From c0a8f89161e9887c38eb5cf701f0f0c05a0e527f Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Tue, 14 Mar 2017 19:18:09 +0000 Subject: [PATCH] - fpbq - advances on lfdeq towards lfdeq_lfpx_conf --- .../fpbq_alt.ma => etc/fpbq/fpbq_alt.etc} | 33 ----- .../basic_2/etc/lfpx/lfpx_lreq.etc | 55 +++++++ .../relations/{btpred_8.ma => btpred_7.ma} | 4 +- .../cpx_lfdeq.ma} | 18 ++- .../lambdadelta/basic_2/rt_transition/fpb.ma | 13 +- .../lambdadelta/basic_2/rt_transition/fpbq.ma | 42 +++--- .../basic_2/rt_transition/fpbq_aaa.ma | 15 +- .../basic_2/rt_transition/lfpx_lfdeq.ma | 110 ++++++++++++-- .../basic_2/rt_transition/lpx_lleq.ma | 136 ------------------ .../basic_2/rt_transition/partial.txt | 3 +- .../lambdadelta/basic_2/web/basic_2_src.tbl | 13 +- 11 files changed, 211 insertions(+), 231 deletions(-) rename matita/matita/contribs/lambdadelta/basic_2/{rt_transition/fpbq_alt.ma => etc/fpbq/fpbq_alt.etc} (67%) create mode 100644 matita/matita/contribs/lambdadelta/basic_2/etc/lfpx/lfpx_lreq.etc rename matita/matita/contribs/lambdadelta/basic_2/notation/relations/{btpred_8.ma => btpred_7.ma} (87%) rename matita/matita/contribs/lambdadelta/basic_2/{notation/relations/btpredalt_8.ma => rt_transition/cpx_lfdeq.ma} (60%) delete mode 100644 matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_lleq.ma diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/etc/fpbq/fpbq_alt.etc similarity index 67% rename from matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_alt.ma rename to matita/matita/contribs/lambdadelta/basic_2/etc/fpbq/fpbq_alt.etc index 2a6cf5087..2607572d6 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_alt.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fpbq/fpbq_alt.etc @@ -18,15 +18,6 @@ include "basic_2/reduction/fpbq.ma". (* "QRST" PARALLEL REDUCTION FOR CLOSURES ***********************************) -(* alternative definition of fpbq *) -definition fpbqa: ∀h. sd h → tri_relation genv lenv term ≝ - λh,o,G1,L1,T1,G2,L2,T2. - ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄. - -interpretation - "'qrst' parallel reduction (closure) alternative" - 'BTPRedAlt h o G1 L1 T1 G2 L2 T2 = (fpbqa h o G1 L1 T1 G2 L2 T2). - (* Basic properties *********************************************************) lemma fleq_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. @@ -40,30 +31,6 @@ lemma fpb_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, /3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/ qed. -(* Main properties **********************************************************) - -theorem fpbq_fpbqa: ∀h,o,G1,G2,L1,L2,T1,T2. - ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → - ⦃G1, L1, T1⦄ ≽≽[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 -[ #G2 #L2 #T2 #H elim (fquq_inv_gen … H) -H - [ /3 width=1 by fpb_fqu, or_intror/ - | * #H1 #H2 #H3 destruct /2 width=1 by or_introl/ - ] -| #T2 #HT12 elim (eq_term_dec T1 T2) - #HnT12 destruct /4 width=1 by fpb_cpx, or_intror, or_introl/ -| #L2 #HL12 elim (lleq_dec … T1 L1 L2 0) - /4 width=1 by fpb_lpx, fleq_intro, or_intror, or_introl/ -| /3 width=1 by fleq_intro, or_introl/ -] -qed. - -theorem fpbqa_inv_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. - ⦃G1, L1, T1⦄ ≽≽[h, o] ⦃G2, L2, T2⦄ → - ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by fleq_fpbq, fpb_fpbq/ -qed-. - (* Advanced eliminators *****************************************************) lemma fpbq_ind_alt: ∀h,o,G1,G2,L1,L2,T1,T2. ∀R:Prop. diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lfpx/lfpx_lreq.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lfpx/lfpx_lreq.etc new file mode 100644 index 000000000..5340b8b72 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/lfpx/lfpx_lreq.etc @@ -0,0 +1,55 @@ +(**************************************************************************) +(* ___ *) +(* ||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/multiple/llor_drop.ma". +include "basic_2/multiple/llpx_sn_llor.ma". +include "basic_2/multiple/llpx_sn_lpx_sn.ma". +include "basic_2/multiple/lleq_lreq.ma". +include "basic_2/multiple/lleq_llor.ma". +include "basic_2/reduction/cpx_lreq.ma". +include "basic_2/reduction/cpx_lleq.ma". +include "basic_2/reduction/lpx_frees.ma". + +(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************) + + +fact lreq_lpx_trans_lleq_aux: ∀h,o,G,L1,L0,l,k. L1 ⩬[l, k] L0 → k = ∞ → + ∀L2. ⦃G, L0⦄ ⊢ ➡[h, o] L2 → + ∃∃L. L ⩬[l, k] L2 & ⦃G, L1⦄ ⊢ ➡[h, o] L & + (∀T. L0 ≡[T, l] L2 ↔ L1 ≡[T, l] L). +#h #o #G #L1 #L0 #l #k #H elim H -L1 -L0 -l -k +[ #l #k #_ #L2 #H >(lpx_inv_atom1 … H) -H + /3 width=5 by ex3_intro, conj/ +| #I1 #I0 #L1 #L0 #V1 #V0 #_ #_ #Hm destruct +| #I #L1 #L0 #V1 #k #HL10 #IHL10 #Hm #Y #H + elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL02 #HV02 #H destruct + lapply (ysucc_inv_Y_dx … Hm) -Hm #Hm + elim (IHL10 … HL02) // -IHL10 -HL02 #L #HL2 #HL1 #IH + @(ex3_intro … (L.ⓑ{I}V2)) /3 width=3 by lpx_pair, lreq_cpx_trans, lreq_pair/ + #T elim (IH T) #HL0dx #HL0sn + @conj #H @(lleq_lreq_repl … H) -H /3 width=1 by lreq_sym, lreq_pair_O_Y/ +| #I1 #I0 #L1 #L0 #V1 #V0 #l #k #HL10 #IHL10 #Hm #Y #H + elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL02 #HV02 #H destruct + elim (IHL10 … HL02) // -IHL10 -HL02 #L #HL2 #HL1 #IH + @(ex3_intro … (L.ⓑ{I1}V1)) /3 width=1 by lpx_pair, lreq_succ/ + #T elim (IH T) #HL0dx #HL0sn + @conj #H @(lleq_lreq_repl … H) -H /3 width=1 by lreq_sym, lreq_succ/ +] +qed-. + +lemma lreq_lpx_trans_lleq: ∀h,o,G,L1,L0,l. L1 ⩬[l, ∞] L0 → + ∀L2. ⦃G, L0⦄ ⊢ ➡[h, o] L2 → + ∃∃L. L ⩬[l, ∞] L2 & ⦃G, L1⦄ ⊢ ➡[h, o] L & + (∀T. L0 ≡[T, l] L2 ↔ L1 ≡[T, l] L). +/2 width=1 by lreq_lpx_trans_lleq_aux/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpred_8.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpred_7.ma similarity index 87% rename from matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpred_8.ma rename to matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpred_7.ma index 63d6a704b..4d62df987 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpred_8.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpred_7.ma @@ -14,6 +14,6 @@ (* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************) -notation "hvbox( ⦃ term 46 G1, break term 46 L1, break term 46 T1 ⦄ ≽ [ break term 46 h, break term 46 o ] ⦃ break term 46 G2, break term 46 L2 , break term 46 T2 ⦄ )" +notation "hvbox( ⦃ term 46 G1, break term 46 L1, break term 46 T1 ⦄ ≽ [ break term 46 h ] ⦃ break term 46 G2, break term 46 L2 , break term 46 T2 ⦄ )" non associative with precedence 45 - for @{ 'BTPRed $h $o $G1 $L1 $T1 $G2 $L2 $T2 }. + for @{ 'BTPRed $h $G1 $L1 $T1 $G2 $L2 $T2 }. diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpredalt_8.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lfdeq.ma similarity index 60% rename from matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpredalt_8.ma rename to matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lfdeq.ma index 8418bda60..3aec365f7 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/btpredalt_8.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lfdeq.ma @@ -12,8 +12,18 @@ (* *) (**************************************************************************) -(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************) +include "basic_2/static/lfdeq.ma". +include "basic_2/rt_transition/cpx_lfxs.ma". -notation "hvbox( ⦃ term 46 G1, break term 46 L1, break term 46 T1 ⦄ ≽ ≽ [ break term 46 h, break term 46 o ] ⦃ break term 46 G2, break term 46 L2 , break term 46 T2 ⦄ )" - non associative with precedence 45 - for @{ 'BTPRedAlt $h $o $G1 $L1 $T1 $G2 $L2 $T2 }. +(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************) + +(* Properties with degree-based equivalence for local environments **********) + +(* Basic_2A1: was just: cpx_lleq_conf_sn *) +lemma cpx_lfdeq_conf_sn: ∀h,o,G. s_r_confluent1 … (cpx h G) (lfdeq h o). +/3 width=6 by cpx_lfxs_conf/ qed-. + +(* Basic_2A1: was just: cpx_lleq_conf_dx *) +lemma cpx_lfdeq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h] T2 → + ∀L1. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2. +/4 width=4 by cpx_lfdeq_conf_sn, lfdeq_sym/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma index f0e7362b2..ca6ddfd09 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma @@ -20,9 +20,9 @@ include "basic_2/rt_transition/lfpr_lfpx.ma". (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************) inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝ -| fpb_fqu: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2 -| fpb_cpx: ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → (T1 ≡[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2 -| fpb_lpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → (L1 ≡[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1 +| fpb_fqu : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2 +| fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → (T1 ≡[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2 +| fpb_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → (L1 ≡[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1 . interpretation @@ -36,6 +36,7 @@ lemma cpm_fpb: ∀n,h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → (T1 ≡[h, ⦃G, L, T1⦄ ≻[h, o] ⦃G, L, T2⦄. /3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed. -lemma lpr_fpb: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → (L1 ≡[h, o, T] L2 → ⊥) → - ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄. -/3 width=1 by fpb_lpx, lfpr_fwd_lfpx/ qed. +(* Basic_2A1: includes: lpr_fpb *) +lemma lfpr_fpb: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → (L1 ≡[h, o, T] L2 → ⊥) → + ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄. +/3 width=1 by fpb_lfpx, lfpr_fwd_lfpx/ qed. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma index c8be98384..023c39fa2 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma @@ -12,31 +12,35 @@ (* *) (**************************************************************************) -include "basic_2/notation/relations/btpred_8.ma". -include "basic_2/substitution/fquq.ma". -include "basic_2/multiple/lleq.ma". -include "basic_2/reduction/lpx.ma". - -(* "QRST" PARALLEL REDUCTION FOR CLOSURES ***********************************) - -inductive fpbq (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝ -| fpbq_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h o G1 L1 T1 G2 L2 T2 -| fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, o] T2 → fpbq h o G1 L1 T1 G1 L1 T2 -| fpbq_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, o] L2 → fpbq h o G1 L1 T1 G1 L2 T1 -| fpbq_lleq: ∀L2. L1 ≡[T1, 0] L2 → fpbq h o G1 L1 T1 G1 L2 T1 +include "basic_2/notation/relations/btpred_7.ma". +include "basic_2/s_transition/fquq.ma". +include "basic_2/rt_transition/lfpr_lfpx.ma". + +(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************) + +(* Basic_2A1: includes: fpbq_lleq *) +inductive fpbq (h) (G1) (L1) (T1): relation3 genv lenv term ≝ +| fpbq_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h G1 L1 T1 G2 L2 T2 +| fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → fpbq h G1 L1 T1 G1 L1 T2 +| fpbq_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → fpbq h G1 L1 T1 G1 L2 T1 . interpretation - "'qrst' parallel reduction (closure)" - 'BTPRed h o G1 L1 T1 G2 L2 T2 = (fpbq h o G1 L1 T1 G2 L2 T2). + "parallel rst-transition (closure)" + 'BTPRed h G1 L1 T1 G2 L2 T2 = (fpbq h G1 L1 T1 G2 L2 T2). (* Basic properties *********************************************************) -lemma fpbq_refl: ∀h,o. tri_reflexive … (fpbq h o). +lemma fpbq_refl: ∀h. tri_reflexive … (fpbq h). /2 width=1 by fpbq_cpx/ qed. -lemma cpr_fpbq: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, o] ⦃G, L, T2⦄. -/3 width=1 by fpbq_cpx, cpr_cpx/ qed. +(* Basic_2A1: includes: cpr_fpbq *) +lemma cpm_fpbq: ∀n,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L, T1⦄ ≽[h] ⦃G, L, T2⦄. +/3 width=2 by fpbq_cpx, cpm_fwd_cpx/ qed. + +lemma lfpr_fpbq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L1, T⦄ ≽[h] ⦃G, L2, T⦄. +/3 width=1 by fpbq_lfpx, lfpr_fwd_lfpx/ qed. -lemma lpr_fpbq: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1, T⦄ ≽[h, o] ⦃G, L2, T⦄. -/3 width=1 by fpbq_lpx, lpr_lpx/ qed. +(* Basic_2A1: removed theorems 2: + fpbq_fpbqa fpbqa_inv_fpbq +*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_aaa.ma index 503216c57..a6c5f719e 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_aaa.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_aaa.ma @@ -13,16 +13,15 @@ (**************************************************************************) include "basic_2/static/aaa_fqus.ma". -include "basic_2/static/aaa_lleq.ma". -include "basic_2/reduction/lpx_aaa.ma". -include "basic_2/reduction/fpbq.ma". +include "basic_2/rt_transition/lfpx_aaa.ma". +include "basic_2/rt_transition/fpbq.ma". -(* "QRST" PARALLEL REDUCTION FOR CLOSURES ***********************************) +(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************) -(* Properties on atomic arity assignment for terms **************************) +(* Properties with atomic arity assignment for terms ************************) -lemma fpbq_aaa_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → +lemma fpbq_aaa_conf: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h] ⦃G2, L2, T2⦄ → ∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 -/3 width=6 by aaa_lleq_conf, lpx_aaa_conf, cpx_aaa_conf, aaa_fquq_conf, ex_intro/ +#h #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 +/3 width=6 by lfpx_aaa_conf, cpx_aaa_conf, aaa_fquq_conf, ex_intro/ qed-. 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-. +*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_lleq.ma deleted file mode 100644 index 8f2f7497b..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_lleq.ma +++ /dev/null @@ -1,136 +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/multiple/llor_drop.ma". -include "basic_2/multiple/llpx_sn_llor.ma". -include "basic_2/multiple/llpx_sn_lpx_sn.ma". -include "basic_2/multiple/lleq_lreq.ma". -include "basic_2/multiple/lleq_llor.ma". -include "basic_2/reduction/cpx_lreq.ma". -include "basic_2/reduction/cpx_lleq.ma". -include "basic_2/reduction/lpx_frees.ma". - -(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************) - -(* Properties on lazy equivalence for local environments ********************) - -(* Note: contains a proof of llpx_cpx_conf *) -lemma lleq_lpx_trans: ∀h,o,G,L2,K2. ⦃G, L2⦄ ⊢ ➡[h, o] K2 → - ∀L1,T,l. L1 ≡[T, l] L2 → - ∃∃K1. ⦃G, L1⦄ ⊢ ➡[h, o] K1 & K1 ≡[T, l] K2. -#h #o #G #L2 #K2 #HLK2 #L1 #T #l #HL12 -lapply (lpx_fwd_length … HLK2) #H1 -lapply (lleq_fwd_length … HL12) #H2 -lapply (lpx_sn_llpx_sn … T … l HLK2) // -HLK2 #H -lapply (lleq_llpx_sn_trans … HL12 … H) /2 width=3 by lleq_cpx_trans/ -HL12 -H #H -elim (llor_total L1 K2 T l) // -H1 -H2 #K1 #HLK1 -lapply (llpx_sn_llor_dx_sym … H … HLK1) -[ /2 width=6 by cpx_frees_trans/ -| /3 width=10 by cpx_llpx_sn_conf, cpx_inv_lift1, cpx_lift/ -| /3 width=5 by llpx_sn_llor_fwd_sn, 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 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-. - -fact lreq_lpx_trans_lleq_aux: ∀h,o,G,L1,L0,l,k. L1 ⩬[l, k] L0 → k = ∞ → - ∀L2. ⦃G, L0⦄ ⊢ ➡[h, o] L2 → - ∃∃L. L ⩬[l, k] L2 & ⦃G, L1⦄ ⊢ ➡[h, o] L & - (∀T. L0 ≡[T, l] L2 ↔ L1 ≡[T, l] L). -#h #o #G #L1 #L0 #l #k #H elim H -L1 -L0 -l -k -[ #l #k #_ #L2 #H >(lpx_inv_atom1 … H) -H - /3 width=5 by ex3_intro, conj/ -| #I1 #I0 #L1 #L0 #V1 #V0 #_ #_ #Hm destruct -| #I #L1 #L0 #V1 #k #HL10 #IHL10 #Hm #Y #H - elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL02 #HV02 #H destruct - lapply (ysucc_inv_Y_dx … Hm) -Hm #Hm - elim (IHL10 … HL02) // -IHL10 -HL02 #L #HL2 #HL1 #IH - @(ex3_intro … (L.ⓑ{I}V2)) /3 width=3 by lpx_pair, lreq_cpx_trans, lreq_pair/ - #T elim (IH T) #HL0dx #HL0sn - @conj #H @(lleq_lreq_repl … H) -H /3 width=1 by lreq_sym, lreq_pair_O_Y/ -| #I1 #I0 #L1 #L0 #V1 #V0 #l #k #HL10 #IHL10 #Hm #Y #H - elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL02 #HV02 #H destruct - elim (IHL10 … HL02) // -IHL10 -HL02 #L #HL2 #HL1 #IH - @(ex3_intro … (L.ⓑ{I1}V1)) /3 width=1 by lpx_pair, lreq_succ/ - #T elim (IH T) #HL0dx #HL0sn - @conj #H @(lleq_lreq_repl … H) -H /3 width=1 by lreq_sym, lreq_succ/ -] -qed-. - -lemma lreq_lpx_trans_lleq: ∀h,o,G,L1,L0,l. L1 ⩬[l, ∞] L0 → - ∀L2. ⦃G, L0⦄ ⊢ ➡[h, o] L2 → - ∃∃L. L ⩬[l, ∞] L2 & ⦃G, L1⦄ ⊢ ➡[h, o] L & - (∀T. L0 ≡[T, l] L2 ↔ L1 ≡[T, l] L). -/2 width=1 by lreq_lpx_trans_lleq_aux/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/partial.txt b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/partial.txt index e8f5e6cd3..d300eb0ff 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/partial.txt +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/partial.txt @@ -1,8 +1,9 @@ cpg.ma cpg_simple.ma cpg_drops.ma cpg_lsubr.ma -cpx.ma cpx_simple.ma cpx_drops.ma cpx_fqus.ma cpx_lsubr.ma cpx_lfxs.ma +cpx.ma cpx_simple.ma cpx_drops.ma cpx_fqus.ma cpx_lsubr.ma cpx_lfxs.ma cpx_lfdeq.ma lfpx.ma lfpx_length.ma lfpx_drops.ma lfpx_fqup.ma lfpx_frees.ma lfpx_lfdeq.ma lfpx_aaa.ma lfpx_lfpx.ma cnx.ma cnx_simple.ma cnx_drops.ma cnx_cnx.ma cpm.ma cpm_simple.ma cpm_drops.ma cpm_lsubr.ma cpm_lfxs.ma cpm_cpx.ma cpr.ma cpr_drops.ma lfpr.ma lfpr_length.ma lfpr_drops.ma lfpr_fqup.ma lfpr_frees.ma lfpr_aaa.ma lfpr_lfpx.ma lfpr_lfpr.ma fpb.ma +fpbq.ma fpbq_aaa.ma diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl index 22f988e72..8df423ca9 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl +++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl @@ -123,18 +123,11 @@ table { ] class "cyan" [ { "rt-transition" * } { - [ { "parallel qrst-transition" * } { -(* [ "fpbq ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_alt ( ⦃?,?,?⦄ ≽≽[?,?] ⦃?,?,?⦄ )" + "fpbq_aaa" * ] *) + [ { "parallel rst-transition" * } { + [ "fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )" "fpbq_aaa" * ] [ "fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" (* "fpb_lleq" + "fpb_fleq" *) * ] } ] -(* - [ { "context-sensitive rt-reduction" * } { - [ "lpx_lleq" * ] - [ "cpx_lleq" * ] - } - ] -*) [ { "t-bound context-sensitive rt-transition" * } { [ "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fqup" + "lfpr_frees" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ] [ "cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpr_drops" * ] @@ -142,7 +135,7 @@ table { } ] [ { "uncounted context-sensitive rt-transition" * } { - [ "cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )" "cnx_simple" + "cnx_drops" *+ "cnx_cnx" ] + [ "cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )" "cnx_simple" + "cnx_drops" + "cnx_cnx" * ] [ "lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fqup" + "lfpx_frees" + "lfpx_lfdeq" + "lfpx_aaa" + "lfpx_lfpx" * ] [ "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" * ] } -- 2.39.2