bug fix in supclosure allows alternative definition of fpbs !

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpx_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
index 72b624fd3449ec8fdb2037166e385c8482cb9b9e..aabc8d9b45e008f2199409185c9a008bcec890e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/relocation/ldrop_ldrop.ma".
-include "basic_2/relocation/fsupq.ma".
+include "basic_2/relocation/fsupq_alt.ma".
 include "basic_2/static/ssta.ma".
 include "basic_2/reduction/cpx.ma".
 
@@ -138,18 +138,32 @@ qed-.
 
 (* Properties on supclosure *************************************************)
 
+lemma fsup_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                      ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃ ⦃G2, L2, U2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 
+/3 width=3 by fsup_pair_sn, fsup_bind_dx, fsup_flat_dx, cpx_pair_sn, cpx_bind, cpx_flat, ex2_intro/
+[ #I #G #L #V2 #U2 #HVU2
+  elim (lift_total U2 0 1)
+  /4 width=9 by fsup_drop, cpx_append, cpx_delta, ldrop_pair, ldrop_ldrop, ex2_intro/
+| #G #L #K #T1 #U1 #e #HLK1 #HTU1 #T2 #HTU2
+  elim (lift_total T2 0 (e+1))
+  /3 width=11 by cpx_lift, fsup_drop, ex2_intro/
+]
+qed-.
+
+lemma fsup_ssta_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                       ∀U2. ⦃G2, L2⦄ ⊢ T2 •[h, g] U2 →
+                       ∀l. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] l+1 →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃ ⦃G2, L2, U2⦄.
+/3 width=5 by fsup_cpx_trans, ssta_cpx/ qed-.
+
 lemma fsupq_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
                        ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/3 width=3 by fsup_fsupq, fsupq_refl, cpx_pair_sn, cpx_bind, cpx_flat, fsup_pair_sn, fsup_bind_dx, fsup_flat_dx, ex2_intro/
-[ #I #G #L1 #V2 #U2 #HVU2
-  elim (lift_total U2 0 1)
-  /4 width=9 by fsupq_refl, fsupq_ldrop, cpx_delta, ldrop_pair, ldrop_ldrop, ex2_intro/
-| #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
-  elim (IHT12 … HTU2) -IHT12 -HTU2 #T
-  elim (lift_total T d e)
-  /3 width=11 by cpx_lift, fsupq_ldrop, ex2_intro/
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fsupq_inv_gen … H) -H
+[ #HT12 elim (fsup_cpx_trans … HT12 … HTU2) /3 width=3 by fsup_fsupq, ex2_intro/
+| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
@@ -158,14 +172,3 @@ lemma fsupq_ssta_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2,
                         ∀l. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] l+1 →
                         ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
 /3 width=5 by fsupq_cpx_trans, ssta_cpx/ qed-.
-
-lemma fsup_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
-                      ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
-                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
-/3 width=3 by fsupq_cpx_trans, fsup_fsupq/ qed-.
-
-lemma fsup_ssta_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
-                       ∀U2. ⦃G2, L2⦄ ⊢ T2 •[h, g] U2 →
-                       ∀l. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] l+1 →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
-/3 width=5 by fsupq_ssta_trans, fsup_fsupq/ qed-.