X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsubstitution%2Ffqus.ma;h=d7b8c866146d3c6d1a1995e5e1542b25e5f06cb0;hb=f282b35b958c9602fb1f47e5677b5805a046ac76;hp=c05bb114531e3e1dec56a3ebbb38eea74628e196;hpb=cb5ca7ea4e826e9331eabeaea44353caab00071e;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma
index c05bb1145..d7b8c8661 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma
@@ -26,15 +26,15 @@ interpretation "star-iterated structural successor (closure)"
 (* Basic eliminators ********************************************************)
 
 lemma fqus_ind: ∀G1,L1,T1. ∀R:relation3 …. R G1 L1 T1 →
-                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃⸮ ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → R G2 L2 T2.
+                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐⸮ ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
+                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → R G2 L2 T2.
 #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
 @(tri_TC_star_ind … IH1 IH2 G2 L2 T2 H) //
 qed-.
 
 lemma fqus_ind_dx: ∀G2,L2,T2. ∀R:relation3 …. R G2 L2 T2 →
-                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃* ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → R G1 L1 T1.
+                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
+                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → R G1 L1 T1.
 #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
 @(tri_TC_star_ind_dx … IH1 IH2 G1 L1 T1 H) //
 qed-.
@@ -44,40 +44,40 @@ qed-.
 lemma fqus_refl: tri_reflexive … fqus.
 /2 width=1 by tri_inj/ qed.
 
-lemma fquq_fqus: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+lemma fquq_fqus: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
 /2 width=1 by tri_inj/ qed.
 
-lemma fqus_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                   ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+lemma fqus_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+                   ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
 /2 width=5 by tri_step/ qed-.
 
-lemma fqus_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃* ⦃G2, L2, T2⦄ →
-                   ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+lemma fqus_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ →
+                   ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
 /2 width=5 by tri_TC_strap/ qed-.
 
-lemma fqus_ldrop: ∀G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ →
+lemma fqus_ldrop: ∀G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊐* ⦃G2, K2, T2⦄ →
                   ∀L1,U1,e. ⇩[e] L1 ≡ K1 → ⇧[0, e] T1 ≡ U1 →
-                  ⦃G1, L1, U1⦄ ⊃* ⦃G2, K2, T2⦄.
+                  ⦃G1, L1, U1⦄ ⊐* ⦃G2, K2, T2⦄.
 #G1 #G2 #K1 #K2 #T1 #T2 #H @(fqus_ind … H) -G2 -K2 -T2
 /3 width=5 by fqus_strap1, fquq_fqus, fquq_drop/
 qed-.
 
-lemma fqup_fqus: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+lemma fqup_fqus: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 /3 width=5 by fqus_strap1, fquq_fqus, fqu_fquq/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma fqus_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
+lemma fqus_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -L2 -T2
 /3 width=3 by fquq_fwd_fw, transitive_le/
 qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma fqup_inv_step_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
-                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ & ⦃G, L, T⦄ ⊃* ⦃G2, L2, T2⦄.
+lemma fqup_inv_step_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ⊐ ⦃G, L, T⦄ & ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄.
 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1 /2 width=5 by ex2_3_intro/
 #G1 #G #L1 #L #T1 #T #H1 #_ * /4 width=9 by fqus_strap2, fqu_fquq, ex2_3_intro/
 qed-.