matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_fqup.ma

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  14
  15 include "basic_2/static/lfxs_fqup.ma".
  16 include "basic_2/rt_transition/lfpx.ma".
  17
  18 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lfpx_refl: ∀h,G,T. reflexive … (lfpx h G T).
  23 /2 width=1 by lfxs_refl/ qed.
  24
  25 lemma lfpx_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
  26                       ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ⬈[h, T] L.ⓑ{I}V2.
  27 /2 width=1 by lfxs_pair_refl/ qed.
  28
  29 (* Advanced inversion lemmas ************************************************)
  30
  31 lemma lfpx_inv_bind_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2 →
  32                           ∧∧ ⦃G, L1⦄ ⊢ ⬈[h, V] L2 & ⦃G, L1.ⓧ⦄ ⊢ ⬈[h, T] L2.ⓧ.
  33 /2 width=3 by lfxs_inv_bind_void/ qed-.
  34
  35 (* Advanced forward lemmas **************************************************)
  36
  37 lemma lfpx_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T.
  38                              ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2 → ⦃G, L1.ⓧ⦄ ⊢ ⬈[h, T] L2.ⓧ.
  39 /2 width=4 by lfxs_fwd_bind_dx_void/ qed-.