X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flfpx.ma;h=4067962d8fe89682653be2bd9b381f5e51b768b2;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=172f88ed52e57a5cd9b8b6321365018eeff34d98;hpb=58ea181757dce19b875b2f5a224fe193b2263004;p=helm.git 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 172f88ed5..4067962d8 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx.ma @@ -14,15 +14,15 @@ include "basic_2/notation/relations/predtysn_5.ma". include "basic_2/static/lfxs.ma". -include "basic_2/rt_transition/cpx.ma". +include "basic_2/rt_transition/cpx_ext.ma". -(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****) +(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********) -definition lfpx: sh → genv → relation3 term lenv lenv ≝ - λh,G. lfxs (cpx h G). +definition lfpx (h) (G): relation3 term lenv lenv ≝ + lfxs (cpx h G). interpretation - "uncounted parallel rt-transition on referred entries (local environment)" + "unbound parallel rt-transition on referred entries (local environment)" 'PRedTySn h T G L1 L2 = (lfpx h G T L1 L2). (* Basic properties ***********************************************************) @@ -30,80 +30,71 @@ interpretation lemma lfpx_atom: ∀h,I,G. ⦃G, ⋆⦄ ⊢ ⬈[h, ⓪{I}] ⋆. /2 width=1 by lfxs_atom/ qed. -lemma lfpx_sort: ∀h,I,G,L1,L2,V1,V2,s. - ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, ⋆s] L2.ⓑ{I}V2. +lemma lfpx_sort: ∀h,I1,I2,G,L1,L2,s. + ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 → ⦃G, L1.ⓘ{I1}⦄ ⊢ ⬈[h, ⋆s] L2.ⓘ{I2}. /2 width=1 by lfxs_sort/ qed. -lemma lfpx_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 lfpx_pair: ∀h,I,G,L1,L2,V1,V2. + ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 → ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, #0] L2.ⓑ{I}V2. +/2 width=1 by lfxs_pair/ qed. -lemma lfpx_lref: ∀h,I,G,L1,L2,V1,V2,i. - ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, #⫯i] L2.ⓑ{I}V2. +lemma lfpx_lref: ∀h,I1,I2,G,L1,L2,i. + ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ⦃G, L1.ⓘ{I1}⦄ ⊢ ⬈[h, #↑i] L2.ⓘ{I2}. /2 width=1 by lfxs_lref/ qed. -lemma lfpx_gref: ∀h,I,G,L1,L2,V1,V2,l. - ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, §l] L2.ⓑ{I}V2. +lemma lfpx_gref: ∀h,I1,I2,G,L1,L2,l. + ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 → ⦃G, L1.ⓘ{I1}⦄ ⊢ ⬈[h, §l] L2.ⓘ{I2}. /2 width=1 by lfxs_gref/ qed. -lemma lfpx_pair_repl_dx: ∀h,I,G,L1,L2,T,V,V1. - ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V1 → - ∀V2. ⦃G, L1⦄ ⊢ V ⬈[h] V2 → - ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V2. -/2 width=2 by lfxs_pair_repl_dx/ qed-. +lemma lfpx_bind_repl_dx: ∀h,I,I1,G,L1,L2,T. + ⦃G, L1.ⓘ{I}⦄ ⊢ ⬈[h, T] L2.ⓘ{I1} → + ∀I2. ⦃G, L1⦄ ⊢ I ⬈[h] I2 → + ⦃G, L1.ⓘ{I}⦄ ⊢ ⬈[h, T] L2.ⓘ{I2}. +/2 width=2 by lfxs_bind_repl_dx/ qed-. (* Basic inversion lemmas ***************************************************) -(* Basic_2A1: uses: lpx_inv_atom1 *) lemma lfpx_inv_atom_sn: ∀h,G,Y2,T. ⦃G, ⋆⦄ ⊢ ⬈[h, T] Y2 → Y2 = ⋆. /2 width=3 by lfxs_inv_atom_sn/ qed-. -(* Basic_2A1: uses: lpx_inv_atom2 *) lemma lfpx_inv_atom_dx: ∀h,G,Y1,T. ⦃G, Y1⦄ ⊢ ⬈[h, T] ⋆ → Y1 = ⋆. /2 width=3 by lfxs_inv_atom_dx/ qed-. lemma lfpx_inv_sort: ∀h,G,Y1,Y2,s. ⦃G, Y1⦄ ⊢ ⬈[h, ⋆s] Y2 → - (Y1 = ⋆ ∧ Y2 = ⋆) ∨ - ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & - Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. + ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ + | ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & + Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. /2 width=1 by lfxs_inv_sort/ qed-. -lemma lfpx_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 lfpx_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. +lemma lfpx_inv_lref: ∀h,G,Y1,Y2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #↑i] Y2 → + ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ + | ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & + Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. /2 width=1 by lfxs_inv_lref/ qed-. lemma lfpx_inv_gref: ∀h,G,Y1,Y2,l. ⦃G, Y1⦄ ⊢ ⬈[h, §l] Y2 → - (Y1 = ⋆ ∧ Y2 = ⋆) ∨ - ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & - Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2. + ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ + | ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & + Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. /2 width=1 by lfxs_inv_gref/ qed-. lemma lfpx_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. + ∧∧ ⦃G, L1⦄ ⊢ ⬈[h, V] L2 & ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V. /2 width=2 by lfxs_inv_bind/ qed-. lemma lfpx_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. + ∧∧ ⦃G, L1⦄ ⊢ ⬈[h, V] L2 & ⦃G, L1⦄ ⊢ ⬈[h, T] L2. /2 width=2 by lfxs_inv_flat/ qed-. (* Advanced inversion lemmas ************************************************) -lemma lfpx_inv_sort_pair_sn: ∀h,I,G,Y2,L1,V1,s. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, ⋆s] Y2 → - ∃∃L2,V2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & Y2 = L2.ⓑ{I}V2. -/2 width=2 by lfxs_inv_sort_pair_sn/ qed-. +lemma lfpx_inv_sort_bind_sn: ∀h,I1,G,Y2,L1,s. ⦃G, L1.ⓘ{I1}⦄ ⊢ ⬈[h, ⋆s] Y2 → + ∃∃I2,L2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & Y2 = L2.ⓘ{I2}. +/2 width=2 by lfxs_inv_sort_bind_sn/ qed-. -lemma lfpx_inv_sort_pair_dx: ∀h,I,G,Y1,L2,V2,s. ⦃G, Y1⦄ ⊢ ⬈[h, ⋆s] L2.ⓑ{I}V2 → - ∃∃L1,V1. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & Y1 = L1.ⓑ{I}V1. -/2 width=2 by lfxs_inv_sort_pair_dx/ qed-. +lemma lfpx_inv_sort_bind_dx: ∀h,I2,G,Y1,L2,s. ⦃G, Y1⦄ ⊢ ⬈[h, ⋆s] L2.ⓘ{I2} → + ∃∃I1,L1. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 & Y1 = L1.ⓘ{I1}. +/2 width=2 by lfxs_inv_sort_bind_dx/ qed-. lemma lfpx_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 & @@ -115,21 +106,21 @@ lemma lfpx_inv_zero_pair_dx: ∀h,I,G,Y1,L2,V2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] L2. Y1 = L1.ⓑ{I}V1. /2 width=1 by lfxs_inv_zero_pair_dx/ qed-. -lemma lfpx_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 lfpx_inv_lref_bind_sn: ∀h,I1,G,Y2,L1,i. ⦃G, L1.ⓘ{I1}⦄ ⊢ ⬈[h, #↑i] Y2 → + ∃∃I2,L2. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & Y2 = L2.ⓘ{I2}. +/2 width=2 by lfxs_inv_lref_bind_sn/ qed-. -lemma lfpx_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-. +lemma lfpx_inv_lref_bind_dx: ∀h,I2,G,Y1,L2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #↑i] L2.ⓘ{I2} → + ∃∃I1,L1. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 & Y1 = L1.ⓘ{I1}. +/2 width=2 by lfxs_inv_lref_bind_dx/ qed-. -lemma lfpx_inv_gref_pair_sn: ∀h,I,G,Y2,L1,V1,l. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, §l] Y2 → - ∃∃L2,V2. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & Y2 = L2.ⓑ{I}V2. -/2 width=2 by lfxs_inv_gref_pair_sn/ qed-. +lemma lfpx_inv_gref_bind_sn: ∀h,I1,G,Y2,L1,l. ⦃G, L1.ⓘ{I1}⦄ ⊢ ⬈[h, §l] Y2 → + ∃∃I2,L2. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & Y2 = L2.ⓘ{I2}. +/2 width=2 by lfxs_inv_gref_bind_sn/ qed-. -lemma lfpx_inv_gref_pair_dx: ∀h,I,G,Y1,L2,V2,l. ⦃G, Y1⦄ ⊢ ⬈[h, §l] L2.ⓑ{I}V2 → - ∃∃L1,V1. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & Y1 = L1.ⓑ{I}V1. -/2 width=2 by lfxs_inv_gref_pair_dx/ qed-. +lemma lfpx_inv_gref_bind_dx: ∀h,I2,G,Y1,L2,l. ⦃G, Y1⦄ ⊢ ⬈[h, §l] L2.ⓘ{I2} → + ∃∃I1,L1. ⦃G, L1⦄ ⊢ ⬈[h, §l] L2 & Y1 = L1.ⓘ{I1}. +/2 width=2 by lfxs_inv_gref_bind_dx/ qed-. (* Basic forward lemmas *****************************************************) @@ -144,7 +135,3 @@ lemma lfpx_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. lemma lfpx_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-. - -(* Basic_2A1: removed theorems 3: - lpx_inv_pair1 lpx_inv_pair2 lpx_inv_pair -*)