From a04fa03fcea0493e89b725960146cc0c06539583 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Sat, 15 Apr 2017 17:49:29 +0000 Subject: [PATCH] lfsx_lfpxs completed! --- .../basic_2/rt_computation/lfpxs.ma | 2 +- .../basic_2/rt_computation/lfsx_lfpxs.ma | 75 +++++++++---------- .../basic_2/rt_computation/partial.txt | 2 +- 3 files changed, 39 insertions(+), 40 deletions(-) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs.ma index 507f4d979..e711286a1 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs.ma @@ -54,5 +54,5 @@ lemma lfpxs_inv_atom2: ∀h,I,G,L1. ⦃G, L1⦄ ⊢ ⬈*[h, ⓪{I}] ⋆ → L1 = lemma lfpxs_fwd_pair_sn: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ②{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, V] L2. /2 width=3 by tc_lfxs_fwd_pair_sn/ qed-. -lemma lfpxs_flat_dx: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2. +lemma lfpxs_fwd_flat_dx: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2. /2 width=3 by tc_lfxs_fwd_flat_dx/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma index d1e4f4de8..31a027834 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfpxs.ma @@ -30,7 +30,7 @@ lemma lfsx_intro_lfpxs: ∀h,o,G,L1,T. (* Basic_2A1: uses: lsx_lpxs_trans *) lemma lfsx_lfpxs_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ → ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄. -#h #o #G #L1 #T #HL1 #L2 #H @(lfpxs_ind … H) -L2 +#h #o #G #L1 #T #HL1 #L2 #H @(lfpxs_ind_sn … H) -L2 /2 width=3 by lfsx_lfpx_trans/ qed-. @@ -73,51 +73,50 @@ qed-. (* Advanced properties ******************************************************) -fact lsx_bind_lpxs_aux: ∀h,o,p,I,G,L1,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L1⦄ → - ∀Y,T. G ⊢ ⬈*[h, o, T] 𝐒⦃Y⦄ → - ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 → - G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L2⦄. +fact lfsx_bind_lfpxs_aux: ∀h,o,p,I,G,L1,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L1⦄ → + ∀Y,T. G ⊢ ⬈*[h, o, T] 𝐒⦃Y⦄ → + ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 → + G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L2⦄. #h #o #p #I #G #L1 #V #H @(lfsx_ind_lfpxs … H) -L1 -#L1 #HL1 #IHL1 #Y #T #H @(lfsx_ind_lfpxs … H) -Y -#Y #HY #IHY #L2 #H #HL12 destruct @lfsx_intro_lfpxs -#L0 #HL20 lapply (lfpxs_trans … HL12 … HL20) -#HL10 #H elim (lfdneq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ] +#L1 #_ #IHL1 #Y #T #H @(lfsx_ind_lfpxs … H) -Y +#Y #HY #IHY #L2 #H #HL12 destruct +@lfsx_intro_lfpxs #L0 #HL20 +lapply (lfpxs_trans … HL12 … HL20) #HL10 #H +elim (lfdneq_inv_bind … H) -H [ -IHY | -HY -IHL1 -HL12 ] [ #HnV elim (lfdeq_dec h o L1 L2 V) - [ #HV @(IHL1 … L0) -IHL1 - [2: /3 width=5 by lfdeq_canc_sn/ - |5: // |3: skip - |6: // - - lfdeq_lfdneq_trans/ - - /3 width=5 by lfsx_lfpxs_trans, lfpxs_pair, lfdeq_canc_sn/ (**) (* full auto too slow *) - | -HnV -HL10 /4 width=5 by lsx_lpxs_trans, lpxs_pair/ + [ #HV @(IHL1 … L0) -IHL1 -HL12 + /3 width=4 by lfsx_lfpxs_trans, lfpxs_fwd_bind_dx, lfpxs_fwd_pair_sn, lfdeq_canc_sn/ (**) (* full auto too slow *) + | -HnV -HL10 /4 width=4 by lfsx_lfpxs_trans, lfpxs_fwd_pair_sn/ ] -| /3 width=4 by lpxs_pair/ +| /3 width=4 by lfpxs_fwd_bind_dx/ ] qed-. -lemma lsx_bind: ∀h,o,a,I,G,L,V,l. G ⊢ ⬈*[h, o, V, l] L → - ∀T. G ⊢ ⬈*[h, o, T, ⫯l] L.ⓑ{I}V → - G ⊢ ⬈*[h, o, ⓑ{a,I}V.T, l] L. -/2 width=3 by lsx_bind_lpxs_aux/ qed. +(* Basic_2A1: uses: lsx_bind *) +lemma lfsx_bind: ∀h,o,p,I,G,L,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ → + ∀T. G ⊢ ⬈*[h, o, T] 𝐒⦃L.ⓑ{I}V⦄ → + G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄. +/2 width=3 by lfsx_bind_lfpxs_aux/ qed. -lemma lsx_flat_lpxs: ∀h,o,I,G,L1,V,l. G ⊢ ⬈*[h, o, V, l] L1 → - ∀L2,T. G ⊢ ⬈*[h, o, T, l] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, o] L2 → - G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L2. -#h #o #I #G #L1 #V #l #H @(lsx_ind_lfpxs … H) -L1 -#L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind_lfpxs … H) -L2 -#L2 #HL2 #IHL2 #HL12 @lsx_intro_lfpxs -#L0 #HL20 lapply (lpxs_trans … HL12 … HL20) -#HL10 #H elim (nlleq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ] -[ #HnV elim (lleq_dec V L1 L2 l) - [ #HV @(IHL1 … L0) /3 width=3 by lsx_lpxs_trans, lleq_canc_sn/ (**) (* full auto too slow: 47s *) - | -HnV -HL10 /3 width=4 by lsx_lpxs_trans/ +(* Basic_2A1: uses: lsx_flat_lpxs *) +lemma lfsx_flat_lfpxs: ∀h,o,I,G,L1,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L1⦄ → + ∀L2,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄ → ⦃G, L1⦄ ⊢ ⬈*[h, ⓕ{I}V.T] L2 → + G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L2⦄. +#h #o #I #G #L1 #V #H @(lfsx_ind_lfpxs … H) -L1 +#L1 #HL1 #IHL1 #L2 #T #H @(lfsx_ind_lfpxs … H) -L2 +#L2 #HL2 #IHL2 #HL12 @lfsx_intro_lfpxs +#L0 #HL20 lapply (lfpxs_trans … HL12 … HL20) +#HL10 #H elim (lfdneq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ] +[ #HnV elim (lfdeq_dec h o L1 L2 V) + [ #HV @(IHL1 … L0) -IHL1 -HL12 + /3 width=5 by lfsx_lfpxs_trans, lfpxs_fwd_flat_dx, lfpxs_fwd_pair_sn, lfdeq_canc_sn/ (**) (* full auto too slow: 47s *) + | -HnV -HL10 /4 width=4 by lfsx_lfpxs_trans, lfpxs_fwd_pair_sn/ ] -| /3 width=1 by/ +| /3 width=3 by lfpxs_fwd_flat_dx/ ] qed-. -lemma lsx_flat: ∀h,o,I,G,L,V,l. G ⊢ ⬈*[h, o, V, l] L → - ∀T. G ⊢ ⬈*[h, o, T, l] L → G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L. -/2 width=3 by lsx_flat_lpxs/ qed. +(* Basic_2A1: uses: lsx_flat *) +lemma lfsx_flat: ∀h,o,I,G,L,V. G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ → + ∀T. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄. +/2 width=3 by lfsx_flat_lfpxs/ qed. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt index 832e88f69..16ff258d1 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt @@ -2,4 +2,4 @@ cpxs.ma cpxs_tdeq.ma cpxs_theq.ma cpxs_theq_vector.ma cpxs_drops.ma cpxs_lsubr.m lfpxs.ma lfpxs_length.ma lfpxs_fqup.ma lfpxs_lfdeq.ma lfpxs_cpxs.ma lfpxs_lfpxs.ma csx.ma csx_simple.ma csx_simple_theq.ma csx_drops.ma csx_lsubr.ma csx_gcp.ma csx_gcr.ma csx_lfpx.ma csx_cnx.ma csx_cpxs.ma csx_csx.ma csx_vector.ma csx_cnx_vector.ma csx_csx_vector.ma -lfsx.ma lfsx_fqup.ma lfsx_lfsx.ma +lfsx.ma lfsx_fqup.ma lfsx_lfpxs.ma lfsx_lfsx.ma -- 2.39.2