TC_strap/ qed.
 
-lemma fqup_pair_sn: â\88\80b,I,G,L,V,T. â¦\83G,L,â\91¡{I}V.Tâ¦\84 â¬\82+[b] â¦\83G,L,Vâ¦\84.
+lemma fqup_pair_sn: â\88\80b,I,G,L,V,T. â\9dªG,L,â\91¡[I]V.Tâ\9d« â¬\82+[b] â\9dªG,L,Vâ\9d«.
 /2 width=1 by fqu_pair_sn, fqu_fqup/ qed.
 
-lemma fqup_bind_dx: â\88\80p,I,G,L,V,T. â¦\83G,L,â\93\91{p,I}V.Tâ¦\84 â¬\82+[â\93\89] â¦\83G,L.â\93\91{I}V,Tâ¦\84.
+lemma fqup_bind_dx: â\88\80p,I,G,L,V,T. â\9dªG,L,â\93\91[p,I]V.Tâ\9d« â¬\82+[â\93\89] â\9dªG,L.â\93\91[I]V,Tâ\9d«.
 /3 width=1 by fqu_bind_dx, fqu_fqup/ qed.
 
-lemma fqup_clear: â\88\80p,I,G,L,V,T. â¦\83G,L,â\93\91{p,I}V.Tâ¦\84 â¬\82+[â\92»] â¦\83G,L.â\93§,Tâ¦\84.
+lemma fqup_clear: â\88\80p,I,G,L,V,T. â\9dªG,L,â\93\91[p,I]V.Tâ\9d« â¬\82+[â\92»] â\9dªG,L.â\93§,Tâ\9d«.
 /3 width=1 by fqu_clear, fqu_fqup/ qed.
 
-lemma fqup_flat_dx: â\88\80b,I,G,L,V,T. â¦\83G,L,â\93\95{I}V.Tâ¦\84 â¬\82+[b] â¦\83G,L,Tâ¦\84.
+lemma fqup_flat_dx: â\88\80b,I,G,L,V,T. â\9dªG,L,â\93\95[I]V.Tâ\9d« â¬\82+[b] â\9dªG,L,Tâ\9d«.
 /2 width=1 by fqu_flat_dx, fqu_fqup/ qed.
 
-lemma fqup_flat_dx_pair_sn: â\88\80b,I1,I2,G,L,V1,V2,T. â¦\83G,L,â\93\95{I1}V1.â\91¡{I2}V2.Tâ¦\84 â¬\82+[b] â¦\83G,L,V2â¦\84.
+lemma fqup_flat_dx_pair_sn: â\88\80b,I1,I2,G,L,V1,V2,T. â\9dªG,L,â\93\95[I1]V1.â\91¡[I2]V2.Tâ\9d« â¬\82+[b] â\9dªG,L,V2â\9d«.
 /2 width=5 by fqu_pair_sn, fqup_strap1/ qed.
 
-lemma fqup_bind_dx_flat_dx: â\88\80p,G,I1,I2,L,V1,V2,T. â¦\83G,L,â\93\91{p,I1}V1.â\93\95{I2}V2.Tâ¦\84 â¬\82+[â\93\89] â¦\83G,L.â\93\91{I1}V1,Tâ¦\84.
+lemma fqup_bind_dx_flat_dx: â\88\80p,G,I1,I2,L,V1,V2,T. â\9dªG,L,â\93\91[p,I1]V1.â\93\95[I2]V2.Tâ\9d« â¬\82+[â\93\89] â\9dªG,L.â\93\91[I1]V1,Tâ\9d«.
 /2 width=5 by fqu_flat_dx, fqup_strap1/ qed.
 
-lemma fqup_flat_dx_bind_dx: â\88\80p,I1,I2,G,L,V1,V2,T. â¦\83G,L,â\93\95{I1}V1.â\93\91{p,I2}V2.Tâ¦\84 â¬\82+[â\93\89] â¦\83G,L.â\93\91{I2}V2,Tâ¦\84.
+lemma fqup_flat_dx_bind_dx: â\88\80p,I1,I2,G,L,V1,V2,T. â\9dªG,L,â\93\95[I1]V1.â\93\91[p,I2]V2.Tâ\9d« â¬\82+[â\93\89] â\9dªG,L.â\93\91[I2]V2,Tâ\9d«.
 /3 width=5 by fqu_bind_dx, fqup_strap1/ qed.
 
 (* Basic eliminators ********************************************************)
 
 lemma fqup_ind: ∀b,G1,L1,T1. ∀Q:relation3 ….
-                (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
-                (â\88\80G,G2,L,L2,T,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 → Q G L T → Q G2 L2 T2) →
-                â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2.
+                (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+                (â\88\80G,G2,L,L2,T,T2. â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« → Q G L T → Q G2 L2 T2) →
+                â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2.
 #b #G1 #L1 #T1 #Q #IH1 #IH2 #G2 #L2 #T2 #H
 @(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
 qed-.
 
 lemma fqup_ind_dx: ∀b,G2,L2,T2. ∀Q:relation3 ….
-                   (â\88\80G1,L1,T1. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 → Q G1 L1 T1) →
-                   (â\88\80G1,G,L1,L,T1,T. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 → Q G L T → Q G1 L1 T1) →
-                   â\88\80G1,L1,T1. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 → Q G1 L1 T1.
+                   (â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« → Q G1 L1 T1) →
+                   (â\88\80G1,G,L1,L,T1,T. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d« → Q G L T → Q G1 L1 T1) →
+                   â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d« → Q G1 L1 T1.
 #b #G2 #L2 #T2 #Q #IH1 #IH2 #G1 #L1 #T1 #H
 @(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
 qed-.
@@ -86,7 +86,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma fqup_zeta (b) (p) (I) (G) (K) (V):
-                â\88\80T1,T2. â\87§*[1]T2 â\89\98 T1 â\86\92 â¦\83G,K,â\93\91{p,I}V.T1â¦\84 â¬\82+[b] â¦\83G,K,T2â¦\84.
+                â\88\80T1,T2. â\87§*[1]T2 â\89\98 T1 â\86\92 â\9dªG,K,â\93\91[p,I]V.T1â\9d« â¬\82+[b] â\9dªG,K,T2â\9d«.
 * /4 width=5 by fqup_strap2, fqu_fqup, fqu_drop, fqu_clear, fqu_bind_dx/ qed.
 
 (* Basic_2A1: removed theorems 1: fqup_drop *)