X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flfpx_lfdeq.ma;h=1ff13898c9c67a82fbdfe48d8fbf43e459ddaff3;hb=c0a8f89161e9887c38eb5cf701f0f0c05a0e527f;hp=d2314455748accf17e35029c43bd6f718d605d5d;hpb=1ddb3f36f9230e326df60e6db7ef2624a9c16930;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma index d23144557..1ff13898c 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma @@ -16,11 +16,10 @@ include "basic_2/relocation/lifts_tdeq.ma". include "basic_2/static/lfdeq_fqup.ma". include "basic_2/rt_transition/lfpx.ma". -(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************) +(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****) -(* Properties with degree-based equivalence for terms ***********************) +(* Properties with degree-based equivalence for local environments **********) -(* Basic_2A1: was just: cpx_lleq_conf *) lemma cpx_tdeq_conf_lexs: ∀h,o,G. R_confluent2_lfxs … (cpx h G) (cdeq h o) (cpx h G) (cdeq h o). #h #o #G #L0 #T0 #T1 #H @(cpx_ind … H) -G -L0 -T0 -T1 /2 width=3 by ex2_intro/ [ #G #L0 #s0 #X0 #H0 #L1 #HL01 #L2 #HL02 @@ -116,15 +115,102 @@ lemma tdeq_cpx_trans: ∀h,o,G,L,T2,T0. T2 ≡[h, o] T0 → elim (cpx_tdeq_conf … HT01 T2) -HT01 /3 width=3 by tdeq_sym, ex2_intro/ qed-. +(* Basic_2A1: was just: cpx_lleq_conf *) +lemma cpx_lfdeq_conf: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → + ∀L2. L0 ≡[h, o, T0] L2 → + ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈[h] T & T1 ≡[h, o] T. +#h #o #G #L0 #T0 #T1 #HT01 #L2 #HL02 +elim (cpx_tdeq_conf_lexs … HT01 T0 … L0 … HL02) -HT01 -HL02 +/2 width=3 by lfxs_refl, ex2_intro/ +qed-. + +(* Basic_2A1: was just: lleq_cpx_trans *) +lemma lfdeq_cpx_trans: ∀h,o,G,L2,L0,T0. L2 ≡[h, o, T0] L0 → + ∀T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 → + ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈[h] T & T ≡[h, o] T1. +#h #o #G #L2 #L0 #T0 #HL20 #T1 #HT01 +elim (cpx_lfdeq_conf … o … HT01 L2) -HT01 +/3 width=3 by lfdeq_sym, tdeq_sym, ex2_intro/ +qed-. + +include "basic_2/static/lfxs_lfxs.ma". + +axiom lfpx_lfdeq_conf: ∀h,o,G,T. confluent2 … (lfpx h G T) (lfdeq h o T). +(* +#H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 +@lfxs_conf +*) +(* Basic_2A1: was just: lleq_lpx_trans *) +lemma lfdeq_lfpx_trans: ∀h,o,G,T,L2,K2. ⦃G, L2⦄ ⊢ ⬈[h, T] K2 → + ∀L1. L1 ≡[h, o, T] L2 → + ∃∃K1. ⦃G, L1⦄ ⊢ ⬈[h, T] K1 & K1 ≡[h, o, T] K2. +#h #o #G #T #L2 #K2 #HLK2 #L1 #HL12 +elim (lfpx_lfdeq_conf … o … HLK2 L1) +/3 width=3 by lfdeq_sym, ex2_intro/ +qed-. (* -lemma cpx_lleq_conf: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h, o] T2 → - ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ⬈[h, o] T2. -/3 width=3 by lleq_cpx_trans, lleq_sym/ qed-. +(* Properties with supclosure ***********************************************) -lemma cpx_lleq_conf_sn: ∀h,o,G. s_r_confluent1 … (cpx h o G) (lleq 0). -/3 width=6 by cpx_llpx_sn_conf, lift_mono, ex2_intro/ qed-. +lemma lpx_lleq_fqu_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2 & K2 ≡[T2, 0] L2. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 +[ #I #G1 #L1 #V1 #X #H1 #H2 elim (lpx_inv_pair2 … H1) -H1 + #K0 #V0 #H1KL1 #_ #H destruct + elim (lleq_inv_lref_ge_dx … H2 ? I L1 V1) -H2 // + #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) + | elim (lleq_inv_flat … H) + ] -H /2 width=4 by fqu_pair_sn, ex3_intro/ +| #a #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_bind_O … H) -H + /3 width=4 by lpx_pair, fqu_bind_dx, ex3_intro/ +| #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 #k #HL1 #HTU1 #K1 #H1KL1 #H2KL1 + elim (drop_O1_le (Ⓕ) (k+1) K1) + [ #K #HK1 lapply (lleq_inv_lift_le … H2KL1 … HK1 HL1 … HTU1 ?) -H2KL1 // + #H2KL elim (lpx_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 (drop_fwd_length_le2 … HL1) -L -T1 -o + lapply (lleq_fwd_length … H2KL1) // + ] +] +qed-. + +lemma lpx_lleq_fquq_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2 & K2 ≡[T2, 0] L2. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1 +elim (fquq_inv_gen … H) -H +[ #H elim (lpx_lleq_fqu_trans … H … H1KL1 H2KL1) -L1 + /3 width=4 by fqu_fquq, ex3_intro/ +| * #HG #HL #HT destruct /2 width=4 by ex3_intro/ +] +qed-. -lemma cpx_lleq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h, o] T2 → - ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2. -/4 width=6 by cpx_lleq_conf_sn, lleq_sym/ qed-. -*) \ No newline at end of file +lemma lpx_lleq_fqup_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2 & K2 ≡[T2, 0] L2. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2 +[ #G2 #L2 #T2 #H #K1 #H1KL1 #H2KL1 elim (lpx_lleq_fqu_trans … H … H1KL1 H2KL1) -L1 + /3 width=4 by fqu_fqup, ex3_intro/ +| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #K1 #H1KL1 #H2KL1 elim (IHT1 … H2KL1) // -L1 + #K #HT1 #H1KL #H2KL elim (lpx_lleq_fqu_trans … HT2 … H1KL H2KL) -L + /3 width=5 by fqup_strap1, ex3_intro/ +] +qed-. + +lemma lpx_lleq_fqus_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → + ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 → K1 ≡[T1, 0] L1 → + ∃∃K2. ⦃G1, K1, T1⦄ ⊐* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2 & K2 ≡[T2, 0] L2. +#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1 +elim (fqus_inv_gen … H) -H +[ #H elim (lpx_lleq_fqup_trans … H … H1KL1 H2KL1) -L1 + /3 width=4 by fqup_fqus, ex3_intro/ +| * #HG #HL #HT destruct /2 width=4 by ex3_intro/ +] +qed-. +*)