X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flfpr.ma;h=92ff748bd22b4f09308dd05c10611b542e5682c2;hb=4738096e93f997fb36d35dd723b87682a2f6de90;hp=cc8550d219d380124adb4d6f135b371d52408fff;hpb=58ea181757dce19b875b2f5a224fe193b2263004;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma index cc8550d21..92ff748bd 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr.ma @@ -14,7 +14,7 @@ include "basic_2/notation/relations/predsn_5.ma". include "basic_2/static/lfxs.ma". -include "basic_2/rt_transition/cpm.ma". +include "basic_2/rt_transition/cpr_ext.ma". (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************) @@ -34,23 +34,23 @@ 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,V1,V2. ⦃G, L1⦄ ⊢ ➡[h, V1] L2 → +lemma lfpr_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_zero/ qed. +/2 width=1 by lfxs_pair/ 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. +lemma lfpr_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 lfpr_gref: ∀h,I,G,L1,L2,V1,V2,l. - ⦃G, L1⦄ ⊢ ➡[h, §l] L2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[h, §l] L2.ⓑ{I}V2. +lemma lfpr_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 lfpr_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 lfpr_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 ***************************************************) @@ -63,47 +63,47 @@ 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_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 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. + ∨∨ 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 lfpr_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 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. + ∧∧ ⦃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. + ∧∧ ⦃G, L1⦄ ⊢ ➡[h, V] L2 & ⦃G, L1⦄ ⊢ ➡[h, T] L2. /2 width=2 by lfxs_inv_flat/ qed-. (* Advanced inversion lemmas ************************************************) -lemma lfpr_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 lfpr_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 lfpr_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 lfpr_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 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 & @@ -115,21 +115,21 @@ lemma lfpr_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 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_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 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-. +lemma lfpr_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 lfpr_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 lfpr_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 lfpr_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 lfpr_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 *****************************************************)