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

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma
index 05a450dae356403b3c59504038b8c7bcd83b40c1..f5f521dd52508de91ceaa6d956794199f1bbc11c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma
@@ -19,14 +19,14 @@ include "static_2/s_computation/fqus.ma".
 
 (* Alternative definition with plus-iterated supclosure *********************)
 
-lemma fqup_fqus: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄.
+lemma fqup_fqus: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ⊐*[b] ⦃G2,L2,T2⦄.
 #b #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_2A1: was: fqus_inv_gen *)
-lemma fqus_inv_fqup: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
+lemma fqus_inv_fqup: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐*[b] ⦃G2,L2,T2⦄ →
+                     ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 //
 #G #G2 #L #L2 #T #T2 #_ *
 [ #H2 * /3 width=5 by fqup_strap1, or_introl/
@@ -37,38 +37,38 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma fqus_strap1_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
+lemma fqus_strap1_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⊐*[b] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⊐[b] ⦃G2,L2,T2⦄ →
+                       ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H1) -H1
 [ /2 width=5 by fqup_strap1/
 | * /2 width=1 by fqu_fqup/
 ]
 qed-.
 
-lemma fqus_strap2_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
+lemma fqus_strap2_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⊐*[b] ⦃G2,L2,T2⦄ →
+                       ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H2) -H2
 [ /2 width=5 by fqup_strap2/
 | * /2 width=1 by fqu_fqup/
 ]
 qed-.
 
-lemma fqus_fqup_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
+lemma fqus_fqup_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⊐*[b] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⊐+[b] ⦃G2,L2,T2⦄ →
+                       ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fqup_ind … H2) -H2 -G2 -L2 -T2
 /2 width=5 by fqus_strap1_fqu, fqup_strap1/
 qed-.
 
-lemma fqup_fqus_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ →
-                       ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
+lemma fqup_fqus_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⊐+[b] ⦃G,L,T⦄ →
+                       ⦃G,L,T⦄ ⊐*[b] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 @(fqup_ind_dx … H1) -H1 -G1 -L1 -T1
 /3 width=5 by fqus_strap2_fqu, fqup_strap2/
 qed-.
 
 (* Advanced inversion lemmas for plus-iterated supclosure *******************)
 
-lemma fqup_inv_step_sn: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
-                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ & ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄.
+lemma fqup_inv_step_sn: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄ →
+                        ∃∃G,L,T. ⦃G1,L1,T1⦄ ⊐[b] ⦃G,L,T⦄ & ⦃G,L,T⦄ ⊐*[b] ⦃G2,L2,T2⦄.
 #b #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-.