X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Frdsx_lpxs.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Frdsx_lpxs.ma;h=0000000000000000000000000000000000000000;hb=a454837a256907d2f83d42ced7be847e10361ea9;hp=77867e07a93d3ea310275d925474e876285ca0d1;hpb=b4283c079ed7069016b8d924bbc7e08872440829;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma deleted file mode 100644 index 77867e07a..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma +++ /dev/null @@ -1,154 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||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/rt_computation/lpxs_rdeq.ma". -include "basic_2/rt_computation/lpxs_lpxs.ma". -include "basic_2/rt_computation/rdsx_rdsx.ma". - -(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******) - -(* Properties with unbound rt-computation for full local environments *******) - -(* Basic_2A1: uses: lsx_intro_alt *) -lemma rdsx_intro_lpxs (h) (G): - ∀L1,T. (∀L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → G ⊢ ⬈*[h,T] 𝐒⦃L2⦄) → - G ⊢ ⬈*[h,T] 𝐒⦃L1⦄. -/4 width=1 by lpx_lpxs, rdsx_intro/ qed-. - -(* Basic_2A1: uses: lsx_lpxs_trans *) -lemma rdsx_lpxs_trans (h) (G): - ∀L1,T. G ⊢ ⬈*[h,T] 𝐒⦃L1⦄ → - ∀L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → G ⊢ ⬈*[h,T] 𝐒⦃L2⦄. -#h #G #L1 #T #HL1 #L2 #H @(lpxs_ind_dx … H) -L2 -/2 width=3 by rdsx_lpx_trans/ -qed-. - -(* Eliminators with unbound rt-computation for full local environments ******) - -lemma rdsx_ind_lpxs_rdeq (h) (G): - ∀T. ∀Q:predicate lenv. - (∀L1. G ⊢ ⬈*[h,T] 𝐒⦃L1⦄ → - (∀L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) → - Q L1 - ) → - ∀L1. G ⊢ ⬈*[h,T] 𝐒⦃L1⦄ → - ∀L0. ⦃G,L1⦄ ⊢ ⬈*[h] L0 → ∀L2. L0 ≛[T] L2 → Q L2. -#h #G #T #Q #IH #L1 #H @(rdsx_ind … H) -L1 -#L1 #HL1 #IH1 #L0 #HL10 #L2 #HL02 -@IH -IH /3 width=3 by rdsx_lpxs_trans, rdsx_rdeq_trans/ -HL1 #K2 #HLK2 #HnLK2 -lapply (rdeq_rdneq_trans … HL02 … HnLK2) -HnLK2 #H -elim (rdeq_lpxs_trans … HLK2 … HL02) -L2 #K0 #HLK0 #HK02 -lapply (rdneq_rdeq_canc_dx … H … HK02) -H #HnLK0 -elim (rdeq_dec L1 L0 T) #H -[ lapply (rdeq_rdneq_trans … H … HnLK0) -H -HnLK0 #Hn10 - lapply (lpxs_trans … HL10 … HLK0) -L0 #H10 - elim (lpxs_rdneq_inv_step_sn … H10 … Hn10) -H10 -Hn10 - /3 width=8 by rdeq_trans/ -| elim (lpxs_rdneq_inv_step_sn … HL10 … H) -HL10 -H #L #K #HL1 #HnL1 #HLK #HKL0 - elim (rdeq_lpxs_trans … HLK0 … HKL0) -L0 - /3 width=8 by lpxs_trans, rdeq_trans/ -] -qed-. - -(* Basic_2A1: uses: lsx_ind_alt *) -lemma rdsx_ind_lpxs (h) (G): - ∀T. ∀Q:predicate lenv. - (∀L1. G ⊢ ⬈*[h,T] 𝐒⦃L1⦄ → - (∀L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) → - Q L1 - ) → - ∀L. G ⊢ ⬈*[h,T] 𝐒⦃L⦄ → Q L. -#h #G #T #Q #IH #L #HL -@(rdsx_ind_lpxs_rdeq … IH … HL) -IH -HL // (**) (* full auto fails *) -qed-. - -(* Advanced properties ******************************************************) - -fact rdsx_bind_lpxs_aux (h) (G): - ∀p,I,L1,V. G ⊢ ⬈*[h,V] 𝐒⦃L1⦄ → - ∀Y,T. G ⊢ ⬈*[h,T] 𝐒⦃Y⦄ → - ∀L2. Y = L2.ⓑ{I}V → ⦃G,L1⦄ ⊢ ⬈*[h] L2 → - G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L2⦄. -#h #G #p #I #L1 #V #H @(rdsx_ind_lpxs … H) -L1 -#L1 #_ #IHL1 #Y #T #H @(rdsx_ind_lpxs … H) -Y -#Y #HY #IHY #L2 #H #HL12 destruct -@rdsx_intro_lpxs #L0 #HL20 -lapply (lpxs_trans … HL12 … HL20) #HL10 #H -elim (rdneq_inv_bind … H) -H [ -IHY | -HY -IHL1 -HL12 ] -[ #HnV elim (rdeq_dec L1 L2 V) - [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10 - /3 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *) - | -HnV -HL10 /4 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx/ - ] -| /3 width=4 by lpxs_bind_refl_dx/ -] -qed-. - -(* Basic_2A1: uses: lsx_bind *) -lemma rdsx_bind (h) (G): - ∀p,I,L,V. G ⊢ ⬈*[h,V] 𝐒⦃L⦄ → - ∀T. G ⊢ ⬈*[h,T] 𝐒⦃L.ⓑ{I}V⦄ → - G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L⦄. -/2 width=3 by rdsx_bind_lpxs_aux/ qed. - -(* Basic_2A1: uses: lsx_flat_lpxs *) -lemma rdsx_flat_lpxs (h) (G): - ∀I,L1,V. G ⊢ ⬈*[h,V] 𝐒⦃L1⦄ → - ∀L2,T. G ⊢ ⬈*[h,T] 𝐒⦃L2⦄ → ⦃G,L1⦄ ⊢ ⬈*[h] L2 → - G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L2⦄. -#h #G #I #L1 #V #H @(rdsx_ind_lpxs … H) -L1 -#L1 #HL1 #IHL1 #L2 #T #H @(rdsx_ind_lpxs … H) -L2 -#L2 #HL2 #IHL2 #HL12 @rdsx_intro_lpxs -#L0 #HL20 lapply (lpxs_trans … HL12 … HL20) -#HL10 #H elim (rdneq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ] -[ #HnV elim (rdeq_dec L1 L2 V) - [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10 - /3 width=5 by rdsx_lpxs_trans, rdeq_canc_sn/ (**) (* full auto too slow: 47s *) - | -HnV -HL10 /3 width=4 by rdsx_lpxs_trans/ - ] -| /3 width=3 by/ -] -qed-. - -(* Basic_2A1: uses: lsx_flat *) -lemma rdsx_flat (h) (G): - ∀I,L,V. G ⊢ ⬈*[h,V] 𝐒⦃L⦄ → - ∀T. G ⊢ ⬈*[h,T] 𝐒⦃L⦄ → G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L⦄. -/2 width=3 by rdsx_flat_lpxs/ qed. - -fact rdsx_bind_lpxs_void_aux (h) (G): - ∀p,I,L1,V. G ⊢ ⬈*[h,V] 𝐒⦃L1⦄ → - ∀Y,T. G ⊢ ⬈*[h,T] 𝐒⦃Y⦄ → - ∀L2. Y = L2.ⓧ → ⦃G,L1⦄ ⊢ ⬈*[h] L2 → - G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L2⦄. -#h #G #p #I #L1 #V #H @(rdsx_ind_lpxs … H) -L1 -#L1 #_ #IHL1 #Y #T #H @(rdsx_ind_lpxs … H) -Y -#Y #HY #IHY #L2 #H #HL12 destruct -@rdsx_intro_lpxs #L0 #HL20 -lapply (lpxs_trans … HL12 … HL20) #HL10 #H -elim (rdneq_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ] -[ #HnV elim (rdeq_dec L1 L2 V) - [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10 - /3 width=6 by rdsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *) - | -HnV -HL10 /4 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx/ - ] -| /3 width=4 by lpxs_bind_refl_dx/ -] -qed-. - -lemma rdsx_bind_void (h) (G): - ∀p,I,L,V. G ⊢ ⬈*[h,V] 𝐒⦃L⦄ → - ∀T. G ⊢ ⬈*[h,T] 𝐒⦃L.ⓧ⦄ → - G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L⦄. -/2 width=3 by rdsx_bind_lpxs_void_aux/ qed.