X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffrees_drops.ma;h=67e3e9992b4a1add09474f7de86323a6002dd3b3;hb=775ab35f714568dfcd672f0dd53a00e1ba7382cd;hp=698427fee1c128d01cda3a9cef95264b05744cc2;hpb=f677b4ef7fa20f1ab36c5ee59598865d5c1b719b;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma index 698427fee..67e3e9992 100644 --- a/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma +++ b/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma @@ -12,7 +12,7 @@ (* *) (**************************************************************************) -include "ground_2/relocation/nstream_coafter.ma". +include "ground/relocation/nstream_coafter.ma". include "static_2/relocation/drops_drops.ma". include "static_2/static/frees_fqup.ma". @@ -20,9 +20,9 @@ include "static_2/static/frees_fqup.ma". (* Advanced properties ******************************************************) -lemma frees_atom_drops: - âb,L,i. â©*[b,ðâ´iâµ] L â â â - âf. ðâ¦f⦠â L ⢠ð +â¦#i⦠â ⫯*[i]âf. +lemma frees_atom_drops: + âb,L,i. â©*[b,ðâ¨iâ©] L â â â + âf. ðâ¨fâ© â L ⢠ð +â¨#iâ© â ⫯*[i]âf. #b #L elim L -L /2 width=1 by frees_atom/ #L #I #IH * [ #H lapply (drops_fwd_isid ⦠H ?) -H // #H destruct @@ -31,8 +31,8 @@ lemma frees_atom_drops: qed. lemma frees_pair_drops: - âf,K,V. K ⢠ð +â¦V⦠â f â - âi,I,L. â©*[i] L â K.â{I}V â L ⢠ð +â¦#i⦠â ⫯*[i] âf. + âf,K,V. K ⢠ð +â¨Vâ© â f â + âi,I,L. â©[i] L â K.â[I]V â L ⢠ð +â¨#iâ© â ⫯*[i] âf. #f #K #V #Hf #i elim i -i [ #I #L #H lapply (drops_fwd_isid ⦠H ?) -H /2 width=1 by frees_pair/ | #i #IH #I #L #H elim (drops_inv_succ ⦠H) -H /3 width=2 by frees_lref/ @@ -40,8 +40,8 @@ lemma frees_pair_drops: qed. lemma frees_unit_drops: - âf. ðâ¦f⦠â âI,K,i,L. â©*[i] L â K.â¤{I} â - L ⢠ð +â¦#i⦠â ⫯*[i] âf. + âf. ðâ¨fâ© â âI,K,i,L. â©[i] L â K.â¤[I] â + L ⢠ð +â¨#iâ© â ⫯*[i] âf. #f #Hf #I #K #i elim i -i [ #L #H lapply (drops_fwd_isid ⦠H ?) -H /2 width=1 by frees_unit/ | #i #IH #Y #H elim (drops_inv_succ ⦠H) -H @@ -50,8 +50,8 @@ lemma frees_unit_drops: qed. lemma frees_lref_pushs: - âf,K,j. K ⢠ð +â¦#j⦠â f â - âi,L. â©*[i] L â K â L ⢠ð +â¦#(i+j)⦠â ⫯*[i] f. + âf,K,j. K ⢠ð +â¨#jâ© â f â + âi,L. â©[i] L â K â L ⢠ð +â¨#(i+j)â© â ⫯*[i] f. #f #K #j #Hf #i elim i -i [ #L #H lapply (drops_fwd_isid ⦠H ?) -H // | #i #IH #L #H elim (drops_inv_succ ⦠H) -H @@ -62,10 +62,10 @@ qed. (* Advanced inversion lemmas ************************************************) lemma frees_inv_lref_drops: - âL,i,f. L ⢠ð +â¦#i⦠â f â - â¨â¨ ââg. â©*[â»,ðâ´iâµ] L â â & ðâ¦g⦠& f = ⫯*[i] âg - | ââg,I,K,V. K ⢠ð +â¦V⦠â g & â©*[i] L â K.â{I}V & f = ⫯*[i] âg - | ââg,I,K. â©*[i] L â K.â¤{I} & ðâ¦g⦠& f = ⫯*[i] âg. + âL,i,f. L ⢠ð +â¨#iâ© â f â + â¨â¨ ââg. â©*[â»,ðâ¨iâ©] L â â & ðâ¨gâ© & f = ⫯*[i] âg + | ââg,I,K,V. K ⢠ð +â¨Vâ© â g & â©[i] L â K.â[I]V & f = ⫯*[i] âg + | ââg,I,K. â©[i] L â K.â¤[I] & ðâ¨gâ© & f = ⫯*[i] âg. #L elim L -L [ #i #g | #L #I #IH * [ #g cases I -I [ #I | #I #V ] -IH | #i #g ] ] #H [ elim (frees_inv_atom ⦠H) -H #f #Hf #H destruct @@ -86,23 +86,23 @@ qed-. (* Properties with generic slicing for local environments *******************) lemma frees_lifts: - âb,f1,K,T. K ⢠ð +â¦T⦠â f1 â + âb,f1,K,T. K ⢠ð +â¨Tâ© â f1 â âf,L. â©*[b,f] L â K â âU. â§*[f] T â U â - âf2. f ~â f1 â f2 â L ⢠ð +â¦U⦠â f2. + âf2. f ~â f1 â f2 â L ⢠ð +â¨Uâ© â f2. #b #f1 #K #T #H lapply (frees_fwd_isfin ⦠H) elim H -f1 -K -T [ #f1 #K #s #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3 - lapply (coafter_isid_inv_dx ⦠H3 ⦠Hf1) -f1 #Hf2 + lapply (pr_coafter_isi_inv_dx ⦠H3 ⦠Hf1) -f1 #Hf2 >(lifts_inv_sort1 ⦠H2) -U /2 width=1 by frees_sort/ | #f1 #i #Hf1 #_ #f #L #H1 #U #H2 #f2 #H3 elim (lifts_inv_lref1 ⦠H2) -H2 #j #Hij #H destruct elim (coafter_fwd_xnx_pushs ⦠Hij H3) -H3 #g2 #Hg2 #H2 destruct - lapply (coafter_isid_inv_dx ⦠Hg2 ⦠Hf1) -f1 #Hf2 + lapply (pr_coafter_isi_inv_dx ⦠Hg2 ⦠Hf1) -f1 #Hf2 elim (drops_inv_atom2 ⦠H1) -H1 #n #g #H1 #Hf - elim (after_at_fwd ⦠Hij ⦠Hf) -f #x #_ #Hj -g -i - lapply (at_inv_uni ⦠Hj) -Hj #H destruct + elim (pr_after_pat_des ⦠Hij ⦠Hf) -f #x #_ #Hj -g -i + lapply (pr_pat_inv_uni ⦠Hj) -Hj #H destruct /3 width=8 by frees_atom_drops, drops_trans/ | #f1 #I #K #V #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3 - lapply (isfin_inv_next ⦠Hf1 ??) -Hf1 [3: |*: // ] #Hf1 + lapply (pr_isf_inv_next ⦠Hf1 ??) -Hf1 [3: |*: // ] #Hf1 lapply (lifts_inv_lref1 ⦠H2) -H2 * #j #Hf #H destruct elim (drops_split_trans_bind2 ⦠H1) -H1 [ |*: // ] #Z #Y #HLY #HYK #H elim (liftsb_inv_pair_sn ⦠H) -H #W #HVW #H destruct @@ -112,40 +112,40 @@ lemma frees_lifts: | #f1 #I #K #Hf1 #_ #f #L #H1 #U #H2 #f2 #H3 lapply (lifts_inv_lref1 ⦠H2) -H2 * #j #Hf #H destruct elim (coafter_fwd_xnx_pushs ⦠Hf H3) -H3 #g2 #H3 #H2 destruct - lapply (coafter_isid_inv_dx ⦠H3 ⦠Hf1) -f1 #Hg2 + lapply (pr_coafter_isi_inv_dx ⦠H3 ⦠Hf1) -f1 #Hg2 elim (drops_split_trans_bind2 ⦠H1 ⦠Hf) -H1 -Hf #Z #Y #HLY #_ #H lapply (liftsb_inv_unit_sn ⦠H) -H #H destruct /2 width=3 by frees_unit_drops/ | #f1 #I #K #i #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3 - lapply (isfin_inv_push ⦠Hf1 ??) -Hf1 [3: |*: // ] #Hf1 + lapply (pr_isf_inv_push ⦠Hf1 ??) -Hf1 [3: |*: // ] #Hf1 lapply (lifts_inv_lref1 ⦠H2) -H2 * #x #Hf #H destruct - elim (at_inv_nxx ⦠Hf) -Hf [ |*: // ] #j #Hf #H destruct + elim (pr_pat_inv_succ_sn ⦠Hf) -Hf [ |*: // ] #j #Hf #H destruct elim (drops_split_trans_bind2 ⦠H1) -H1 [ |*: // ] #Z #Y #HLY #HYK #_ elim (coafter_fwd_xpx_pushs ⦠0 ⦠H3) [ |*: // ] #g2 #H3 #H2 destruct lapply (drops_isuni_fwd_drop2 ⦠HLY) -HLY // #HLY lapply (IH ⦠HYK ⦠H3) -IH -H3 -HYK [4: |*: /2 width=2 by lifts_lref/ ] - >plus_S1 /2 width=3 by frees_lref_pushs/ (**) (* full auto fails *) + >nplus_succ_sn /2 width=3 by frees_lref_pushs/ (**) (* full auto fails *) | #f1 #K #l #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3 - lapply (coafter_isid_inv_dx ⦠H3 ⦠Hf1) -f1 #Hf2 + lapply (pr_coafter_isi_inv_dx ⦠H3 ⦠Hf1) -f1 #Hf2 >(lifts_inv_gref1 ⦠H2) -U /2 width=1 by frees_gref/ | #f1V #f1T #f1 #p #I #K #V #T #_ #_ #H1f1 #IHV #IHT #H2f1 #f #L #H1 #Y #H2 #f2 #H3 - elim (sor_inv_isfin3 ⦠H1f1) // #Hf1V #H - lapply (isfin_inv_tl ⦠H) -H + elim (pr_sor_inv_isf ⦠H1f1) // #Hf1V #H + lapply (pr_isf_inv_tl ⦠H) -H elim (lifts_inv_bind1 ⦠H2) -H2 #W #U #HVW #HTU #H destruct - elim (coafter_sor ⦠H3 ⦠H1f1) /2 width=5 by coafter_isfin2_fwd/ -H3 -H1f1 #f2V #f2T #Hf2V #H - elim (coafter_inv_tl1 ⦠H) -H + elim (pr_sor_coafter_dx_tans ⦠H3 ⦠H1f1) /2 width=5 by pr_coafter_des_ist_isf/ -H3 -H1f1 #f2V #f2T #Hf2V #H + elim (pr_coafter_inv_tl_dx ⦠H) -H /5 width=5 by frees_bind, drops_skip, ext2_pair/ | #f1V #f1T #f1 #I #K #V #T #_ #_ #H1f1 #IHV #IHT #H2f1 #f #L #H1 #Y #H2 #f2 #H3 - elim (sor_inv_isfin3 ⦠H1f1) // + elim (pr_sor_inv_isf ⦠H1f1) // elim (lifts_inv_flat1 ⦠H2) -H2 #W #U #HVW #HTU #H destruct - elim (coafter_sor ⦠H3 ⦠H1f1) - /3 width=5 by coafter_isfin2_fwd, frees_flat/ + elim (pr_sor_coafter_dx_tans ⦠H3 ⦠H1f1) + /3 width=5 by pr_coafter_des_ist_isf, frees_flat/ ] qed-. lemma frees_lifts_SO: - âb,L,K. â©*[b,ðâ´1âµ] L â K â âT,U. â§*[1] T â U â - âf. K ⢠ð +â¦T⦠â f â L ⢠ð +â¦U⦠â ⫯f. + âb,L,K. â©*[b,ðâ¨1â©] L â K â âT,U. â§[1] T â U â + âf. K ⢠ð +â¨Tâ© â f â L ⢠ð +â¨Uâ© â ⫯f. #b #L #K #HLK #T #U #HTU #f #Hf @(frees_lifts b ⦠Hf ⦠HTU) // (**) (* auto fails *) qed. @@ -153,88 +153,88 @@ qed. (* Forward lemmas with generic slicing for local environments ***************) lemma frees_fwd_coafter: - âb,f2,L,U. L ⢠ð +â¦U⦠â f2 â + âb,f2,L,U. L ⢠ð +â¨Uâ© â f2 â âf,K. â©*[b,f] L â K â âT. â§*[f] T â U â - âf1. K ⢠ð +â¦T⦠â f1 â f ~â f1 â f2. -/4 width=11 by frees_lifts, frees_mono, coafter_eq_repl_back0/ qed-. + âf1. K ⢠ð +â¨Tâ© â f1 â f ~â f1 â f2. +/4 width=11 by frees_lifts, frees_mono, pr_coafter_eq_repl_back/ qed-. (* Inversion lemmas with generic slicing for local environments *************) lemma frees_inv_lifts_ex: - âb,f2,L,U. L ⢠ð +â¦U⦠â f2 â + âb,f2,L,U. L ⢠ð +â¨Uâ© â f2 â âf,K. â©*[b,f] L â K â âT. â§*[f] T â U â - ââf1. f ~â f1 â f2 & K ⢠ð +â¦T⦠â f1. + ââf1. f ~â f1 â f2 & K ⢠ð +â¨Tâ© â f1. #b #f2 #L #U #Hf2 #f #K #HLK #T elim (frees_total K T) /3 width=9 by frees_fwd_coafter, ex2_intro/ qed-. lemma frees_inv_lifts_SO: - âb,f,L,U. L ⢠ð +â¦U⦠â f â - âK. â©*[b,ðâ´1âµ] L â K â âT. â§*[1] T â U â - K ⢠ð +â¦T⦠â ⫱f. + âb,f,L,U. L ⢠ð +â¨Uâ© â f â + âK. â©*[b,ðâ¨1â©] L â K â âT. â§[1] T â U â + K ⢠ð +â¨Tâ© â â«°f. #b #f #L #U #H #K #HLK #T #HTU elim(frees_inv_lifts_ex ⦠H ⦠HLK ⦠HTU) -b -L -U -#f1 #Hf #Hf1 elim (coafter_inv_nxx ⦠Hf) -Hf -/3 width=5 by frees_eq_repl_back, coafter_isid_inv_sn/ +#f1 #Hf #Hf1 elim (pr_coafter_inv_next_sn ⦠Hf) -Hf +/3 width=5 by frees_eq_repl_back, pr_coafter_isi_inv_sn/ qed-. lemma frees_inv_lifts: - âb,f2,L,U. L ⢠ð +â¦U⦠â f2 â + âb,f2,L,U. L ⢠ð +â¨Uâ© â f2 â âf,K. â©*[b,f] L â K â âT. â§*[f] T â U â - âf1. f ~â f1 â f2 â K ⢠ð +â¦T⦠â f1. + âf1. f ~â f1 â f2 â K ⢠ð +â¨Tâ© â f1. #b #f2 #L #U #H #f #K #HLK #T #HTU #f1 #Hf2 elim (frees_inv_lifts_ex ⦠H ⦠HLK ⦠HTU) -b -L -U -/3 width=7 by frees_eq_repl_back, coafter_inj/ +/3 width=7 by frees_eq_repl_back, pr_coafter_inj/ qed-. (* Note: this is used by rex_conf and might be modified *) lemma frees_inv_drops_next: - âf1,L1,T1. L1 ⢠ð +â¦T1⦠â f1 â - âI2,L2,V2,n. â©*[n] L1 â L2.â{I2}V2 â - âg1. âg1 = ⫱*[n] f1 â - ââg2. L2 ⢠ð +â¦V2⦠â g2 & g2 â g1. + âf1,L1,T1. L1 ⢠ð +â¨T1â© â f1 â + âI2,L2,V2,i. â©[i] L1 â L2.â[I2]V2 â + âg1. âg1 = â«°*[i] f1 â + ââg2. L2 ⢠ð +â¨V2â© â g2 & g2 â g1. #f1 #L1 #T1 #H elim H -f1 -L1 -T1 -[ #f1 #L1 #s #Hf1 #I2 #L2 #V2 #n #_ #g1 #H1 -I2 -L1 -s - lapply (isid_tls n ⦠Hf1) -Hf1