update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / fpb_reqx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma
index de168279c11e69bd2ae9b4d07e1110ebfd38a98f..19aeffac62f3a44351657bbd4539cfe8c681c1b0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma
@@ -21,28 +21,30 @@ include "basic_2/rt_transition/fpb.ma".
 
 (* Properties with sort-irrelevant equivalence for local environments *******)
 
-lemma teqx_fpb_trans: ∀h,U2,U1. U2 ≛ U1 →
-                      ∀G1,G2,L1,L2,T1. ⦃G1,L1,U1⦄ ≻[h] ⦃G2,L2,T1⦄ → 
-                      ∃∃L,T2. ⦃G1,L1,U2⦄ ≻[h] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
-#h #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
+lemma teqx_fpb_trans:
+      ∀U2,U1. U2 ≛ U1 →
+      ∀G1,G2,L1,L2,T1. ❪G1,L1,U1❫ ≻ ❪G2,L2,T1❫ →
+      ∃∃L,T2. ❪G1,L1,U2❫ ≻ ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
+#U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
 [ #G2 #L2 #T1 #H
   elim (teqx_fqu_trans … H … HU21) -H
   /3 width=5 by fpb_fqu, ex3_2_intro/
 | #T1 #HUT1 #HnUT1
-  elim (teqx_cpx_trans … HU21 … HUT1) -HUT1
+  lapply (teqx_cpx_trans … HU21 … HUT1) -HUT1
   /6 width=5 by fpb_cpx, teqx_canc_sn, teqx_trans, ex3_2_intro/
 | /6 width=5 by fpb_lpx, rpx_teqx_div, teqx_reqx_conf, ex3_2_intro/
 ]
 qed-.
 
 (* Basic_2A1: was just: lleq_fpb_trans *)
-lemma reqx_fpb_trans: ∀h,F,K1,K2,T. K1 ≛[T] K2 →
-                      ∀G,L2,U. ⦃F,K2,T⦄ ≻[h] ⦃G,L2,U⦄ →
-                      ∃∃L1,U0. ⦃F,K1,T⦄ ≻[h] ⦃G,L1,U0⦄ & U0 ≛ U & L1 ≛[U] L2.
-#h #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
+lemma reqx_fpb_trans:
+      ∀F,K1,K2,T. K1 ≛[T] K2 →
+      ∀G,L2,U. ❪F,K2,T❫ ≻ ❪G,L2,U❫ →
+      ∃∃L1,U0. ❪F,K1,T❫ ≻ ❪G,L1,U0❫ & U0 ≛ U & L1 ≛[U] L2.
+#F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
 [ #G #L2 #U #H2 elim (reqx_fqu_trans … H2 … HT) -K2
   /3 width=5 by fpb_fqu, ex3_2_intro/
-| #U #HTU #HnTU elim (reqx_cpx_trans … HT … HTU) -HTU
+| #U #HTU #HnTU lapply (reqx_cpx_trans … HT … HTU) -HTU
   /5 width=11 by fpb_cpx, cpx_reqx_conf_sn, teqx_trans, teqx_reqx_conf, ex3_2_intro/ (**) (* time: 36s on dev *)
 | #L2 #HKL2 #HnKL2 elim (reqx_lpx_trans … HKL2 … HT) -HKL2
   /6 width=5 by fpb_lpx, (* 2x *) reqx_canc_sn, ex3_2_intro/