X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flpxs_lleq.ma;h=42e34097a4db92ba9d9e7bf4c3375f679b41d747;hb=33f8507cadd3b36dc9afa227d8968dda66fe2034;hp=536288f01851f0368806c06b60f49a21dddefff0;hpb=07d915d411ffabeb0c7cd678f00cbeca53ae8276;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma index 536288f01..42e34097a 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma @@ -14,7 +14,7 @@ include "basic_2/reduction/lpx_lleq.ma". include "basic_2/computation/cpxs_leq.ma". -include "basic_2/computation/lpxs_ldrop.ma". +include "basic_2/computation/lpxs_drop.ma". include "basic_2/computation/lpxs_cpxs.ma". (* SN EXTENDED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ******************) @@ -22,22 +22,22 @@ include "basic_2/computation/lpxs_cpxs.ma". (* Properties on lazy equivalence for local environments ********************) lemma lleq_lpxs_trans: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡*[h, g] K2 → - ∀L1,T,d. L1 ⋕[T, d] L2 → - ∃∃K1. ⦃G, L1⦄ ⊢ ➡*[h, g] K1 & K1 ⋕[T, d] K2. + ∀L1,T,d. L1 ≡[T, d] L2 → + ∃∃K1. ⦃G, L1⦄ ⊢ ➡*[h, g] K1 & K1 ≡[T, d] K2. #h #g #G #L2 #K2 #H @(lpxs_ind … H) -K2 /2 width=3 by ex2_intro/ #K #K2 #_ #HK2 #IH #L1 #T #d #HT elim (IH … HT) -L2 #L #HL1 #HT elim (lleq_lpx_trans … HK2 … HT) -K /3 width=3 by lpxs_strap1, ex2_intro/ qed-. -lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[T1, 0] L1 → - ∃∃K2. ⦃G1, K1, T1⦄ ⊃ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[T2, 0] L2. +lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ≡[T2, 0] L2. #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [ #I #G1 #L1 #V1 #X #H1 #H2 elim (lpxs_inv_pair2 … H1) -H1 #K0 #V0 #H1KL1 #_ #H destruct elim (lleq_inv_lref_ge_dx … H2 ? I L1 V1) -H2 // - #K1 #H #H2KL1 lapply (ldrop_inv_O2 … H) -H #H destruct + #K1 #H #H2KL1 lapply (drop_inv_O2 … H) -H #H destruct /2 width=4 by fqu_lref_O, ex3_intro/ | * [ #a ] #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H [ elim (lleq_inv_bind … H) @@ -48,20 +48,20 @@ lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, | #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_flat … H) -H /2 width=4 by fqu_flat_dx, ex3_intro/ | #G1 #L1 #L #T1 #U1 #e #HL1 #HTU1 #K1 #H1KL1 #H2KL1 - elim (ldrop_O1_le (e+1) K1) + elim (drop_O1_le (Ⓕ) (e+1) K1) [ #K #HK1 lapply (lleq_inv_lift_le … H2KL1 … HK1 HL1 … HTU1 ?) -H2KL1 // - #H2KL elim (lpxs_ldrop_trans_O1 … H1KL1 … HL1) -L1 - #K0 #HK10 #H1KL lapply (ldrop_mono … HK10 … HK1) -HK10 #H destruct + #H2KL elim (lpxs_drop_trans_O1 … H1KL1 … HL1) -L1 + #K0 #HK10 #H1KL lapply (drop_mono … HK10 … HK1) -HK10 #H destruct /3 width=4 by fqu_drop, ex3_intro/ - | lapply (ldrop_fwd_length_le2 … HL1) -L -T1 -g + | lapply (drop_fwd_length_le2 … HL1) -L -T1 -g lapply (lleq_fwd_length … H2KL1) // ] ] qed-. -lemma lpxs_lleq_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[T1, 0] L1 → - ∃∃K2. ⦃G1, K1, T1⦄ ⊃⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[T2, 0] L2. +lemma lpxs_lleq_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ≡[T2, 0] L2. #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1 elim (fquq_inv_gen … H) -H [ #H elim (lpxs_lleq_fqu_trans … H … H1KL1 H2KL1) -L1 @@ -70,9 +70,9 @@ elim (fquq_inv_gen … H) -H ] qed-. -lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[T1, 0] L1 → - ∃∃K2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[T2, 0] L2. +lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ≡[T2, 0] L2. #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2 [ #G2 #L2 #T2 #H #K1 #H1KL1 #H2KL1 elim (lpxs_lleq_fqu_trans … H … H1KL1 H2KL1) -L1 /3 width=4 by fqu_fqup, ex3_intro/ @@ -82,9 +82,9 @@ lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G ] qed-. -lemma lpxs_lleq_fqus_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[T1, 0] L1 → - ∃∃K2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[T2, 0] L2. +lemma lpxs_lleq_fqus_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ≡[T2, 0] L2. #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1 elim (fqus_inv_gen … H) -H [ #H elim (lpxs_lleq_fqup_trans … H … H1KL1 H2KL1) -L1 @@ -93,10 +93,10 @@ elim (fqus_inv_gen … H) -H ] qed-. -fact leq_lpxs_trans_lleq_aux: ∀h,g,G,L1,L0,d,e. L1 ≃[d, e] L0 → e = ∞ → +fact leq_lpxs_trans_lleq_aux: ∀h,g,G,L1,L0,d,e. L1 ⩬[d, e] L0 → e = ∞ → ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 → - ∃∃L. L ≃[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L & - (∀T. L0 ⋕[T, d] L2 ↔ L1 ⋕[T, d] L). + ∃∃L. L ⩬[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L & + (∀T. L0 ≡[T, d] L2 ↔ L1 ≡[T, d] L). #h #g #G #L1 #L0 #d #e #H elim H -L1 -L0 -d -e [ #d #e #_ #L2 #H >(lpxs_inv_atom1 … H) -H /3 width=5 by ex3_intro, conj/ @@ -117,8 +117,8 @@ fact leq_lpxs_trans_lleq_aux: ∀h,g,G,L1,L0,d,e. L1 ≃[d, e] L0 → e = ∞ ] qed-. -lemma leq_lpxs_trans_lleq: ∀h,g,G,L1,L0,d. L1 ≃[d, ∞] L0 → +lemma leq_lpxs_trans_lleq: ∀h,g,G,L1,L0,d. L1 ⩬[d, ∞] L0 → ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 → - ∃∃L. L ≃[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L & - (∀T. L0 ⋕[T, d] L2 ↔ L1 ⋕[T, d] L). + ∃∃L. L ⩬[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L & + (∀T. L0 ≡[T, d] L2 ↔ L1 ≡[T, d] L). /2 width=1 by leq_lpxs_trans_lleq_aux/ qed-.