From: Ferruccio Guidi Date: Wed, 14 Sep 2016 11:10:51 +0000 (+0000) Subject: first results on lfpr as a base for the diamond property ... X-Git-Tag: make_still_working~540 X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=commitdiff_plain;h=45996e63afdb9802935990660c4912d58035e016 first results on lfpr as a base for the diamond property ... --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma new file mode 100644 index 000000000..a38aff49d --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma @@ -0,0 +1,130 @@ +(**************************************************************************) +(* ___ *) +(* ||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/notation/relations/predsn_5.ma". +include "basic_2/static/lfxs.ma". +include "basic_2/rt_transition/cpm.ma". + +(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************) + +definition lfpr: sh → genv → relation3 term lenv lenv ≝ + λh,G. lfxs (cpm 0 h G). + +interpretation + "parallel r-transition on referred entries (local environment)" + 'PRedSn h T G L1 L2 = (lfpr h G T L1 L2). + +(* Basic properties ***********************************************************) + +lemma lfpr_atom: ∀h,I,G. ⦃G, ⋆⦄ ⊢ ➡[h, ⓪{I}] ⋆. +/2 width=1 by lfxs_atom/ qed. + +lemma lfpr_sort: ∀h,I,G,L1,L2,V1,V2,s. + ⦃G, L1⦄ ⊢ ➡[h, ⋆s] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, ⋆s] L2.ⓑ{I}V2. +/2 width=1 by lfxs_sort/ qed. + +lemma lfpr_zero: ∀h,I,G,L1,L2,V. + ⦃G, L1⦄ ⊢ ➡[h, V] L2 → ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡[h, #0] L2.ⓑ{I}V. +/2 width=1 by lfxs_zero/ qed. + +lemma lfpr_lref: ∀h,I,G,L1,L2,V1,V2,i. + ⦃G, L1⦄ ⊢ ➡[h, #i] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, #⫯i] L2.ⓑ{I}V2. +/2 width=1 by lfxs_lref/ qed. + +lemma lfpr_gref: ∀h,I,G,L1,L2,V1,V2,l. + ⦃G, L1⦄ ⊢ ➡[h, §l] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, §l] L2.ⓑ{I}V2. +/2 width=1 by lfxs_gref/ qed. + +(* Basic inversion lemmas ***************************************************) + +lemma lfpr_inv_atom_sn: ∀h,I,G,Y2. ⦃G, ⋆⦄ ⊢ ➡[h, ⓪{I}] Y2 → Y2 = ⋆. +/2 width=3 by lfxs_inv_atom_sn/ qed-. + +lemma lfpr_inv_atom_dx: ∀h,I,G,Y1. ⦃G, Y1⦄ ⊢ ➡[h, ⓪{I}] ⋆ → Y1 = ⋆. +/2 width=3 by lfxs_inv_atom_dx/ qed-. + +lemma lfpr_inv_zero: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ➡[h, #0] Y2 → + (Y1 = ⋆ ∧ Y2 = ⋆) ∨ + ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ➡[h, V1] L2 & + ⦃G, L1⦄ ⊢ V1 ➡[h] V2 & + Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. +/2 width=1 by lfxs_inv_zero/ qed-. + +lemma lfpr_inv_lref: ∀h,G,Y1,Y2,i. ⦃G, Y1⦄ ⊢ ➡[h, #⫯i] Y2 → + (Y1 = ⋆ ∧ Y2 = ⋆) ∨ + ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 & + Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. +/2 width=1 by lfxs_inv_lref/ qed-. + +lemma lfpr_inv_bind: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 → + ⦃G, L1⦄ ⊢ ➡[h, V] L2 ∧ ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡[h, T] L2.ⓑ{I}V. +/2 width=2 by lfxs_inv_bind/ qed-. + +lemma lfpr_inv_flat: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡[h, ⓕ{I}V.T] L2 → + ⦃G, L1⦄ ⊢ ➡[h, V] L2 ∧ ⦃G, L1⦄ ⊢ ➡[h, T] L2. +/2 width=2 by lfxs_inv_flat/ qed-. + +(* Advanced inversion lemmas ************************************************) + +lemma lfpr_inv_zero_pair_sn: ∀h,I,G,Y2,L1,V1. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, #0] Y2 → + ∃∃L2,V2. ⦃G, L1⦄ ⊢ ➡[h, V1] L2 & ⦃G, L1⦄ ⊢ V1 ➡[h] V2 & + Y2 = L2.ⓑ{I}V2. +/2 width=1 by lfxs_inv_zero_pair_sn/ qed-. + +lemma lfpr_inv_zero_pair_dx: ∀h,I,G,Y1,L2,V2. ⦃G, Y1⦄ ⊢ ➡[h, #0] L2.ⓑ{I}V2 → + ∃∃L1,V1. ⦃G, L1⦄ ⊢ ➡[h, V1] L2 & ⦃G, L1⦄ ⊢ V1 ➡[h] V2 & + Y1 = L1.ⓑ{I}V1. +/2 width=1 by lfxs_inv_zero_pair_dx/ qed-. + +lemma lfpr_inv_lref_pair_sn: ∀h,I,G,Y2,L1,V1,i. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, #⫯i] Y2 → + ∃∃L2,V2. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 & Y2 = L2.ⓑ{I}V2. +/2 width=2 by lfxs_inv_lref_pair_sn/ qed-. + +lemma lfpr_inv_lref_pair_dx: ∀h,I,G,Y1,L2,V2,i. ⦃G, Y1⦄ ⊢ ➡[h, #⫯i] L2.ⓑ{I}V2 → + ∃∃L1,V1. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 & Y1 = L1.ⓑ{I}V1. +/2 width=2 by lfxs_inv_lref_pair_dx/ qed-. + +(* Basic forward lemmas *****************************************************) + +lemma lfpr_fwd_bind_sn: ∀h,p,I,G,L1,L2,V,T. + ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 → ⦃G, L1⦄ ⊢ ➡[h, V] L2. +/2 width=4 by lfxs_fwd_bind_sn/ qed-. + +lemma lfpr_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. + ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 → ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡[h, T] L2.ⓑ{I}V. +/2 width=2 by lfxs_fwd_bind_dx/ qed-. + +lemma lfpr_fwd_flat_sn: ∀h,I,G,L1,L2,V,T. + ⦃G, L1⦄ ⊢ ➡[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ➡[h, V] L2. +/2 width=3 by lfxs_fwd_flat_sn/ qed-. + +lemma lfpr_fwd_flat_dx: ∀h,I,G,L1,L2,V,T. + ⦃G, L1⦄ ⊢ ➡[h, ⓕ{I}V.T] L2 → ⦃G, L1⦄ ⊢ ➡[h, T] L2. +/2 width=3 by lfxs_fwd_flat_dx/ qed-. + +lemma lfpr_fwd_pair_sn: ∀h,I,G,L1,L2,V,T. + ⦃G, L1⦄ ⊢ ➡[h, ②{I}V.T] L2 → ⦃G, L1⦄ ⊢ ➡[h, V] L2. +/2 width=3 by lfxs_fwd_pair_sn/ qed-. + +(* Basic_2A1: removed theorems 11: + lpr_inv_atom1 lpr_inv_pair1 lpr_inv_atom2 lpr_inv_pair2 + lpr_refl lpr_pair + lpr_fwd_length lpr_lpx + lpr_drop_conf drop_lpr_trans lpr_drop_trans_O1 +*) +(* Basic_1: removed theorems 7: wcpr0_gen_sort wcpr0_gen_head + wcpr0_getl wcpr0_getl_back + pr0_subst1_back + wcpr0_drop wcpr0_drop_back +*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_drops.ma new file mode 100644 index 000000000..b3deebd85 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_drops.ma @@ -0,0 +1,32 @@ +(**************************************************************************) +(* ___ *) +(* ||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/static/lfxs_drops.ma". +include "basic_2/rt_transition/cpm_drops.ma". +include "basic_2/rt_transition/lfpr.ma". + +(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************) + +(* Properties with generic slicing for local environments *******************) + +lemma drops_lfpr_trans: ∀h,G. dedropable_sn (cpm 0 h G). +/3 width=6 by lfxs_liftable_dedropable, cpm_lifts/ qed-. + +(* Inversion lemmas with generic slicing for local environments *************) + +lemma lfpr_drops_conf: ∀h,G. dropable_sn (cpm 0 h G). +/2 width=5 by lfxs_dropable_sn/ qed-. + +lemma lfpr_drops_trans: ∀h,G. dropable_dx (cpm 0 h G). +/2 width=5 by lfxs_dropable_dx/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma new file mode 100644 index 000000000..297993014 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma @@ -0,0 +1,24 @@ +(**************************************************************************) +(* ___ *) +(* ||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/static/lfxs_fqup.ma". +include "basic_2/rt_transition/lfpr.ma". + +(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************) + +(* Advanced properties ******************************************************) + +(* Note: lemma 250 *) +lemma lfpr_refl: ∀h,G,T. reflexive … (lfpr h G T). +/2 width=1 by lfxs_refl/ qed. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_length.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_length.ma new file mode 100644 index 000000000..19db3f337 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_length.ma @@ -0,0 +1,23 @@ +(**************************************************************************) +(* ___ *) +(* ||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/static/lfxs_length.ma". +include "basic_2/rt_transition/lfpr.ma". + +(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************) + +(* Forward lemmas with length for local environments ************************) + +lemma lfpr_fwd_length: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → |L1| = |L2|. +/2 width=3 by lfxs_fwd_length/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_lfpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_lfpx.ma new file mode 100644 index 000000000..47323a86d --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_lfpx.ma @@ -0,0 +1,24 @@ +(**************************************************************************) +(* ___ *) +(* ||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/rt_transition/lfpx.ma". +include "basic_2/rt_transition/cpm_cpx.ma". +include "basic_2/rt_transition/lfpr.ma". + +(* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************) + +(* Fwd. lemmas with unc. rt-transition for local env.s on referred entries **) + +lemma lfpr_fwd_lfpx: ∀h,T,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2. +/3 width=3 by cpm_fwd_cpx, lfxs_co/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma index 21c37f3b3..57c0184be 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma @@ -55,14 +55,14 @@ lemma lfpx_inv_atom_dx: ∀h,I,G,Y1. ⦃G, Y1⦄ ⊢ ⬈[h, ⓪{I}] ⋆ → Y1 = /2 width=3 by lfxs_inv_atom_dx/ qed-. lemma lfpx_inv_zero: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 → - (Y1 = ⋆ ∧ Y2 = ⋆) ∨ + (Y1 = ⋆ ∧ Y2 = ⋆) ∨ ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 & Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. /2 width=1 by lfxs_inv_zero/ qed-. lemma lfpx_inv_lref: ∀h,G,Y1,Y2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #⫯i] Y2 → - (Y1 = ⋆ ∧ Y2 = ⋆) ∨ + (Y1 = ⋆ ∧ Y2 = ⋆) ∨ ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. /2 width=1 by lfxs_inv_lref/ qed-. @@ -97,7 +97,7 @@ lemma lfpx_inv_lref_pair_dx: ∀h,I,G,Y1,L2,V2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #⫯i] (* Basic forward lemmas *****************************************************) -lemma lfpx_fwd_bind_sn: ∀h,p,I,G,L1,L2,V,T. +lemma lfpx_fwd_bind_sn: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, V] L2. /2 width=4 by lfxs_fwd_bind_sn/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma deleted file mode 100644 index 24cea1f7e..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma +++ /dev/null @@ -1,65 +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/notation/relations/predsn_3.ma". -include "basic_2/substitution/lpx_sn.ma". -include "basic_2/reduction/cpr.ma". - -(* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************) - -definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (cpr G). - -interpretation "parallel reduction (local environment, sn variant)" - 'PRedSn G L1 L2 = (lpr G L1 L2). - -(* Basic inversion lemmas ***************************************************) - -(* Basic_1: includes: wcpr0_gen_sort *) -lemma lpr_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡ L2 → L2 = ⋆. -/2 width=4 by lpx_sn_inv_atom1_aux/ qed-. - -(* Basic_1: includes: wcpr0_gen_head *) -lemma lpr_inv_pair1: ∀I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ L2 → - ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L2 = K2.ⓑ{I}V2. -/2 width=3 by lpx_sn_inv_pair1_aux/ qed-. - -lemma lpr_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡ ⋆ → L1 = ⋆. -/2 width=4 by lpx_sn_inv_atom2_aux/ qed-. - -lemma lpr_inv_pair2: ∀I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡ K2.ⓑ{I}V2 → - ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L1 = K1. ⓑ{I} V1. -/2 width=3 by lpx_sn_inv_pair2_aux/ qed-. - -(* Basic properties *********************************************************) - -(* Note: lemma 250 *) -lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L. -/2 width=1 by lpx_sn_refl/ qed. - -lemma lpr_pair: ∀I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡ K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 → - ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2. -/2 width=1 by lpx_sn_pair/ qed. - -(* Basic forward lemmas *****************************************************) - -lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|. -/2 width=2 by lpx_sn_fwd_length/ qed-. - -lemma lpr_lpx: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡[h, o] L2. -#h #o #G #L1 #L2 #H elim H -L1 -L2 /3 width=1 by lpx_pair, cpr_cpx/ -qed. - -(* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back - pr0_subst1_back -*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_drop.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_drop.ma deleted file mode 100644 index 5ec500e5f..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_drop.ma +++ /dev/null @@ -1,96 +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/substitution/lpx_sn_drop.ma". -include "basic_2/substitution/fquq_alt.ma". -include "basic_2/reduction/cpr_lift.ma". -include "basic_2/reduction/lpr.ma". - -(* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************) - -(* Properties on local environment slicing ***********************************) - -(* Basic_1: includes: wcpr0_drop *) -lemma lpr_drop_conf: ∀G. dropable_sn (lpr G). -/3 width=6 by lpx_sn_deliftable_dropable, cpr_inv_lift1/ qed-. - -(* Basic_1: includes: wcpr0_drop_back *) -lemma drop_lpr_trans: ∀G. dedropable_sn (lpr G). -/3 width=10 by lpx_sn_liftable_dedropable, cpr_lift/ qed-. - -lemma lpr_drop_trans_O1: ∀G. dropable_dx (lpr G). -/2 width=3 by lpx_sn_dropable/ qed-. - -(* Properties on context-sensitive parallel reduction for terms *************) - -lemma fqu_cpr_trans_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄. -#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 -/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/ -#G #L #K #U #T #k #HLK #HUT #U2 #HU2 -elim (lift_total U2 0 (k+1)) #T2 #HUT2 -lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/ -qed-. - -lemma fquq_cpr_trans_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. -#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H -[ #HT12 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/ -| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ -] -qed-. - -lemma fqu_cpr_trans_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄. -#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 -/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/ -#G #L #K #U #T #k #HLK #HUT #U2 #HU2 -elim (lift_total U2 0 (k+1)) #T2 #HUT2 -lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/ -qed-. - -lemma fquq_cpr_trans_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. -#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H -[ #HT12 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/ -| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ -] -qed-. - -lemma fqu_lpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → - ∀K2. ⦃G2, L2⦄ ⊢ ➡ K2 → - ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡ K1 & ⦃G1, L1⦄ ⊢ T1 ➡ T & ⦃G1, K1, T⦄ ⊐ ⦃G2, K2, T2⦄. -#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 -/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_flat_dx, lpr_pair, ex3_2_intro/ -[ #a #I #G2 #L2 #V2 #T2 #X #H elim (lpr_inv_pair1 … H) -H - #K2 #W2 #HLK2 #HVW2 #H destruct - /3 width=5 by fqu_fquq, cpr_pair_sn, fqu_bind_dx, ex3_2_intro/ -| #G #L1 #K1 #T1 #U1 #k #HLK1 #HTU1 #K2 #HK12 - elim (drop_lpr_trans … HLK1 … HK12) -HK12 - /3 width=7 by fqu_drop, ex3_2_intro/ -] -qed-. - -lemma fquq_lpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∀K2. ⦃G2, L2⦄ ⊢ ➡ K2 → - ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡ K1 & ⦃G1, L1⦄ ⊢ T1 ➡ T & ⦃G1, K1, T⦄ ⊐⸮ ⦃G2, K2, T2⦄. -#G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 elim (fquq_inv_gen … H) -H -[ #HT12 elim (fqu_lpr_trans … HT12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/ -| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ -] -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma new file mode 100644 index 000000000..4c0a26e56 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma @@ -0,0 +1,62 @@ +(* Properties on context-sensitive parallel reduction for terms *************) + +lemma fqu_cpr_trans_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → + ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄. +#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 +/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/ +#G #L #K #U #T #k #HLK #HUT #U2 #HU2 +elim (lift_total U2 0 (k+1)) #T2 #HUT2 +lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/ +qed-. + +lemma fquq_cpr_trans_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → + ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. +#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H +[ #HT12 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/ +| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ +] +qed-. + +lemma fqu_cpr_trans_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → + ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄. +#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 +/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/ +#G #L #K #U #T #k #HLK #HUT #U2 #HU2 +elim (lift_total U2 0 (k+1)) #T2 #HUT2 +lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/ +qed-. + +lemma fquq_cpr_trans_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 → + ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. +#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H +[ #HT12 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/ +| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ +] +qed-. + +lemma fqu_lpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → + ∀K2. ⦃G2, L2⦄ ⊢ ➡ K2 → + ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡ K1 & ⦃G1, L1⦄ ⊢ T1 ➡ T & ⦃G1, K1, T⦄ ⊐ ⦃G2, K2, T2⦄. +#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 +/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_flat_dx, lpr_pair, ex3_2_intro/ +[ #a #I #G2 #L2 #V2 #T2 #X #H elim (lpr_inv_pair1 … H) -H + #K2 #W2 #HLK2 #HVW2 #H destruct + /3 width=5 by fqu_fquq, cpr_pair_sn, fqu_bind_dx, ex3_2_intro/ +| #G #L1 #K1 #T1 #U1 #k #HLK1 #HTU1 #K2 #HK12 + elim (drop_lpr_trans … HLK1 … HK12) -HK12 + /3 width=7 by fqu_drop, ex3_2_intro/ +] +qed-. + +lemma fquq_lpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → + ∀K2. ⦃G2, L2⦄ ⊢ ➡ K2 → + ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡ K1 & ⦃G1, L1⦄ ⊢ T1 ➡ T & ⦃G1, K1, T⦄ ⊐⸮ ⦃G2, K2, T2⦄. +#G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 elim (fquq_inv_gen … H) -H +[ #HT12 elim (fqu_lpr_trans … HT12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/ +| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ +] +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 32cf5942c..63773c485 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/partial.txt +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/partial.txt @@ -3,3 +3,4 @@ cpx.ma cpx_simple.ma cpx_drops.ma cpx_lsubr.ma lfpx.ma lfpx_length.ma lfpx_drops.ma lfpx_fqup.ma cpm.ma cpm_simple.ma cpm_drops.ma cpm_lsubr.ma cpm_cpx.ma cpr.ma cpr_drops.ma +lfpr.ma lfpr_length.ma lfpr_drops.ma lfpr_fqup.ma lfpr_lfpx.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 0221fc36f..5b07ac493 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 @@ -144,7 +144,7 @@ table { ] *) [ { "t-bound context-sensitive rt-transition" * } { -(* [ "lpr ( ⦃?,?⦄ ⊢ ➡ ? )" "lpr_drop" + "lpr_lpr" * ] *) + [ "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fqup" + "lfpr_lfpx" * ] [ "cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpr_drops" (* + "cpr_llpx_sn" + "cpr_cir" *) * ] [ "cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpm_simple" + "cpm_drops" + "cpm_lsubr" + "cpm_cpx" * ] }