X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Faaa_lift.ma;h=91723374f87e518f3ceffead086ff3066da1d4cb;hb=c60524dec7ace912c416a90d6b926bee8553250b;hp=736f45d98ae6086bb9ae463a32992f0117f17a03;hpb=f10cfe417b6b8ec1c7ac85c6ecf5fb1b3fdf37db;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma index 736f45d98..91723374f 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma @@ -19,54 +19,54 @@ include "basic_2/static/aaa.ma". (* Properties on basic relocation *******************************************) -lemma aaa_lift: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀L2,s,d,e. ⬇[s, d, e] L2 ≡ L1 → - ∀T2. ⬆[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ T2 ⁝ A. +lemma aaa_lift: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀L2,s,l,m. ⬇[s, l, m] L2 ≡ L1 → + ∀T2. ⬆[l, m] T1 ≡ T2 → ⦃G, L2⦄ ⊢ T2 ⁝ A. #G #L1 #T1 #A #H elim H -G -L1 -T1 -A -[ #G #L1 #k #L2 #s #d #e #_ #T2 #H +[ #G #L1 #k #L2 #s #l #m #_ #T2 #H >(lift_inv_sort1 … H) -H // -| #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #s #d #e #HL21 #T2 #H - elim (lift_inv_lref1 … H) -H * #Hid #H destruct +| #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #s #l #m #HL21 #T2 #H + elim (lift_inv_lref1 … H) -H * #Hil #H destruct [ elim (drop_trans_le … HL21 … HLK1) -L1 /2 width=2 by lt_to_le/ #X #HLK2 #H - elim (drop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hid #K2 #V2 #HK21 #HV12 #H destruct + elim (drop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hil #K2 #V2 #HK21 #HV12 #H destruct /3 width=9 by aaa_lref/ | lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=9 by aaa_lref, drop_inv_gen/ ] -| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #d #e #HL21 #X #H +| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #l #m #HL21 #X #H elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=5 by aaa_abbr, drop_skip/ -| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #d #e #HL21 #X #H +| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #l #m #HL21 #X #H elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=5 by aaa_abst, drop_skip/ -| #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #d #e #HL21 #X #H +| #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #s #l #m #HL21 #X #H elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=5 by aaa_appl/ -| #G #L1 #V1 #T1 #A #_ #_ #IH1 #IH2 #L2 #s #d #e #HL21 #X #H +| #G #L1 #V1 #T1 #A #_ #_ #IH1 #IH2 #L2 #s #l #m #HL21 #X #H elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=5 by aaa_cast/ ] qed. -lemma aaa_inv_lift: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀L1,s,d,e. ⬇[s, d, e] L2 ≡ L1 → - ∀T1. ⬆[d, e] T1 ≡ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A. +lemma aaa_inv_lift: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀L1,s,l,m. ⬇[s, l, m] L2 ≡ L1 → + ∀T1. ⬆[l, m] T1 ≡ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A. #G #L2 #T2 #A #H elim H -G -L2 -T2 -A -[ #G #L2 #k #L1 #s #d #e #_ #T1 #H +[ #G #L2 #k #L1 #s #l #m #_ #T1 #H >(lift_inv_sort2 … H) -H // -| #I #G #L2 #K2 #V2 #B #i #HLK2 #_ #IHB #L1 #s #d #e #HL21 #T1 #H - elim (lift_inv_lref2 … H) -H * #Hid #H destruct +| #I #G #L2 #K2 #V2 #B #i #HLK2 #_ #IHB #L1 #s #l #m #HL21 #T1 #H + elim (lift_inv_lref2 … H) -H * #Hil #H destruct [ elim (drop_conf_lt … HL21 … HLK2) -L2 /3 width=9 by aaa_lref/ | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2 /3 width=9 by aaa_lref/ ] -| #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #d #e #HL21 #X #H +| #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #l #m #HL21 #X #H elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /4 width=5 by aaa_abbr, drop_skip/ -| #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #d #e #HL21 #X #H +| #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #l #m #HL21 #X #H elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /4 width=5 by aaa_abst, drop_skip/ -| #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #d #e #HL21 #X #H +| #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #s #l #m #HL21 #X #H elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /3 width=5 by aaa_appl/ -| #G #L2 #V2 #T2 #A #_ #_ #IH1 #IH2 #L1 #s #d #e #HL21 #X #H +| #G #L2 #V2 #T2 #A #_ #_ #IH1 #IH2 #L1 #s #l #m #HL21 #X #H elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /3 width=5 by aaa_cast/ ]