From: Ferruccio Guidi Date: Wed, 7 Aug 2013 14:44:32 +0000 (+0000) Subject: partial commit: "conversion" and "equivalence" components ... X-Git-Tag: make_still_working~1118 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=cac628104788b9400cc1a33407272fd4c35f2402;p=helm.git partial commit: "conversion" and "equivalence" components ... --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma index 5be5601ea..116e15950 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma @@ -12,29 +12,29 @@ (* *) (**************************************************************************) -include "basic_2/notation/relations/pconv_3.ma". +include "basic_2/notation/relations/pconv_4.ma". include "basic_2/reduction/cpr.ma". (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************) -definition cpc: lenv → relation term ≝ - λL,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1. +definition cpc: relation4 genv lenv term term ≝ + λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1. interpretation "context-sensitive parallel conversion (term)" - 'PConv L T1 T2 = (cpc L T1 T2). + 'PConv G L T1 T2 = (cpc G L T1 T2). (* Basic properties *********************************************************) -lemma cpc_refl: ∀L. reflexive … (cpc L). +lemma cpc_refl: ∀G,L. reflexive … (cpc G L). /2 width=1/ qed. -lemma cpc_sym: ∀L. symmetric … (cpc L). -#L #T1 #T2 * /2 width=1/ +lemma cpc_sym: ∀G,L. symmetric … (cpc L G). +#G #L #T1 #T2 * /2 width=1/ qed. (* Basic forward lemmas *****************************************************) -lemma cpc_fwd_cpr: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T. -#L #T1 #T2 * /2 width=3/ -qed. +lemma cpc_fwd_cpr: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T. +#G #L #T1 #T2 * /2 width=3/ +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma index 092d2a9a7..714d3e712 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma @@ -18,6 +18,6 @@ include "basic_2/conversion/cpc.ma". (* Main properties **********************************************************) -theorem cpc_conf: ∀L,T0,T1,T2. ⦃G, L⦄ ⊢ T0 ⬌ T1 → ⦃G, L⦄ ⊢ T0 ⬌ T2 → +theorem cpc_conf: ∀G,L,T0,T1,T2. ⦃G, L⦄ ⊢ T0 ⬌ T1 → ⦃G, L⦄ ⊢ T0 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ⬌ T & ⦃G, L⦄ ⊢ T2 ⬌ T. -/3 width=3/ qed. +/3 width=3/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma index a7e5b7514..deb838412 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma @@ -12,73 +12,74 @@ (* *) (**************************************************************************) -include "basic_2/notation/relations/pconvstar_3.ma". +include "basic_2/notation/relations/pconvstar_4.ma". include "basic_2/conversion/cpc.ma". (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************) -definition cpcs: lenv → relation term ≝ LTC … cpc. +definition cpcs: relation4 genv lenv term term ≝ + λG. LTC … (cpc G). interpretation "context-sensitive parallel equivalence (term)" - 'PConvStar L T1 T2 = (cpcs L T1 T2). + 'PConvStar G L T1 T2 = (cpcs G L T1 T2). (* Basic eliminators ********************************************************) -lemma cpcs_ind: ∀L,T1. ∀R:predicate term. R T1 → +lemma cpcs_ind: ∀G,L,T1. ∀R:predicate term. R T1 → (∀T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → R T → R T2) → ∀T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → R T2. -#L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) // +#G #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) // qed-. -lemma cpcs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 → +lemma cpcs_ind_dx: ∀G,L,T2. ∀R:predicate term. R T2 → (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → R T → R T1) → ∀T1. ⦃G, L⦄ ⊢ T1 ⬌* T2 → R T1. -#L #T2 #R #HT2 #IHT2 #T1 #HT12 +#G #L #T2 #R #HT2 #IHT2 #T1 #HT12 @(TC_star_ind_dx … HT2 IHT2 … HT12) // qed-. (* Basic properties *********************************************************) (* Basic_1: was: pc3_refl *) -lemma cpcs_refl: ∀L. reflexive … (cpcs L). +lemma cpcs_refl: ∀G,L. reflexive … (cpcs G L). /2 width=1/ qed. (* Basic_1: was: pc3_s *) -lemma cpcs_sym: ∀L. symmetric … (cpcs L). -#L @TC_symmetric // qed. +lemma cpcs_sym: ∀G,L. symmetric … (cpcs G L). +#G #L @TC_symmetric // qed. -lemma cpc_cpcs: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T2. +lemma cpc_cpcs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T2. /2 width=1/ qed. -lemma cpcs_strap1: ∀L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L @step qed. +lemma cpcs_strap1: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L @step qed. -lemma cpcs_strap2: ∀L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L @TC_strap qed. +lemma cpcs_strap2: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L @TC_strap qed. (* Basic_1: was: pc3_pr2_r *) -lemma cpr_cpcs_dx: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpr_cpcs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=1/ qed. (* Basic_1: was: pc3_pr2_x *) -lemma cpr_cpcs_sn: ∀L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡ T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpr_cpcs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡ T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=1/ qed. -lemma cpcs_cpr_strap1: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpcs_cpr_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3/ qed. (* Basic_1: was: pc3_pr2_u *) -lemma cpcs_cpr_strap2: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpcs_cpr_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3/ qed. -lemma cpcs_cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpcs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3/ qed. -lemma cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3/ qed-. (* Basic_1: was: pc3_pr2_u2 *) -lemma cpcs_cpr_conf: ∀L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpcs_cpr_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3/ qed. (* Basic_1: removed theorems 9: diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma index 1a5e48687..ce4bf678e 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma @@ -19,10 +19,10 @@ include "basic_2/equivalence/cpcs_cpcs.ma". (* Main properties about atomic arity assignment on terms *******************) -theorem aaa_cpcs_mono: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → +theorem aaa_cpcs_mono: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 → A1 = A2. -#L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2 +#G #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2 lapply (aaa_cprs_conf … HA1 … HT1) -T1 #HA1 lapply (aaa_cprs_conf … HA2 … HT2) -T2 #HA2 diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma index 125cc70fe..e6ef1a9ad 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma @@ -20,9 +20,9 @@ include "basic_2/equivalence/cpcs_cprs.ma". (* Advanced inversion lemmas ************************************************) -lemma cpcs_inv_cprs: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → +lemma cpcs_inv_cprs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡* T & ⦃G, L⦄ ⊢ T2 ➡* T. -#L #T1 #T2 #H @(cpcs_ind … H) -T2 +#G #L #T1 #T2 #H @(cpcs_ind … H) -T2 [ /3 width=3/ | #T #T2 #_ #HT2 * #T0 #HT10 elim HT2 -HT2 #HT2 #HT0 [ elim (cprs_strip … HT0 … HT2) -T #T #HT0 #HT2 @@ -33,38 +33,38 @@ lemma cpcs_inv_cprs: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → qed-. (* Basic_1: was: pc3_gen_sort *) -lemma cpcs_inv_sort: ∀L,k1,k2. ⦃G, L⦄ ⊢ ⋆k1 ⬌* ⋆k2 → k1 = k2. -#L #k1 #k2 #H +lemma cpcs_inv_sort: ∀G,L,k1,k2. ⦃G, L⦄ ⊢ ⋆k1 ⬌* ⋆k2 → k1 = k2. +#G #L #k1 #k2 #H elim (cpcs_inv_cprs … H) -H #T #H1 >(cprs_inv_sort1 … H1) -T #H2 lapply (cprs_inv_sort1 … H2) -L #H destruct // qed-. -lemma cpcs_inv_abst1: ∀a,L,W1,T1,T. ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ⬌* T → +lemma cpcs_inv_abst1: ∀a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ⬌* T → ∃∃W2,T2. ⦃G, L⦄ ⊢ T ➡* ⓛ{a}W2.T2 & ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2. -#a #L #W1 #T1 #T #H +#a #G #L #W1 #T1 #T #H elim (cpcs_inv_cprs … H) -H #X #H1 #H2 elim (cprs_inv_abst1 … H1) -H1 #W2 #T2 #HW12 #HT12 #H destruct @(ex2_2_intro … H2) -H2 /2 width=2/ (**) (* explicit constructor, /3 width=6/ is slow *) qed-. -lemma cpcs_inv_abst2: ∀a,L,W1,T1,T. ⦃G, L⦄ ⊢ T ⬌* ⓛ{a}W1.T1 → +lemma cpcs_inv_abst2: ∀a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ T ⬌* ⓛ{a}W1.T1 → ∃∃W2,T2. ⦃G, L⦄ ⊢ T ➡* ⓛ{a}W2.T2 & ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2. /3 width=1 by cpcs_inv_abst1, cpcs_sym/ qed-. (* Basic_1: was: pc3_gen_sort_abst *) -lemma cpcs_inv_sort_abst: ∀a,L,W,T,k. ⦃G, L⦄ ⊢ ⋆k ⬌* ⓛ{a}W.T → ⊥. -#a #L #W #T #k #H +lemma cpcs_inv_sort_abst: ∀a,G,L,W,T,k. ⦃G, L⦄ ⊢ ⋆k ⬌* ⓛ{a}W.T → ⊥. +#a #G #L #W #T #k #H elim (cpcs_inv_cprs … H) -H #X #H1 >(cprs_inv_sort1 … H1) -X #H2 elim (cprs_inv_abst1 … H2) -H2 #W0 #T0 #_ #_ #H destruct qed-. (* Basic_1: was: pc3_gen_lift *) -lemma cpcs_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → +lemma cpcs_inv_lift: ∀G,L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 → - ⦃G, L⦄ ⊢ U1 ⬌* U2 → K ⊢ T1 ⬌* T2. -#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12 + ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, K⦄ ⊢ T1 ⬌* T2. +#G #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12 elim (cpcs_inv_cprs … HU12) -HU12 #U #HU1 #HU2 elim (cprs_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HTU #HT1 elim (cprs_inv_lift1 … HU2 … HLK … HTU2) -L -U2 #X #HXU @@ -73,100 +73,105 @@ qed-. (* Advanced properties ******************************************************) -lemma lpr_cpcs_trans: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2. -#L1 #L2 #HL12 #T1 #T2 #H +lemma lpr_cpcs_trans: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → + ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌* T2 → ⦃G, L1⦄ ⊢ T1 ⬌* T2. +#G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2 lapply (lpr_cprs_trans … HT1 … HL12) -HT1 lapply (lpr_cprs_trans … HT2 … HL12) -L2 /2 width=3/ qed-. -lemma lprs_cpcs_trans: ∀L1,L2. L1 ⊢ ➡* L2 → ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2. -#L1 #L2 #HL12 #T1 #T2 #H +lemma lprs_cpcs_trans: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → + ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌* T2 → ⦃G, L1⦄ ⊢ T1 ⬌* T2. +#G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2 lapply (lprs_cprs_trans … HT1 … HL12) -HT1 lapply (lprs_cprs_trans … HT2 … HL12) -L2 /2 width=3/ qed-. -lemma cpr_cprs_conf_cpcs: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T #T1 #T2 #HT1 #HT2 +lemma cpr_cprs_conf_cpcs: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T #T1 #T2 #HT1 #HT2 elim (cprs_strip … HT1 … HT2) /2 width=3 by cpr_cprs_div/ qed-. -lemma cprs_cpr_conf_cpcs: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T1. -#L #T #T1 #T2 #HT1 #HT2 +lemma cprs_cpr_conf_cpcs: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T1. +#G #L #T #T1 #T2 #HT1 #HT2 elim (cprs_strip … HT1 … HT2) /2 width=3 by cprs_cpr_div/ qed-. -lemma cprs_conf_cpcs: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T #T1 #T2 #HT1 #HT2 +lemma cprs_conf_cpcs: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T #T1 #T2 #HT1 #HT2 elim (cprs_conf … HT1 … HT2) /2 width=3/ qed-. -lemma lprs_cprs_conf: ∀L1,L2. L1 ⊢ ➡* L2 → ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2. -#L1 #L2 #HL12 #T1 #T2 #HT12 +lemma lprs_cprs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → + ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2. +#G #L1 #L2 #HL12 #T1 #T2 #HT12 elim (lprs_cprs_conf_dx … HT12 … HL12) -L1 /2 width=3/ qed-. (* Basic_1: was: pc3_wcpr0_t *) (* Basic_1: note: pc3_wcpr0_t should be renamed *) -lemma lpr_cprs_conf: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2. +lemma lpr_cprs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → + ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2. /3 width=5 by lprs_cprs_conf, lpr_lprs/ qed-. (* Basic_1: was only: pc3_pr0_pr2_t *) (* Basic_1: note: pc3_pr0_pr2_t should be renamed *) -lemma lpr_cpr_conf: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2. +lemma lpr_cpr_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → + ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2. /3 width=5 by lpr_cprs_conf, cpr_cprs/ qed-. (* Basic_1: was only: pc3_thin_dx *) -lemma cpcs_flat: ∀L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → - ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1. T1 ⬌* ⓕ{I}V2. T2. -#L #V1 #V2 #HV12 #T1 #T2 #HT12 #I +lemma cpcs_flat: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → + ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ⬌* ⓕ{I}V2.T2. +#G #L #V1 #V2 #HV12 #T1 #T2 #HT12 #I elim (cpcs_inv_cprs … HV12) -HV12 #V #HV1 #HV2 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_flat, cprs_div/ (**) (* /3 width=5/ is too slow *) qed. -lemma cpcs_flat_dx_cpr_rev: ∀L,V1,V2. ⦃G, L⦄ ⊢ V2 ➡ V1 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → - ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1. T1 ⬌* ⓕ{I}V2. T2. +lemma cpcs_flat_dx_cpr_rev: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V2 ➡ V1 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → + ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ⬌* ⓕ{I}V2.T2. /3 width=1/ qed. -lemma cpcs_bind_dx: ∀a,I,L,V,T1,T2. L.ⓑ{I}V ⊢ T1 ⬌* T2 → - ⦃G, L⦄ ⊢ ⓑ{a,I}V. T1 ⬌* ⓑ{a,I}V. T2. -#a #I #L #V #T1 #T2 #HT12 +lemma cpcs_bind_dx: ∀a,I,G,L,V,T1,T2. ⦃G, L.ⓑ{I}V⦄ ⊢ T1 ⬌* T2 → + ⦃G, L⦄ ⊢ ⓑ{a,I}V.T1 ⬌* ⓑ{a,I}V.T2. +#a #I #G #L #V #T1 #T2 #HT12 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_div, cprs_bind/ (**) (* /3 width=5/ is a bit slow *) qed. -lemma cpcs_bind_sn: ∀a,I,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T ⬌* ⓑ{a,I}V2. T. -#a #I #L #V1 #V2 #T #HV12 +lemma cpcs_bind_sn: ∀a,I,G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T ⬌* ⓑ{a,I}V2. T. +#a #I #G #L #V1 #V2 #T #HV12 elim (cpcs_inv_cprs … HV12) -HV12 /3 width=5 by cprs_div, cprs_bind/ (**) (* /3 width=5/ is a bit slow *) qed. -lemma lsubr_cpcs_trans: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 → - ∀L2. L2 ⊑ L1 → L2 ⊢ T1 ⬌* T2. -#L1 #T1 #T2 #HT12 +lemma lsubr_cpcs_trans: ∀G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬌* T2 → + ∀L2. L2 ⊑ L1 → ⦃G, L2⦄ ⊢ T1 ⬌* T2. +#G #L1 #T1 #T2 #HT12 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_div, lsubr_cprs_trans/ (**) (* /3 width=5/ is a bit slow *) qed-. (* Basic_1: was: pc3_lift *) -lemma cpcs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → +lemma cpcs_lift: ∀G,L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 → - K ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ U1 ⬌* U2. -#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12 + ⦃G, K⦄ ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ U1 ⬌* U2. +#G #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2 elim (lift_total T d e) #U #HTU lapply (cprs_lift … HT1 … HLK … HTU1 … HTU) -T1 #HU1 lapply (cprs_lift … HT2 … HLK … HTU2 … HTU) -K -T2 -T -d -e /2 width=3/ qed. -lemma cpcs_strip: ∀L,T1,T. ⦃G, L⦄ ⊢ T ⬌* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌ T2 → +lemma cpcs_strip: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ⬌* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌ T2 → ∃∃T0. ⦃G, L⦄ ⊢ T1 ⬌ T0 & ⦃G, L⦄ ⊢ T2 ⬌* T0. -#L #T1 #T @TC_strip1 /2 width=3/ qed-. +#G #L #T1 #T @TC_strip1 /2 width=3 by cpc_conf/ qed-. (* More inversion lemmas ****************************************************) -lemma cpcs_inv_abst_sn: ∀a1,a2,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 → - ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & L.ⓛW1 ⊢ T1 ⬌* T2 & a1 = a2. -#a1 #a2 #L #W1 #W2 #T1 #T2 #H +lemma cpcs_inv_abst_sn: ∀a1,a2,G,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 → + ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬌* T2 & a1 = a2. +#a1 #a2 #G #L #W1 #W2 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H #T #H1 #H2 elim (cprs_inv_abst1 … H1) -H1 #W0 #T0 #HW10 #HT10 #H destruct elim (cprs_inv_abst1 … H2) -H2 #W #T #HW2 #HT2 #H destruct @@ -175,9 +180,9 @@ lapply (lprs_cpcs_trans … (L.ⓛW1) … HT2) /2 width=1/ -HT2 #HT2 /4 width=3 by and3_intro, cprs_div, cpcs_cprs_div, cpcs_sym/ qed-. -lemma cpcs_inv_abst_dx: ∀a1,a2,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 → - ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & L. ⓛW2 ⊢ T1 ⬌* T2 & a1 = a2. -#a1 #a2 #L #W1 #W2 #T1 #T2 #HT12 +lemma cpcs_inv_abst_dx: ∀a1,a2,G,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 → + ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & ⦃G, L.ⓛW2⦄ ⊢ T1 ⬌* T2 & a1 = a2. +#a1 #a2 #G #L #W1 #W2 #T1 #T2 #HT12 lapply (cpcs_sym … HT12) -HT12 #HT12 elim (cpcs_inv_abst_sn … HT12) -HT12 /3 width=1/ qed-. @@ -185,29 +190,32 @@ qed-. (* Main properties **********************************************************) (* Basic_1: was pc3_t *) -theorem cpcs_trans: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T #HT1 #T2 @(trans_TC … HT1) qed-. +theorem cpcs_trans: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T #HT1 #T2 @(trans_TC … HT1) qed-. -theorem cpcs_canc_sn: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ⬌* T1 → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +theorem cpcs_canc_sn: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ⬌* T1 → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3 by cpcs_trans, cpcs_sym/ qed-. (**) (* /3 width=3/ is too slow *) -theorem cpcs_canc_dx: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T2 ⬌* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +theorem cpcs_canc_dx: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T2 ⬌* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3 by cpcs_trans, cpcs_sym/ qed-. (**) (* /3 width=3/ is too slow *) -lemma cpcs_bind1: ∀a,I,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. L.ⓑ{I}V1 ⊢ T1 ⬌* T2 → +lemma cpcs_bind1: ∀a,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → + ∀T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ⬌* ⓑ{a,I}V2. T2. -#a #I #L #V1 #V2 #HV12 #T1 #T2 #HT12 +#a #I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cpcs_trans … (ⓑ{a,I}V1.T2)) /2 width=1/ qed. -lemma cpcs_bind2: ∀a,I,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. L.ⓑ{I}V2 ⊢ T1 ⬌* T2 → +lemma cpcs_bind2: ∀a,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → + ∀T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ⬌* ⓑ{a,I}V2. T2. -#a #I #L #V1 #V2 #HV12 #T1 #T2 #HT12 +#a #I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cpcs_trans … (ⓑ{a,I}V2.T1)) /2 width=1/ qed. (* Basic_1: was: pc3_wcpr0 *) -lemma lpr_cpcs_conf: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2. -#L1 #L2 #HL12 #T1 #T2 #H +lemma lpr_cpcs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → + ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ⬌* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2. +#G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H /3 width=5 by cpcs_canc_dx, lpr_cprs_conf/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma index 30ee9fb9d..69641dbf7 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma @@ -20,40 +20,40 @@ include "basic_2/equivalence/cpcs.ma". (* Properties about context sensitive computation on terms ******************) (* Basic_1: was: pc3_pr3_r *) -lemma cpcs_cprs_dx: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /3 width=3/ +lemma cpcs_cprs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /3 width=3/ qed. (* Basic_1: was: pc3_pr3_x *) -lemma cpcs_cprs_sn: ∀L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/ +lemma cpcs_cprs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/ qed. -lemma cpcs_cprs_strap1: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /2 width=3/ +lemma cpcs_cprs_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /2 width=3/ qed. -lemma cpcs_cprs_strap2: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /width=1/ /2 width=3/ +lemma cpcs_cprs_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /width=1/ /2 width=3/ qed. -lemma cpcs_cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /2 width=3/ +lemma cpcs_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /2 width=3/ qed. (* Basic_1: was: pc3_pr3_conf *) -lemma cpcs_cprs_conf: ∀L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /width=1/ /2 width=3/ +lemma cpcs_cprs_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /width=1/ /2 width=3/ qed. (* Basic_1: was: pc3_pr3_t *) (* Basic_1: note: pc3_pr3_t should be renamed *) -lemma cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. -#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=1/ /2 width=3/ +lemma cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=1/ /2 width=3/ qed. -lemma cprs_cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cprs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=5 by cpr_cprs, cprs_div/ qed-. -lemma cpr_cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. +lemma cpr_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2. /3 width=3 by cpr_cprs, cprs_div/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_3.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_3.ma deleted file mode 100644 index c4a789ab8..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_3.ma +++ /dev/null @@ -1,19 +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 *) -(* *) -(**************************************************************************) - -(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************) - -notation "hvbox( ⦃G, L⦄ ⊢ break term 46 T1 ⬌ break term 46 T2 )" - non associative with precedence 45 - for @{ 'PConv $L $T1 $T2 }. diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_4.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_4.ma new file mode 100644 index 000000000..a7563d0c0 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_4.ma @@ -0,0 +1,19 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *) +(* *) +(**************************************************************************) + +(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************) + +notation "hvbox( ⦃ term 46 G, break term 46 L ⦄ ⊢ break term 46 T1 ⬌ break term 46 T2 )" + non associative with precedence 45 + for @{ 'PConv $G $L $T1 $T2 }. diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_3.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_3.ma deleted file mode 100644 index 2088bc68d..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_3.ma +++ /dev/null @@ -1,19 +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 *) -(* *) -(**************************************************************************) - -(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************) - -notation "hvbox( ⦃G, L⦄ ⊢ break term 46 T1 ⬌* break term 46 T2 )" - non associative with precedence 45 - for @{ 'PConvStar $L $T1 $T2 }. diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_4.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_4.ma new file mode 100644 index 000000000..f263e5d06 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_4.ma @@ -0,0 +1,19 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *) +(* *) +(**************************************************************************) + +(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************) + +notation "hvbox( ⦃ term 46 G, break term 46 L ⦄ ⊢ break term 46 T1 ⬌* break term 46 T2 )" + non associative with precedence 45 + for @{ 'PConvStar $G $L $T1 $T2 }. 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 7a7d92d17..0bd584cac 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 @@ -40,19 +40,19 @@ table { ] *) [ { "\"big tree\" parallel computation" * } { - [ "yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )" "yprs_yprs" "ygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )" "ygt_ygt" * ] + [ "yprs ( ? ⊢ ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "yprs_yprs" "ygt ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "ygt_ygt" * ] } ] [ { "\"big tree\" parallel reduction" * } { - [ "ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )" "ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )" * ] + [ "ypr ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "ysc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" * ] } ] [ { "local env. ref. for stratified native validity" * } { - [ "lsubsv ( ? ⊢ ? ¡⊑[?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ] + [ "lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ] } ] [ { "stratified native validity" * } { - [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?] )" "snv_lift" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_lpr" + "snv_lpr" + "snv_cpcs" * ] + [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_lpr" + "snv_lpr" + "snv_cpcs" * ] } ] } @@ -60,7 +60,7 @@ table { class "blue" [ { "equivalence" * } { [ { "context-sensitive equivalence" * } { - [ "cpcs ( ? ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ] + [ "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ] } ] } @@ -68,7 +68,7 @@ table { class "sky" [ { "conversion" * } { [ { "context-sensitive conversion" * } { - [ "cpc ( ? ⊢ ? ⬌ ? )" "cpc_cpc" * ] + [ "cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )" "cpc_cpc" * ] } ] }