X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Fda_lift.ma;h=3f3926c1752d28551344098bf38eb8da179149ec;hb=c60524dec7ace912c416a90d6b926bee8553250b;hp=0e7428fa3fe19ed6571c7c3e757830a71eb95e79;hpb=f10cfe417b6b8ec1c7ac85c6ecf5fb1b3fdf37db;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/da_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/static/da_lift.ma index 0e7428fa3..3f3926c17 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/da_lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/da_lift.ma @@ -19,32 +19,32 @@ include "basic_2/static/da.ma". (* Properties on relocation *************************************************) -lemma da_lift: ∀h,g,G,L1,T1,l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l → - ∀L2,s,d,e. ⬇[s, d, e] L2 ≡ L1 → ∀T2. ⬆[d, e] T1 ≡ T2 → - ⦃G, L2⦄ ⊢ T2 ▪[h, g] l. -#h #g #G #L1 #T1 #l #H elim H -G -L1 -T1 -l -[ #G #L1 #k #l #Hkl #L2 #s #d #e #_ #X #H +lemma da_lift: ∀h,g,G,L1,T1,d. ⦃G, L1⦄ ⊢ T1 ▪[h, g] d → + ∀L2,s,l,m. ⬇[s, l, m] L2 ≡ L1 → ∀T2. ⬆[l, m] T1 ≡ T2 → + ⦃G, L2⦄ ⊢ T2 ▪[h, g] d. +#h #g #G #L1 #T1 #d #H elim H -G -L1 -T1 -d +[ #G #L1 #k #d #Hkd #L2 #s #l #m #_ #X #H >(lift_inv_sort1 … H) -X /2 width=1 by da_sort/ -| #G #L1 #K1 #V1 #i #l #HLK1 #_ #IHV1 #L2 #s #d #e #HL21 #X #H - elim (lift_inv_lref1 … H) * #Hid #H destruct +| #G #L1 #K1 #V1 #i #d #HLK1 #_ #IHV1 #L2 #s #l #m #HL21 #X #H + elim (lift_inv_lref1 … 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 da_ldef/ | lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=8 by da_ldef, drop_inv_gen/ ] -| #G #L1 #K1 #W1 #i #l #HLK1 #_ #IHW1 #L2 #s #d #e #HL21 #X #H - elim (lift_inv_lref1 … H) * #Hid #H destruct +| #G #L1 #K1 #W1 #i #d #HLK1 #_ #IHW1 #L2 #s #l #m #HL21 #X #H + elim (lift_inv_lref1 … 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 #W2 #HK21 #HW12 #H destruct + elim (drop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hil #K2 #W2 #HK21 #HW12 #H destruct /3 width=8 by da_ldec/ | lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=8 by da_ldec, drop_inv_gen/ ] -| #a #I #G #L1 #V1 #T1 #l #_ #IHT1 #L2 #s #d #e #HL21 #X #H +| #a #I #G #L1 #V1 #T1 #d #_ #IHT1 #L2 #s #l #m #HL21 #X #H elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HU12 #H destruct /4 width=5 by da_bind, drop_skip/ -| #I #G #L1 #V1 #T1 #l #_ #IHT1 #L2 #s #d #e #HL21 #X #H +| #I #G #L1 #V1 #T1 #d #_ #IHT1 #L2 #s #l #m #HL21 #X #H elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HU12 #H destruct /3 width=5 by da_flat/ ] @@ -52,26 +52,26 @@ qed. (* Inversion lemmas on relocation *******************************************) -lemma da_inv_lift: ∀h,g,G,L2,T2,l. ⦃G, L2⦄ ⊢ T2 ▪[h, g] l → - ∀L1,s,d,e. ⬇[s, d, e] L2 ≡ L1 → ∀T1. ⬆[d, e] T1 ≡ T2 → - ⦃G, L1⦄ ⊢ T1 ▪[h, g] l. -#h #g #G #L2 #T2 #l #H elim H -G -L2 -T2 -l -[ #G #L2 #k #l #Hkl #L1 #s #d #e #_ #X #H +lemma da_inv_lift: ∀h,g,G,L2,T2,d. ⦃G, L2⦄ ⊢ T2 ▪[h, g] d → + ∀L1,s,l,m. ⬇[s, l, m] L2 ≡ L1 → ∀T1. ⬆[l, m] T1 ≡ T2 → + ⦃G, L1⦄ ⊢ T1 ▪[h, g] d. +#h #g #G #L2 #T2 #d #H elim H -G -L2 -T2 -d +[ #G #L2 #k #d #Hkd #L1 #s #l #m #_ #X #H >(lift_inv_sort2 … H) -X /2 width=1 by da_sort/ -| #G #L2 #K2 #V2 #i #l #HLK2 #HV2 #IHV2 #L1 #s #d #e #HL21 #X #H - elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HV2 | -IHV2 ] +| #G #L2 #K2 #V2 #i #d #HLK2 #HV2 #IHV2 #L1 #s #l #m #HL21 #X #H + elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HV2 | -IHV2 ] [ elim (drop_conf_lt … HL21 … HLK2) -L2 /3 width=8 by da_ldef/ | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2 /2 width=4 by da_ldef/ ] -| #G #L2 #K2 #W2 #i #l #HLK2 #HW2 #IHW2 #L1 #s #d #e #HL21 #X #H - elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HW2 | -IHW2 ] +| #G #L2 #K2 #W2 #i #d #HLK2 #HW2 #IHW2 #L1 #s #l #m #HL21 #X #H + elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HW2 | -IHW2 ] [ elim (drop_conf_lt … HL21 … HLK2) -L2 /3 width=8 by da_ldec/ | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2 /2 width=4 by da_ldec/ ] -| #a #I #G #L2 #V2 #T2 #l #_ #IHT2 #L1 #s #d #e #HL21 #X #H +| #a #I #G #L2 #V2 #T2 #d #_ #IHT2 #L1 #s #l #m #HL21 #X #H elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /4 width=5 by da_bind, drop_skip/ -| #I #G #L2 #V2 #T2 #l #_ #IHT2 #L1 #s #d #e #HL21 #X #H +| #I #G #L2 #V2 #T2 #d #_ #IHT2 #L1 #s #l #m #HL21 #X #H elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /3 width=5 by da_flat/ ]