- the relation for pointwise extensions now takes a binder as argument

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup.ma
index e68fe729b677cc3de04a028dd9f25b84e43dd66b..1e1ede2f2054bf2166132f63b714efc7298f08d5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup.ma
@@ -24,62 +24,62 @@ interpretation "plus-iterated structural successor (closure)"
 
 (* Basic properties *********************************************************)
 
-lemma fqu_fqup: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+lemma fqu_fqup: â\88\80G1,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\8a\90+ ⦃G2, L2, T2⦄.
 /2 width=1 by tri_inj/ qed.
 
 lemma fqup_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2.
-                   â¦\83G1, L1, T1â¦\84 â\8a\83+ â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83 ⦃G2, L2, T2⦄ →
-                   â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+                   â¦\83G1, L1, T1â¦\84 â\8a\90+ â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90 ⦃G2, L2, T2⦄ →
+                   â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄.
 /2 width=5 by tri_step/ qed.
 
 lemma fqup_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2.
-                   â¦\83G1, L1, T1â¦\84 â\8a\83 â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83+ ⦃G2, L2, T2⦄ →
-                   â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+                   â¦\83G1, L1, T1â¦\84 â\8a\90 â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90+ ⦃G2, L2, T2⦄ →
+                   â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄.
 /2 width=5 by tri_TC_strap/ qed.
 
 lemma fqup_ldrop: ∀G1,G2,L1,K1,K2,T1,T2,U1,e. ⇩[e] L1 ≡ K1 → ⇧[0, e] T1 ≡ U1 →
-                  â¦\83G1, K1, T1â¦\84 â\8a\83+ â¦\83G2, K2, T2â¦\84 â\86\92 â¦\83G1, L1, U1â¦\84 â\8a\83+ ⦃G2, K2, T2⦄.
+                  â¦\83G1, K1, T1â¦\84 â\8a\90+ â¦\83G2, K2, T2â¦\84 â\86\92 â¦\83G1, L1, U1â¦\84 â\8a\90+ ⦃G2, K2, T2⦄.
 #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #e #HLK1 #HTU1 #HT12 elim (eq_or_gt … e) #H destruct
 [ >(ldrop_inv_O2 … HLK1) -L1 <(lift_inv_O2 … HTU1) -U1 //
 | /3 width=5 by fqup_strap2, fqu_drop_lt/
 ]
 qed-.
 
-lemma fqup_lref: â\88\80I,G,L,K,V,i. â\87©[i] L â\89¡ K.â\93\91{I}V â\86\92 â¦\83G, L, #iâ¦\84 â\8a\83+ ⦃G, K, V⦄.
+lemma fqup_lref: â\88\80I,G,L,K,V,i. â\87©[i] L â\89¡ K.â\93\91{I}V â\86\92 â¦\83G, L, #iâ¦\84 â\8a\90+ ⦃G, K, V⦄.
 /3 width=6 by fqu_lref_O, fqu_fqup, lift_lref_ge, fqup_ldrop/ qed.
 
-lemma fqup_pair_sn: â\88\80I,G,L,V,T. â¦\83G, L, â\91¡{I}V.Tâ¦\84 â\8a\83+ ⦃G, L, V⦄.
+lemma fqup_pair_sn: â\88\80I,G,L,V,T. â¦\83G, L, â\91¡{I}V.Tâ¦\84 â\8a\90+ ⦃G, L, V⦄.
 /2 width=1 by fqu_pair_sn, fqu_fqup/ qed.
 
-lemma fqup_bind_dx: â\88\80a,I,G,L,V,T. â¦\83G, L, â\93\91{a,I}V.Tâ¦\84 â\8a\83+ ⦃G, L.ⓑ{I}V, T⦄.
+lemma fqup_bind_dx: â\88\80a,I,G,L,V,T. â¦\83G, L, â\93\91{a,I}V.Tâ¦\84 â\8a\90+ ⦃G, L.ⓑ{I}V, T⦄.
 /2 width=1 by fqu_bind_dx, fqu_fqup/ qed.
 
-lemma fqup_flat_dx: â\88\80I,G,L,V,T. â¦\83G, L, â\93\95{I}V.Tâ¦\84 â\8a\83+ ⦃G, L, T⦄.
+lemma fqup_flat_dx: â\88\80I,G,L,V,T. â¦\83G, L, â\93\95{I}V.Tâ¦\84 â\8a\90+ ⦃G, L, T⦄.
 /2 width=1 by fqu_flat_dx, fqu_fqup/ qed.
 
-lemma fqup_flat_dx_pair_sn: â\88\80I1,I2,G,L,V1,V2,T. â¦\83G, L, â\93\95{I1}V1.â\91¡{I2}V2.Tâ¦\84 â\8a\83+ ⦃G, L, V2⦄.
+lemma fqup_flat_dx_pair_sn: â\88\80I1,I2,G,L,V1,V2,T. â¦\83G, L, â\93\95{I1}V1.â\91¡{I2}V2.Tâ¦\84 â\8a\90+ ⦃G, L, V2⦄.
 /2 width=5 by fqu_pair_sn, fqup_strap1/ qed.
 
-lemma fqup_bind_dx_flat_dx: â\88\80a,G,I1,I2,L,V1,V2,T. â¦\83G, L, â\93\91{a,I1}V1.â\93\95{I2}V2.Tâ¦\84 â\8a\83+ ⦃G, L.ⓑ{I1}V1, T⦄.
+lemma fqup_bind_dx_flat_dx: â\88\80a,G,I1,I2,L,V1,V2,T. â¦\83G, L, â\93\91{a,I1}V1.â\93\95{I2}V2.Tâ¦\84 â\8a\90+ ⦃G, L.ⓑ{I1}V1, T⦄.
 /2 width=5 by fqu_flat_dx, fqup_strap1/ qed.
 
-lemma fqup_flat_dx_bind_dx: â\88\80a,I1,I2,G,L,V1,V2,T. â¦\83G, L, â\93\95{I1}V1.â\93\91{a,I2}V2.Tâ¦\84 â\8a\83+ ⦃G, L.ⓑ{I2}V2, T⦄.
+lemma fqup_flat_dx_bind_dx: â\88\80a,I1,I2,G,L,V1,V2,T. â¦\83G, L, â\93\95{I1}V1.â\93\91{a,I2}V2.Tâ¦\84 â\8a\90+ ⦃G, L.ⓑ{I2}V2, T⦄.
 /2 width=5 by fqu_bind_dx, fqup_strap1/ qed.
 
 (* Basic eliminators ********************************************************)
 
 lemma fqup_ind: ∀G1,L1,T1. ∀R:relation3 ….
-                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                (â\88\80G,G2,L,L2,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83 ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ → R G2 L2 T2.
+                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                (â\88\80G,G2,L,L2,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90 ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
+                â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ → R G2 L2 T2.
 #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
 @(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
 qed-.
 
 lemma fqup_ind_dx: ∀G2,L2,T2. ∀R:relation3 ….
-                   (â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\8a\83 ⦃G2, L2, T2⦄ → R G1 L1 T1) →
-                   (â\88\80G1,G,L1,L,T1,T. â¦\83G1, L1, T1â¦\84 â\8a\83 â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83+ ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ → R G1 L1 T1.
+                   (â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\8a\90 ⦃G2, L2, T2⦄ → R G1 L1 T1) →
+                   (â\88\80G1,G,L1,L,T1,T. â¦\83G1, L1, T1â¦\84 â\8a\90 â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90+ ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
+                   â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ → R G1 L1 T1.
 #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
 @(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
 qed-.
@@ -87,7 +87,7 @@ qed-.
 (* Basic forward lemmas *****************************************************)
 
 lemma fqup_fwd_fw: ∀G1,G2,L1,L2,T1,T2.
-                   â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
+                   â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 /3 width=3 by fqu_fwd_fw, transitive_lt/
 qed-.
@@ -95,14 +95,14 @@ qed-.
 (* Advanced eliminators *****************************************************)
 
 lemma fqup_wf_ind: ∀R:relation3 …. (
-                      â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                      â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                       R G1 L1 T1
                    ) → ∀G1,L1,T1. R G1 L1 T1.
 #R #HR @(f3_ind … fw) #n #IHn #G1 #L1 #T1 #H destruct /4 width=1 by fqup_fwd_fw/
 qed-.
 
 lemma fqup_wf_ind_eq: ∀R:relation3 …. (
-                         â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                         â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                          ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → R G2 L2 T2
                       ) → ∀G1,L1,T1. R G1 L1 T1.
 #R #HR @(f3_ind … fw) #n #IHn #G1 #L1 #T1 #H destruct /4 width=7 by fqup_fwd_fw/