X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flsubsx.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flsubsx.ma;h=0000000000000000000000000000000000000000;hb=a454837a256907d2f83d42ced7be847e10361ea9;hp=e2fb3664846dc1231bbd9dbf17861cef8812806c;hpb=b4283c079ed7069016b8d924bbc7e08872440829;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx.ma deleted file mode 100644 index e2fb36648..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx.ma +++ /dev/null @@ -1,160 +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/lsubeqx_5.ma". -include "basic_2/rt_computation/rdsx.ma". - -(* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNBOUND RT-TRANSITION **********) - -(* Note: this should be an instance of a more general sex *) -(* Basic_2A1: uses: lcosx *) -inductive lsubsx (h) (G): rtmap → relation lenv ≝ -| lsubsx_atom: ∀f. lsubsx h G f (⋆) (⋆) -| lsubsx_push: ∀f,I,K1,K2. lsubsx h G f K1 K2 → - lsubsx h G (⫯f) (K1.ⓘ{I}) (K2.ⓘ{I}) -| lsubsx_unit: ∀f,I,K1,K2. lsubsx h G f K1 K2 → - lsubsx h G (↑f) (K1.ⓤ{I}) (K2.ⓧ) -| lsubsx_pair: ∀f,I,K1,K2,V. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ → - lsubsx h G f K1 K2 → lsubsx h G (↑f) (K1.ⓑ{I}V) (K2.ⓧ) -. - -interpretation - "local environment refinement (clear)" - 'LSubEqX h f G L1 L2 = (lsubsx h G f L1 L2). - -(* Basic inversion lemmas ***************************************************) - -fact lsubsx_inv_atom_sn_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⊆ⓧ[h,g] L2 → - L1 = ⋆ → L2 = ⋆. -#h #g #G #L1 #L2 * -g -L1 -L2 // -[ #f #I #K1 #K2 #_ #H destruct -| #f #I #K1 #K2 #_ #H destruct -| #f #I #K1 #K2 #V #_ #_ #H destruct -] -qed-. - -lemma lsubsx_inv_atom_sn: ∀h,g,G,L2. G ⊢ ⋆ ⊆ⓧ[h,g] L2 → L2 = ⋆. -/2 width=7 by lsubsx_inv_atom_sn_aux/ qed-. - -fact lsubsx_inv_push_sn_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⊆ⓧ[h,g] L2 → - ∀f,I,K1. g = ⫯f → L1 = K1.ⓘ{I} → - ∃∃K2. G ⊢ K1 ⊆ⓧ[h,f] K2 & L2 = K2.ⓘ{I}. -#h #g #G #L1 #L2 * -g -L1 -L2 -[ #f #g #J #L1 #_ #H destruct -| #f #I #K1 #K2 #HK12 #g #J #L1 #H1 #H2 destruct - <(injective_push … H1) -g /2 width=3 by ex2_intro/ -| #f #I #K1 #K2 #_ #g #J #L1 #H - elim (discr_next_push … H) -| #f #I #K1 #K2 #V #_ #_ #g #J #L1 #H - elim (discr_next_push … H) -] -qed-. - -lemma lsubsx_inv_push_sn: ∀h,f,I,G,K1,L2. G ⊢ K1.ⓘ{I} ⊆ⓧ[h,⫯f] L2 → - ∃∃K2. G ⊢ K1 ⊆ⓧ[h,f] K2 & L2 = K2.ⓘ{I}. -/2 width=5 by lsubsx_inv_push_sn_aux/ qed-. - -fact lsubsx_inv_unit_sn_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⊆ⓧ[h,g] L2 → - ∀f,I,K1. g = ↑f → L1 = K1.ⓤ{I} → - ∃∃K2. G ⊢ K1 ⊆ⓧ[h,f] K2 & L2 = K2.ⓧ. -#h #g #G #L1 #L2 * -g -L1 -L2 -[ #f #g #J #L1 #_ #H destruct -| #f #I #K1 #K2 #_ #g #J #L1 #H - elim (discr_push_next … H) -| #f #I #K1 #K2 #HK12 #g #J #L1 #H1 #H2 destruct - <(injective_next … H1) -g /2 width=3 by ex2_intro/ -| #f #I #K1 #K2 #V #_ #_ #g #J #L1 #_ #H destruct -] -qed-. - -lemma lsubsx_inv_unit_sn: ∀h,f,I,G,K1,L2. G ⊢ K1.ⓤ{I} ⊆ⓧ[h,↑f] L2 → - ∃∃K2. G ⊢ K1 ⊆ⓧ[h,f] K2 & L2 = K2.ⓧ. -/2 width=6 by lsubsx_inv_unit_sn_aux/ qed-. - -fact lsubsx_inv_pair_sn_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⊆ⓧ[h,g] L2 → - ∀f,I,K1,V. g = ↑f → L1 = K1.ⓑ{I}V → - ∃∃K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ & - G ⊢ K1 ⊆ⓧ[h,f] K2 & L2 = K2.ⓧ. -#h #g #G #L1 #L2 * -g -L1 -L2 -[ #f #g #J #L1 #W #_ #H destruct -| #f #I #K1 #K2 #_ #g #J #L1 #W #H - elim (discr_push_next … H) -| #f #I #K1 #K2 #_ #g #J #L1 #W #_ #H destruct -| #f #I #K1 #K2 #V #HV #HK12 #g #J #L1 #W #H1 #H2 destruct - <(injective_next … H1) -g /2 width=4 by ex3_intro/ -] -qed-. - -(* Basic_2A1: uses: lcosx_inv_pair *) -lemma lsubsx_inv_pair_sn: ∀h,f,I,G,K1,L2,V. G ⊢ K1.ⓑ{I}V ⊆ⓧ[h,↑f] L2 → - ∃∃K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ & - G ⊢ K1 ⊆ⓧ[h,f] K2 & L2 = K2.ⓧ. -/2 width=6 by lsubsx_inv_pair_sn_aux/ qed-. - -(* Advanced inversion lemmas ************************************************) - -lemma lsubsx_inv_pair_sn_gen: ∀h,g,I,G,K1,L2,V. G ⊢ K1.ⓑ{I}V ⊆ⓧ[h,g] L2 → - ∨∨ ∃∃f,K2. G ⊢ K1 ⊆ⓧ[h,f] K2 & g = ⫯f & L2 = K2.ⓑ{I}V - | ∃∃f,K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ & - G ⊢ K1 ⊆ⓧ[h,f] K2 & g = ↑f & L2 = K2.ⓧ. -#h #g #I #G #K1 #L2 #V #H -elim (pn_split g) * #f #Hf destruct -[ elim (lsubsx_inv_push_sn … H) -H /3 width=5 by ex3_2_intro, or_introl/ -| elim (lsubsx_inv_pair_sn … H) -H /3 width=6 by ex4_2_intro, or_intror/ -] -qed-. - -(* Advanced forward lemmas **************************************************) - -lemma lsubsx_fwd_bind_sn: ∀h,g,I1,G,K1,L2. G ⊢ K1.ⓘ{I1} ⊆ⓧ[h,g] L2 → - ∃∃I2,K2. G ⊢ K1 ⊆ⓧ[h,⫱g] K2 & L2 = K2.ⓘ{I2}. -#h #g #I1 #G #K1 #L2 -elim (pn_split g) * #f #Hf destruct -[ #H elim (lsubsx_inv_push_sn … H) -H -| cases I1 -I1 #I1 - [ #H elim (lsubsx_inv_unit_sn … H) -H - | #V #H elim (lsubsx_inv_pair_sn … H) -H - ] -] -/2 width=4 by ex2_2_intro/ -qed-. - -(* Basic properties *********************************************************) - -lemma lsubsx_eq_repl_back: ∀h,G,L1,L2. eq_repl_back … (λf. G ⊢ L1 ⊆ⓧ[h,f] L2). -#h #G #L1 #L2 #f1 #H elim H -L1 -L2 -f1 // -[ #f #I #L1 #L2 #_ #IH #x #H - elim (eq_inv_px … H) -H /3 width=3 by lsubsx_push/ -| #f #I #L1 #L2 #_ #IH #x #H - elim (eq_inv_nx … H) -H /3 width=3 by lsubsx_unit/ -| #f #I #L1 #L2 #V #HV #_ #IH #x #H - elim (eq_inv_nx … H) -H /3 width=3 by lsubsx_pair/ -] -qed-. - -lemma lsubsx_eq_repl_fwd: ∀h,G,L1,L2. eq_repl_fwd … (λf. G ⊢ L1 ⊆ⓧ[h,f] L2). -#h #G #L1 #L2 @eq_repl_sym /2 width=3 by lsubsx_eq_repl_back/ -qed-. - -(* Advanced properties ******************************************************) - -(* Basic_2A1: uses: lcosx_O *) -lemma lsubsx_refl: ∀h,f,G. 𝐈⦃f⦄ → reflexive … (lsubsx h G f). -#h #f #G #Hf #L elim L -L -/3 width=3 by lsubsx_eq_repl_back, lsubsx_push, eq_push_inv_isid/ -qed. - -(* Basic_2A1: removed theorems 2: - lcosx_drop_trans_lt lcosx_inv_succ -*)