X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Funfold%2Flstas_lift.ma;h=770d967255f1ef2cbcf1842bce5f12caae250412;hb=c60524dec7ace912c416a90d6b926bee8553250b;hp=aea1d9f85709a35c8dfa4a45e91cb27fb9ac10a8;hpb=f10cfe417b6b8ec1c7ac85c6ecf5fb1b3fdf37db;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_lift.ma index aea1d9f85..770d96725 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_lift.ma @@ -20,48 +20,48 @@ include "basic_2/unfold/lstas.ma". (* Properties on relocation *************************************************) (* Basic_1: was just: sty0_lift *) -lemma lstas_lift: ∀h,G,l. l_liftable (lstas h G l). -#h #G #l #L1 #T1 #U1 #H elim H -G -L1 -T1 -U1 -l -[ #G #L1 #l #k #L2 #s #d #e #HL21 #X1 #H1 #X2 #H2 +lemma lstas_lift: ∀h,G,d. d_liftable (lstas h G d). +#h #G #d #L1 #T1 #U1 #H elim H -G -L1 -T1 -U1 -d +[ #G #L1 #d #k #L2 #s #l #m #HL21 #X1 #H1 #X2 #H2 >(lift_inv_sort1 … H1) -X1 >(lift_inv_sort1 … H2) -X2 // -| #G #L1 #K1 #V1 #W1 #W #i #l #HLK1 #_ #HW1 #IHVW1 #L2 #s #d #e #HL21 #X #H #U2 #HWU2 - elim (lift_inv_lref1 … H) * #Hid #H destruct +| #G #L1 #K1 #V1 #W1 #W #i #d #HLK1 #_ #HW1 #IHVW1 #L2 #s #l #m #HL21 #X #H #U2 #HWU2 + elim (lift_inv_lref1 … H) * #Hil #H destruct [ elim (lift_trans_ge … HW1 … HWU2) -W // #W2 #HW12 #HWU2 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 lstas_ldef/ | lapply (lift_trans_be … HW1 … HWU2 ? ?) -W /2 width=1 by le_S/ #HW1U2 lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=9 by lstas_ldef, drop_inv_gen/ ] -| #G #L1 #K1 #V1 #W1 #i #HLK1 #_ #IHVW1 #L2 #s #d #e #HL21 #X #H #U2 #HWU2 +| #G #L1 #K1 #V1 #W1 #i #HLK1 #_ #IHVW1 #L2 #s #l #m #HL21 #X #H #U2 #HWU2 >(lift_mono … HWU2 … H) -U2 - elim (lift_inv_lref1 … H) * #Hid #H destruct - [ elim (lift_total W1 (d-i-1) e) #W2 #HW12 + elim (lift_inv_lref1 … H) * #Hil #H destruct + [ elim (lift_total W1 (l-i-1) m) #W2 #HW12 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=10 by lstas_zero/ | lapply (drop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=10 by lstas_zero, drop_inv_gen/ ] -| #G #L1 #K1 #W1 #V1 #W #i #l #HLK1 #_ #HW1 #IHWV1 #L2 #s #d #e #HL21 #X #H #U2 #HWU2 - elim (lift_inv_lref1 … H) * #Hid #H destruct +| #G #L1 #K1 #W1 #V1 #W #i #d #HLK1 #_ #HW1 #IHWV1 #L2 #s #l #m #HL21 #X #H #U2 #HWU2 + elim (lift_inv_lref1 … H) * #Hil #H destruct [ elim (lift_trans_ge … HW1 … HWU2) -W // (lift_inv_sort2 … H) -X /2 width=3 by lstas_sort, lift_sort, ex2_intro/ -| #G #L2 #K2 #V2 #W2 #W #i #l #HLK2 #HVW2 #HW2 #IHVW2 #L1 #s #d #e #HL21 #X #H - elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HVW2 | -IHVW2 ] +| #G #L2 #K2 #V2 #W2 #W #i #d #HLK2 #HVW2 #HW2 #IHVW2 #L1 #s #l #m #HL21 #X #H + elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HVW2 | -IHVW2 ] [ elim (drop_conf_lt … HL21 … HLK2) -L2 // #K1 #V1 #HLK1 #HK21 #HV12 elim (IHVW2 … HK21 … HV12) -K2 -V2 #W1 #HW12 #HVW1 elim (lift_trans_le … HW12 … HW2) -W2 // >minus_plus minus_minus_m_m /3 width=8 by lstas_ldef, le_S, ex2_intro/ ] -| #G #L2 #K2 #W2 #V2 #i #HLK2 #HWV2 #IHWV2 #L1 #s #d #e #HL21 #X #H - elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HWV2 | -IHWV2 ] +| #G #L2 #K2 #W2 #V2 #i #HLK2 #HWV2 #IHWV2 #L1 #s #l #m #HL21 #X #H + elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HWV2 | -IHWV2 ] [ elim (drop_conf_lt … HL21 … HLK2) -L2 // #K1 #W1 #HLK1 #HK21 #HW12 elim (IHWV2 … HK21 … HW12) -K2 /3 width=5 by lstas_zero, lift_lref_lt, ex2_intro/ | lapply (drop_conf_ge … HL21 … HLK2 ?) -L2 /3 width=5 by lstas_zero, lift_lref_ge_minus, ex2_intro/ ] -| #G #L2 #K2 #W2 #V2 #W #i #l #HLK2 #HWV2 #HW2 #IHWV2 #L1 #s #d #e #HL21 #X #H - elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HWV2 | -IHWV2 ] +| #G #L2 #K2 #W2 #V2 #W #i #d #HLK2 #HWV2 #HW2 #IHWV2 #L1 #s #l #m #HL21 #X #H + elim (lift_inv_lref2 … H) * #Hil #H destruct [ -HWV2 | -IHWV2 ] [ elim (drop_conf_lt … HL21 … HLK2) -L2 // #K1 #W1 #HLK1 #HK21 #HW12 elim (IHWV2 … HK21 … HW12) -K2 #V1 #HV12 #HWV1 elim (lift_trans_le … HV12 … HW2) -W2 // >minus_plus minus_minus_m_m /3 width=8 by lstas_succ, le_S, ex2_intro/ ] -| #a #I #G #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #s #d #e #HL21 #X #H +| #a #I #G #L2 #V2 #T2 #U2 #d #_ #IHTU2 #L1 #s #l #m #HL21 #X #H elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct elim (IHTU2 (L1.ⓑ{I}V1) … HT12) -IHTU2 -HT12 /3 width=5 by lstas_bind, drop_skip, lift_bind, ex2_intro/ -| #G #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #s #d #e #HL21 #X #H +| #G #L2 #V2 #T2 #U2 #d #_ #IHTU2 #L1 #s #l #m #HL21 #X #H elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=5 by lstas_appl, lift_flat, ex2_intro/ -| #G #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #s #d #e #HL21 #X #H +| #G #L2 #W2 #T2 #U2 #d #_ #IHTU2 #L1 #s #l #m #HL21 #X #H elim (lift_inv_flat2 … H) -H #W1 #T1 #_ #HT12 #H destruct elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=3 by lstas_cast, ex2_intro/ ] @@ -115,69 +115,69 @@ qed-. (* Advanced inversion lemmas ************************************************) -lemma lstas_split_aux: ∀h,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •*[h, l] T2 → ∀l1,l2. l = l1 + l2 → - ∃∃T. ⦃G, L⦄ ⊢ T1 •*[h, l1] T & ⦃G, L⦄ ⊢ T •*[h, l2] T2. -#h #G #L #T1 #T2 #l #H elim H -G -L -T1 -T2 -l -[ #G #L #l #k #l1 #l2 #H destruct +lemma lstas_split_aux: ∀h,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*[h, d] T2 → ∀d1,d2. d = d1 + d2 → + ∃∃T. ⦃G, L⦄ ⊢ T1 •*[h, d1] T & ⦃G, L⦄ ⊢ T •*[h, d2] T2. +#h #G #L #T1 #T2 #d #H elim H -G -L -T1 -T2 -d +[ #G #L #d #k #d1 #d2 #H destruct >commutative_plus >iter_plus /2 width=3 by lstas_sort, ex2_intro/ -| #G #L #K #V1 #V2 #U2 #i #l #HLK #_ #VU2 #IHV12 #l1 #l2 #H destruct - elim (IHV12 l1 l2) -IHV12 // #V +| #G #L #K #V1 #V2 #U2 #i #d #HLK #_ #VU2 #IHV12 #d1 #d2 #H destruct + elim (IHV12 d1 d2) -IHV12 // #V elim (lift_total V 0 (i+1)) lapply (drop_fwd_drop2 … HLK) /3 width=12 by lstas_lift, lstas_ldef, ex2_intro/ -| #G #L #K #W1 #W2 #i #HLK #HW12 #_ #l1 #l2 #H +| #G #L #K #W1 #W2 #i #HLK #HW12 #_ #d1 #d2 #H elim (zero_eq_plus … H) -H #H1 #H2 destruct /3 width=5 by lstas_zero, ex2_intro/ -| #G #L #K #W1 #W2 #U2 #i #l #HLK #HW12 #HWU2 #IHW12 #l1 @(nat_ind_plus … l1) -l1 - [ #l2 normalize #H destruct - elim (IHW12 0 l) -IHW12 // +| #G #L #K #W1 #W2 #U2 #i #d #HLK #HW12 #HWU2 #IHW12 #d1 @(nat_ind_plus … d1) -d1 + [ #d2 normalize #H destruct + elim (IHW12 0 d) -IHW12 // lapply (drop_fwd_drop2 … HLK) /3 width=8 by lstas_succ, lstas_zero, ex2_intro/ - | #l1 #_ #l2