X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffsle_drops.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffsle_drops.ma;h=0000000000000000000000000000000000000000;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hp=441c6b468df6ca86817de617fcbf9ad63ad468c7;hpb=222044da28742b24584549ba86b1805a87def070;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.ma deleted file mode 100644 index 441c6b468..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.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/static/frees_drops.ma". -include "basic_2/static/fsle_length.ma". - -(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************) - -(* Advanced properties ******************************************************) - -lemma fsle_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 → ∀L1,L2. |L2| ≤ |L1| → - ∀T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ⦃L1.ⓧ, U1⦄ ⊆ ⦃L2, T2⦄. -#T1 #U1 #HTU1 #L1 #L2 #H1L #T2 -* #n #m #f #g #Hf #Hg #H2L #Hfg -lapply (lveq_length_fwd_dx … H2L ?) // -H1L #H destruct -lapply (frees_lifts_SO (Ⓣ) (L1.ⓧ) … HTU1 … Hf) -[ /3 width=4 by drops_refl, drops_drop/ ] -T1 #Hf -@(ex4_4_intro … Hf Hg) /2 width=4 by lveq_void_sn/ (**) (* explict constructor *) -qed-. - -lemma fsle_lifts_SO_sn: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ → - ∀W1. ⬆*[1] V1 ≘ W1 → ∀I1,I2. ⦃K1.ⓘ{I1}, W1⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄. -#K1 #K2 #HK #V1 #V2 -* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12 -#W1 #HVW1 #I1 #I2 -elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct -/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, sle_weak, ex4_4_intro/ -qed. - -lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ⦃K1, T1⦄ ⊆ ⦃K2, T2⦄ → - ∀U1,U2. ⬆*[1] T1 ≘ U1 → ⬆*[1] T2 ≘ U2 → - ∀I1,I2. ⦃K1.ⓘ{I1}, U1⦄ ⊆ ⦃K2.ⓘ{I2}, U2⦄. -#K1 #K2 #HK #T1 #T2 -* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12 -#U1 #U2 #HTU1 #HTU2 #I1 #I2 -elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct -/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, sle_push, ex4_4_intro/ -qed. - -(* Advanced inversion lemmas ************************************************) - -lemma fsle_inv_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 → - ∀I1,I2,L1,L2,V1,V2,U2. ⦃L1.ⓑ{I1}V1,U1⦄ ⊆ ⦃L2.ⓑ{I2}V2, U2⦄ → - ∀p. ⦃L1, T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.U2⦄. -#T1 #U1 #HTU1 #I1 #I2 #L1 #L2 #V1 #V2 #U2 -* #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p -elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct -elim (frees_total L2 V2) #g1 #Hg1 -elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_ -lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1) -[1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2 -lapply (sor_inv_sle_dx … Hg) #H0g -/5 width=10 by frees_bind, sle_tl, sle_trans, ex4_4_intro/ -qed-.