X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flcosx.ma;h=8997c6ec9b567531a19bae6ec23b32d0e817aa23;hb=c60524dec7ace912c416a90d6b926bee8553250b;hp=03187e34c8d49604d649b6b09165ed1bb9e60bcf;hpb=f10cfe417b6b8ec1c7ac85c6ecf5fb1b3fdf37db;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma index 03187e34c..8997c6ec9 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma @@ -18,15 +18,15 @@ include "basic_2/computation/lsx.ma". (* SN EXTENDED STRONGLY CONORMALIZING LOCAL ENVIRONMENTS ********************) inductive lcosx (h) (g) (G): relation2 ynat lenv ≝ -| lcosx_sort: ∀d. lcosx h g G d (⋆) +| lcosx_sort: ∀l. lcosx h g G l (⋆) | lcosx_skip: ∀I,L,T. lcosx h g G 0 L → lcosx h g G 0 (L.ⓑ{I}T) -| lcosx_pair: ∀I,L,T,d. G ⊢ ⬊*[h, g, T, d] L → - lcosx h g G d L → lcosx h g G (⫯d) (L.ⓑ{I}T) +| lcosx_pair: ∀I,L,T,l. G ⊢ ⬊*[h, g, T, l] L → + lcosx h g G l L → lcosx h g G (⫯l) (L.ⓑ{I}T) . interpretation "sn extended strong conormalization (local environment)" - 'CoSN h g d G L = (lcosx h g G d L). + 'CoSN h g l G L = (lcosx h g G l L). (* Basic properties *********************************************************) @@ -34,43 +34,43 @@ lemma lcosx_O: ∀h,g,G,L. G ⊢ ~⬊*[h, g, 0] L. #h #g #G #L elim L /2 width=1 by lcosx_skip/ qed. -lemma lcosx_drop_trans_lt: ∀h,g,G,L,d. G ⊢ ~⬊*[h, g, d] L → - ∀I,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → i < d → - G ⊢ ~⬊*[h, g, ⫰(d-i)] K ∧ G ⊢ ⬊*[h, g, V, ⫰(d-i)] K. -#h #g #G #L #d #H elim H -L -d -[ #d #J #K #V #i #H elim (drop_inv_atom1 … H) -H #H destruct +lemma lcosx_drop_trans_lt: ∀h,g,G,L,l. G ⊢ ~⬊*[h, g, l] L → + ∀I,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → i < l → + G ⊢ ~⬊*[h, g, ⫰(l-i)] K ∧ G ⊢ ⬊*[h, g, V, ⫰(l-i)] K. +#h #g #G #L #l #H elim H -L -l +[ #l #J #K #V #i #H elim (drop_inv_atom1 … H) -H #H destruct | #I #L #T #_ #_ #J #K #V #i #_ #H elim (ylt_yle_false … H) -H // -| #I #L #T #d #HT #HL #IHL #J #K #V #i #H #Hid +| #I #L #T #l #HT #HL #IHL #J #K #V #i #H #Hil elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK destruct [ >ypred_succ /2 width=1 by conj/ - | lapply (ylt_pred … Hid ?) -Hid /2 width=1 by ylt_inj/ >ypred_succ #Hid + | lapply (ylt_pred … Hil ?) -Hil /2 width=1 by ylt_inj/ >ypred_succ #Hil elim (IHL … HLK ?) -IHL -HLK yminus_SO2 // - <(ypred_succ d) in ⊢ (%→%→?); >yminus_pred /2 width=1 by ylt_inj, conj/ + <(ypred_succ l) in ⊢ (%→%→?); >yminus_pred /2 width=1 by ylt_inj, conj/ ] ] qed-. (* Basic inversion lemmas ***************************************************) -fact lcosx_inv_succ_aux: ∀h,g,G,L,x. G ⊢ ~⬊*[h, g, x] L → ∀d. x = ⫯d → +fact lcosx_inv_succ_aux: ∀h,g,G,L,x. G ⊢ ~⬊*[h, g, x] L → ∀l. x = ⫯l → L = ⋆ ∨ - ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, d] K & - G ⊢ ⬊*[h, g, V, d] K. -#h #g #G #L #d * -L -d /2 width=1 by or_introl/ + ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, l] K & + G ⊢ ⬊*[h, g, V, l] K. +#h #g #G #L #l * -L -l /2 width=1 by or_introl/ [ #I #L #T #_ #x #H elim (ysucc_inv_O_sn … H) -| #I #L #T #d #HT #HL #x #H <(ysucc_inj … H) -x +| #I #L #T #l #HT #HL #x #H <(ysucc_inj … H) -x /3 width=6 by ex3_3_intro, or_intror/ ] qed-. -lemma lcosx_inv_succ: ∀h,g,G,L,d. G ⊢ ~⬊*[h, g, ⫯d] L → L = ⋆ ∨ - ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, d] K & - G ⊢ ⬊*[h, g, V, d] K. +lemma lcosx_inv_succ: ∀h,g,G,L,l. G ⊢ ~⬊*[h, g, ⫯l] L → L = ⋆ ∨ + ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, l] K & + G ⊢ ⬊*[h, g, V, l] K. /2 width=3 by lcosx_inv_succ_aux/ qed-. -lemma lcosx_inv_pair: ∀h,g,I,G,L,T,d. G ⊢ ~⬊*[h, g, ⫯d] L.ⓑ{I}T → - G ⊢ ~⬊*[h, g, d] L ∧ G ⊢ ⬊*[h, g, T, d] L. -#h #g #I #G #L #T #d #H elim (lcosx_inv_succ … H) -H +lemma lcosx_inv_pair: ∀h,g,I,G,L,T,l. G ⊢ ~⬊*[h, g, ⫯l] L.ⓑ{I}T → + G ⊢ ~⬊*[h, g, l] L ∧ G ⊢ ⬊*[h, g, T, l] L. +#h #g #I #G #L #T #l #H elim (lcosx_inv_succ … H) -H [ #H destruct | * #Z #Y #X #H destruct /2 width=1 by conj/ ]