X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flsubc_drops.ma;h=1916a81b4f619d99ad13858a21182b7418f935ac;hp=d39dd68166c107f78068a79641f051cbd2379869;hb=222044da28742b24584549ba86b1805a87def070;hpb=38571b4c3881f2b59b7a2cdd016c83b161d3d755

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubc_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubc_drops.ma
index d39dd6816..1916a81b4 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubc_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubc_drops.ma
@@ -23,19 +23,19 @@ include "basic_2/static/lsubc.ma".
 (* Basic_1: includes: csubc_drop_conf_O *)
 (* Basic_2A1: includes: lsubc_drop_O1_trans *)
 lemma lsubc_drops_trans_isuni: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 →
-                               ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≡ K2 →
-                               ∃∃K1. ⬇*[b, f] L1 ≡ K1 & G ⊢ K1 ⫃[RP] K2.
+                               ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2 →
+                               ∃∃K1. ⬇*[b, f] L1 ≘ K1 & G ⊢ K1 ⫃[RP] K2.
 #RP #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
-| #I #L1 #L2 #V #HL12 #IH #b #f #K2 #Hf #H
-  elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
+| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
   [ #Hf #H destruct -IH
-    /3 width=3 by lsubc_pair, drops_refl, ex2_intro/
+    /3 width=3 by lsubc_bind, drops_refl, ex2_intro/
   | #g #Hg #HLK2 #H destruct -HL12
     elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
   ]
 | #L1 #L2 #V #W #A #HV #H1W #H2W #HL12 #IH #b #f #K2 #Hf #H
-  elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
   [ #Hf #H destruct -IH
     /3 width=8 by drops_refl, lsubc_beta, ex2_intro/
   | #g #Hg #HLK2 #H destruct -HL12
@@ -48,22 +48,23 @@ qed-.
 (* Basic_1: includes: csubc_drop_conf_rev *)
 (* Basic_2A1: includes: drop_lsubc_trans *)
 lemma drops_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
-                         ∀b,f,G,L1,K1. ⬇*[b, f] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
-                         ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[b, f] L2 ≡ K2.
+                         ∀b,f,G,L1,K1. ⬇*[b, f] L1 ≘ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+                         ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[b, f] L2 ≘ K2.
 #RR #RS #RP #HR #b #f #G #L1 #K1 #H elim H -f -L1 -K1
 [ #f #Hf #Y #H lapply (lsubc_inv_atom1 … H) -H
   #H destruct /4 width=3 by lsubc_atom, drops_atom, ex2_intro/
-| #f #I #L1 #K1 #V1 #_ #IH #K2 #HK12 elim (IH … HK12) -K1
-  /3 width=5 by lsubc_pair, drops_drop, ex2_intro/
-| #f #I #L1 #K1 #V1 #V2 #HLK1 #HV21 #IH #X #H elim (lsubc_inv_pair1 … H) -H *
+| #f #I #L1 #K1 #_ #IH #K2 #HK12 elim (IH … HK12) -K1
+  /3 width=5 by lsubc_bind, drops_drop, ex2_intro/
+| #f #Z #I #L1 #K1 #HLK1 #HZ #IH #Y #H elim (lsubc_inv_bind1 … H) -H *
   [ #K2 #HK12 #H destruct -HLK1
-    elim (IH … HK12) -K1 /3 width=5 by lsubc_pair, drops_skip, ex2_intro/
-  | #K2 #V #W2 #A #HV #H1W2 #H2W2 #HK12 #H1 #H2 #H3 destruct
+    elim (IH … HK12) -K1 /3 width=5 by lsubc_bind, drops_skip, ex2_intro/
+  | #K2 #V2 #W2 #A #HV2 #H1W2 #H2W2 #HK12 #H1 #H2 destruct
+    elim (liftsb_inv_pair_sn … HZ) -HZ #V1 #HV21 #H destruct
     elim (lifts_inv_flat1 … HV21) -HV21 #W3 #V3 #HW23 #HV3 #H destruct
     elim (IH … HK12) -IH -HK12 #K #HL1K #HK2
-    lapply (acr_lifts … HR … HV … HLK1 … HV3) -HV
+    lapply (acr_lifts … HR … HV2 … HLK1 … HV3) -HV2
     lapply (acr_lifts … HR … H1W2 … HLK1 … HW23) -H1W2
-    /4 width=10 by lsubc_beta, aaa_lifts, drops_skip, ex2_intro/
+    /4 width=10 by lsubc_beta, aaa_lifts, drops_skip, ext2_pair, ex2_intro/
   ]
 ]
 qed-.