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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "static_2/static/feqg.ma".
16 include "basic_2/rt_transition/cpx_reqg.ma".
17 include "basic_2/rt_transition/rpx_reqg.ma".
19 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS **************)
21 (* Properties with generic equivalence for closures *************************)
23 lemma feqg_cpx_trans_cpx (S):
24 reflexive … S → symmetric … S →
25 ∀G1,G2,L1,L2,T1,T. ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T❩ →
26 ∀T2. ❨G2,L2❩ ⊢ T ⬈ T2 → ❨G1,L1❩ ⊢ T1 ⬈ T2.
27 #S #H1S #H2S #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
28 elim (feqg_inv_gen_dx … H) -H // #H #HL12 #HT1 destruct
29 @(cpx_teqg_repl_reqg … HT2)
30 /2 width=7 by reqg_sym, teqg_sym, teqg_refl/
33 lemma feqg_cpx_trans_feqg (S):
34 reflexive … S → symmetric … S →
35 ∀G1,G2,L1,L2,T1,T. ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T❩ →
36 ∀T2. ❨G2,L2❩ ⊢ T ⬈ T2 → ❨G1,L1,T2❩ ≛[S] ❨G2,L2,T2❩.
37 #S #H1S #H2S #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
38 elim (feqg_inv_gen_dx … H) -H // #H #HL12 #_ destruct
39 lapply (cpx_reqg_conf_dx … HT2 … HL12) -HT2 -HL12 // #HL12
40 /3 width=1 by feqg_intro_sn, teqg_refl/