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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/rex_lex.ma".
16 include "basic_2/rt_transition/rpx_fsle.ma".
17 include "basic_2/rt_transition/lpx.ma".
19 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
21 (* Properties with syntactic equivalence for referred local environments ****)
24 ∀L1,L2,T. L1 ≡[T] L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
25 /2 width=1 by req_fwd_rex/ qed.
27 (* Properties with extended rt-transition for full local envs ***************)
30 ∀L1,L2,T. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
31 /2 width=1 by rex_lex/ qed.
33 (* Inversion lemmas with extended rt-transition for full local envs *********)
35 lemma rpx_inv_lpx_req (G):
36 ∀L1,L2,T. ❪G,L1❫ ⊢ ⬈[T] L2 →
37 ∃∃L. ❪G,L1❫ ⊢ ⬈ L & L ≡[T] L2.
38 /3 width=3 by rpx_fsge_comp, rex_inv_lex_req/ qed-.