X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flsx_lpxs.ma;h=0accd974f7751d572c73535c06fe5566d56f5bc8;hb=d71ad5c0d52dff8bc4b77216fbcb0b65ecd7d391;hp=b3cb36781d06201c48e92f8f67f6f8c1bbd785a0;hpb=376fd7774ef0fa2f30a4afb25aab6158e3cd04b7;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma index b3cb36781..0accd974f 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma @@ -12,52 +12,20 @@ (* *) (**************************************************************************) -include "basic_2/computation/lpxs_lleq.ma". include "basic_2/computation/lpxs_lpxs.ma". -include "basic_2/computation/lsx.ma". +include "basic_2/computation/lsx_alt.ma". (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************) (* Advanced properties ******************************************************) -lemma lsx_leqy_conf: ∀h,g,G,L1,T,d. G ⊢ ⋕⬊*[h, g, T, d] L1 → - ∀L2. L1 ⊑×[d, ∞] L2 → |L1| = |L2| → G ⊢ ⋕⬊*[h, g, T, d] L2. -#h #g #G #L1 #T #d #H @(lsx_ind … H) -L1 -#L1 #_ #IHL1 #L2 #H1L12 #H2L12 @lsx_intro -#L3 #H1L23 #HnL23 lapply (lpxs_fwd_length … H1L23) -#H2L23 elim (lsuby_lpxs_trans_lleq … H1L12 … H1L23) -H1L12 -H1L23 -#L0 #H1L03 #H1L10 #H lapply (lpxs_fwd_length … H1L10) -#H2L10 elim (H T) -H // -#_ #H @(IHL1 … H1L10) -IHL1 -H1L10 /3 width=1 by/ -qed-. - -lemma lsx_ge: ∀h,g,G,L,T,d1,d2. d1 ≤ d2 → - G ⊢ ⋕⬊*[h, g, T, d1] L → G ⊢ ⋕⬊*[h, g, T, d2] L. -#h #g #G #L #T #d1 #d2 #Hd12 #H @(lsx_ind … H) -L -/5 width=7 by lsx_intro, lleq_ge/ -qed-. - -lemma lsx_lleq_trans: ∀h,g,T,G,L1,d. G ⊢ ⋕⬊*[h, g, T, d] L1 → - ∀L2. L1 ⋕[T, d] L2 → G ⊢ ⋕⬊*[h, g, T, d] L2. -#h #g #T #G #L1 #d #H @(lsx_ind … H) -L1 -#L1 #_ #IHL1 #L2 #HL12 @lsx_intro -#K2 #HLK2 #HnLK2 elim (lleq_lpxs_trans … HLK2 … HL12) -HLK2 -/5 width=4 by lleq_canc_sn, lleq_trans/ -qed-. - -lemma lsx_lpxs_trans: ∀h,g,T,G,L1,d. G ⊢ ⋕⬊*[h, g, T, d] L1 → - ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⋕⬊*[h, g, T, d] L2. -#h #g #T #G #L1 #d #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12 -elim (lleq_dec T L1 L2 d) /3 width=4 by lsx_lleq_trans/ -qed-. - -fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 → - ∀Y,T. G ⊢ ⋕⬊*[h, g, T, ⫯d] Y → +fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⬊*[h, g, V, d] L1 → + ∀Y,T. G ⊢ ⬊*[h, g, T, ⫯d] Y → ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → - G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L2. -#h #g #a #I #G #L1 #V #d #H @(lsx_ind … H) -L1 -#L1 #HL1 #IHL1 #Y #T #H @(lsx_ind … H) -Y -#Y #HY #IHY #L2 #H #HL12 destruct @lsx_intro + G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, d] L2. +#h #g #a #I #G #L1 #V #d #H @(lsx_ind_alt … H) -L1 +#L1 #HL1 #IHL1 #Y #T #H @(lsx_ind_alt … H) -Y +#Y #HY #IHY #L2 #H #HL12 destruct @lsx_intro_alt #L0 #HL20 lapply (lpxs_trans … HL12 … HL20) #HL10 #H elim (nlleq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ] [ #HnV elim (lleq_dec V L1 L2 d) @@ -68,17 +36,17 @@ fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 → ] qed-. -lemma lsx_bind: ∀h,g,a,I,G,L,V,d. G ⊢ ⋕⬊*[h, g, V, d] L → - ∀T. G ⊢ ⋕⬊*[h, g, T, ⫯d] L.ⓑ{I}V → - G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L. +lemma lsx_bind: ∀h,g,a,I,G,L,V,d. G ⊢ ⬊*[h, g, V, d] L → + ∀T. G ⊢ ⬊*[h, g, T, ⫯d] L.ⓑ{I}V → + G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, d] L. /2 width=3 by lsx_bind_lpxs_aux/ qed. -lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 → - ∀L2,T. G ⊢ ⋕⬊*[h, g, T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → - G ⊢ ⋕⬊*[h, g, ⓕ{I}V.T, d] L2. -#h #g #I #G #L1 #V #d #H @(lsx_ind … H) -L1 -#L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind … H) -L2 -#L2 #HL2 #IHL2 #HL12 @lsx_intro +lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⬊*[h, g, V, d] L1 → + ∀L2,T. G ⊢ ⬊*[h, g, T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → + G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L2. +#h #g #I #G #L1 #V #d #H @(lsx_ind_alt … H) -L1 +#L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind_alt … H) -L2 +#L2 #HL2 #IHL2 #HL12 @lsx_intro_alt #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 d) @@ -89,38 +57,6 @@ lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 → ] qed-. -lemma lsx_flat: ∀h,g,I,G,L,V,d. G ⊢ ⋕⬊*[h, g, V, d] L → - ∀T. G ⊢ ⋕⬊*[h, g, T, d] L → G ⊢ ⋕⬊*[h, g, ⓕ{I}V.T, d] L. +lemma lsx_flat: ∀h,g,I,G,L,V,d. G ⊢ ⬊*[h, g, V, d] L → + ∀T. G ⊢ ⬊*[h, g, T, d] L → G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L. /2 width=3 by lsx_flat_lpxs/ qed. - -(* Advanced forward lemmas **************************************************) - -lemma lsx_fwd_lref_be: ∀h,g,I,G,L,d,i. d ≤ yinj i → G ⊢ ⋕⬊*[h, g, #i, d] L → - ∀K,V. ⇩[i] L ≡ K.ⓑ{I}V → G ⊢ ⋕⬊*[h, g, V, 0] K. -#h #g #I #G #L #d #i #Hdi #H @(lsx_ind … H) -L -#L1 #_ #IHL1 #K1 #V #HLK1 @lsx_intro -#K2 #HK12 #HnK12 lapply (ldrop_fwd_drop2 … HLK1) -#H2LK1 elim (ldrop_lpxs_trans … H2LK1 … HK12) -H2LK1 -HK12 -#L2 #HL12 #H2LK2 #H elim (leq_ldrop_conf_be … H … HLK1) -H /2 width=1 by ylt_inj/ -#Y #_ #HLK2 lapply (ldrop_fwd_drop2 … HLK2) -#HY lapply (ldrop_mono … HY … H2LK2) -HY -H2LK2 #H destruct -/4 width=10 by lleq_inv_lref_ge/ -qed-. - -lemma lsx_fwd_bind_dx: ∀h,g,a,I,G,L,V,T,d. G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L → - G ⊢ ⋕⬊*[h, g, T, ⫯d] L.ⓑ{I}V. -#h #g #a #I #G #L #V1 #T #d #H @(lsx_ind … H) -L -#L1 #_ #IHL1 @lsx_intro -#Y #H #HT elim (lpxs_inv_pair1 … H) -H -#L2 #V2 #HL12 #_ #H destruct -@(lsx_leqy_conf … (L2.ⓑ{I}V1)) /2 width=1 by lsuby_succ/ -@IHL1 // #H @HT -IHL1 -HL12 -HT -@(lleq_lsuby_trans … (L2.ⓑ{I}V1)) -/2 width=2 by lleq_fwd_bind_dx, lsuby_succ/ -qed-. - -(* Advanced inversion lemmas ************************************************) - -lemma lsx_inv_bind: ∀h,g,a,I,G,L,V,T,d. G ⊢ ⋕⬊*[h, g, ⓑ{a, I}V.T, d] L → - G ⊢ ⋕⬊*[h, g, V, d] L ∧ G ⊢ ⋕⬊*[h, g, T, ⫯d] L.ⓑ{I}V. -/3 width=4 by lsx_fwd_bind_sn, lsx_fwd_bind_dx, conj/ qed-.