From: Ferruccio Guidi Date: Tue, 6 Nov 2018 09:57:00 +0000 (+0100) Subject: update in basic_2 X-Git-Tag: make_still_working~269 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=bbb6dd07ecb430bf06bb52c2506626106449a5af;p=helm.git update in basic_2 + lpce --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_4.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_4.ma new file mode 100644 index 000000000..ba25a067b --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_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 L1 ⦄ ⊢ ⬌η[ break term 46 h ] break term 46 L2 )" + non associative with precedence 45 + for @{ 'PConvEta $h $G $L1 $L2 }. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma new file mode 100644 index 000000000..8aca0e26b --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma @@ -0,0 +1,69 @@ +(**************************************************************************) +(* ___ *) +(* ||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 "static_2/relocation/lex.ma". +include "basic_2/notation/relations/pconveta_4.ma". +include "basic_2/rt_conversion/cpce.ma". + +(* PARALLEL ETA-CONVERSION FOR FULL LOCAL ENVIRONMENTS **********************) + +definition lpce (h) (G): relation lenv ≝ lex (cpce h G). + +interpretation + "parallel eta-conversion on all entries (local environment)" + 'PConvEta h G L1 L2 = (lpce h G L1 L2). + +(* Advanced properties ******************************************************) + +lemma lpce_pair (h) (G): + ∀K1,K2,V1,V2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 → ⦃G,K1⦄ ⊢ V1 ⬌η[h] V2 → + ∀I. ⦃G,K1.ⓑ{I}V1⦄ ⊢ ⬌η[h] K2.ⓑ{I}V2. +/2 width=1 by lex_pair/ qed. + +(* Basic inversion lemmas ***************************************************) + +lemma lpce_inv_atom_sn (h) (G): + ∀L2. ⦃G,⋆⦄ ⊢ ⬌η[h] L2 → L2 = ⋆. +/2 width=2 by lex_inv_atom_sn/ qed-. + +lemma lpce_inv_atom_dx (h) (G): + ∀L1. ⦃G,L1⦄ ⊢ ⬌η[h] ⋆ → L1 = ⋆. +/2 width=2 by lex_inv_atom_dx/ qed-. + +(* Advanced inversion lemmas ************************************************) + +lemma lpce_inv_unit_sn (h) (G): + ∀I,L2,K1. ⦃G,K1.ⓤ{I}⦄ ⊢ ⬌η[h] L2 → + ∃∃K2. ⦃G, K1⦄ ⊢ ⬌η[h] K2 & L2 = K2.ⓤ{I}. +/2 width=1 by lex_inv_unit_sn/ qed-. + +lemma lpce_inv_pair_sn (h) (G): + ∀I,L2,K1,V1. ⦃G,K1.ⓑ{I}V1⦄ ⊢ ⬌η[h] L2 → + ∃∃K2,V2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ V1 ⬌η[h] V2 & L2 = K2.ⓑ{I}V2. +/2 width=1 by lex_inv_pair_sn/ qed-. + +lemma lpce_inv_unit_dx (h) (G): + ∀I,L1,K2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓤ{I} → + ∃∃K1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & L1 = K1.ⓤ{I}. +/2 width=1 by lex_inv_unit_dx/ qed-. + +lemma lpce_inv_pair_dx (h) (G): + ∀I,L1,K2,V2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓑ{I}V2 → + ∃∃K1,V1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ V1 ⬌η[h] V2 & L1 = K1.ⓑ{I}V1. +/2 width=1 by lex_inv_pair_dx/ qed-. + +lemma lpce_inv_pair (h) (G): + ∀I1,I2,L1,L2,V1,V2. ⦃G,L1.ⓑ{I1}V1⦄ ⊢ ⬌η[h] L2.ⓑ{I2}V2 → + ∧∧ ⦃G,L1⦄ ⊢ ⬌η[h] L2 & ⦃G,L1⦄ ⊢ V1 ⬌η[h] V2 & I1 = I2. +/2 width=1 by lex_inv_pair/ qed-. 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 236b4f999..8cd2fd30f 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 @@ -41,6 +41,7 @@ table { class "blue" [ { "rt-conversion" * } { [ { "context-sensitive parallel eta-conversion" * } { + [ [ "for lenvs on all entries" ] "lpce ( ⦃?,?⦄ ⊢ ⬌η[?] ? )" * ] [ [ "for terms" ] "cpce" + "( ⦃?,?⦄ ⊢ ? ⬌η[?] ? )" * ] } ]