partial commit: "reduction" component

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma
index 120e5e60efa03d3d447f3396908e84106ae7ab79..734921de30d3bb9439dc913202b3e9f56c7fe453 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma
@@ -22,25 +22,26 @@ include "basic_2/reduction/lpr.ma".
 (* Properies on local environment slicing ***********************************)
 
 (* Basic_1: includes: wcpr0_drop *)
-lemma lpr_ldrop_conf: dropable_sn lpr.
+lemma lpr_ldrop_conf: ∀G. dropable_sn (lpr G).
 /3 width=5 by lpx_sn_deliftable_dropable, cpr_inv_lift1/ qed-.
 
 (* Basic_1: includes: wcpr0_drop_back *)
-lemma ldrop_lpr_trans: dedropable_sn lpr.
+lemma ldrop_lpr_trans: ∀G. dedropable_sn (lpr G).
 /3 width=9 by lpx_sn_liftable_dedropable, cpr_lift/ qed-.
 
-lemma lpr_ldrop_trans_O1: dropable_dx lpr.
+lemma lpr_ldrop_trans_O1: ∀G. dropable_dx (lpr G).
 /2 width=3 by lpx_sn_dropable/ qed-.
 
 (* Properties on context-sensitive parallel reduction for terms *************)
 
-lemma fsup_cpr_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ➡ U2 →
-                      ∃∃L,U1. L1 ⊢ ➡ L & ⦃G, L⦄ ⊢ T1 ➡ U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
-#L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
-[ #L #K #U #T #d #e #HLK #HUT #He #U2 #HU2
+lemma fsup_cpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                      ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
+                      ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃ ⦃G2, L2, U2⦄.
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
+[ #G #L #K #U #T #d #e #HLK #HUT #He #U2 #HU2
   elim (lift_total U2 d e) #T2 #HUT2
   lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9/
-| #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
+| #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
   elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HT2
   elim (lift_total T d e) #U #HTU
   elim (ldrop_lpr_trans … HLK1 … HK1) -HLK1 -HK1 #L2 #HL12 #HL2K