- commit of the "substitution" component

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma
index ef5af3100b3e3882703b4db210e2d662a064cf19..c05bb114531e3e1dec56a3ebbb38eea74628e196 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqus.ma
@@ -14,6 +14,7 @@
 
 include "basic_2/notation/relations/suptermstar_6.ma".
 include "basic_2/relocation/fquq.ma".
+include "basic_2/substitution/fqup.ma".
 
 (* STAR-ITERATED SUPCLOSURE *************************************************)
 
@@ -48,22 +49,35 @@ lemma fquq_fqus: ∀G1,G2,L1,L2,T1,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.
+/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⦄.
-/2 width=5 by tri_TC_strap/ qed.
+/2 width=5 by tri_TC_strap/ qed-.
 
 lemma fqus_ldrop: ∀G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ →
-                  ∀L1,U1,e. ⇩[0, e] L1 ≡ K1 → ⇧[0, e] T1 ≡ U1 →
+                  ∀L1,U1,e. ⇩[e] L1 ≡ K1 → ⇧[0, e] T1 ≡ U1 →
                   ⦃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⦄.
+#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}.
 #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⦄.
+#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-.