+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/reduction/fpbc_fleq.ma".
-include "basic_2/computation/fpbg.ma".
-
-(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
-
-(* Properties on lazy equivalence for closures ******************************)
-
-lemma fpbg_fleq_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ →
- ∀G2,L2,T2. ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T #H @(fpbg_ind … H) -G -L -T
-[ /3 width=5 by fpbc_fpbg, fpbc_fleq_trans/
-| /4 width=9 by fpbg_strap1, fpbc_fleq_trans/
-]
-qed-.
-
-lemma fleq_fpbg_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
- ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≡[0] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G #G2 #L #L2 #T #T2 #H @(fpbg_ind_dx … H) -G -L -T
-[ /3 width=5 by fpbc_fpbg, fleq_fpbc_trans/
-| /4 width=9 by fpbg_strap2, fleq_fpbc_trans/
-]
-qed-.