X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_lfxs.ma;h=89b84566be4e1e6aadced8a7c63dd302c36dbf69;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=95b89cd809e2cbca53835b2fe0ae071c9a93768b;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma index 95b89cd80..89b84566b 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma @@ -13,18 +13,20 @@ (**************************************************************************) include "basic_2/relocation/lexs_lexs.ma". -include "basic_2/static/frees_drops.ma". +include "basic_2/static/frees_fqup.ma". include "basic_2/static/lfxs.ma". (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****) -(* Advanced properties ******************************************************) +(* Advanced inversion lemmas ************************************************) lemma lfxs_inv_frees: ∀R,L1,L2,T. L1 ⪤*[R, T] L2 → - ∀f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → L1 ⪤*[cext2 R, cfull, f] L2. + ∀f. L1 ⊢ 𝐅*⦃T⦄ ≘ f → L1 ⪤*[cext2 R, cfull, f] L2. #R #L1 #L2 #T * /3 width=6 by frees_mono, lexs_eq_repl_back/ qed-. +(* Advanced properties ******************************************************) + (* Basic_2A1: uses: llpx_sn_dec *) lemma lfxs_dec: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) → ∀L1,L2,T. Decidable (L1 ⪤*[R, T] L2). @@ -34,61 +36,6 @@ elim (lexs_dec (cext2 R) cfull … L1 L2 f) /4 width=3 by lfxs_inv_frees, cfull_dec, ext2_dec, ex2_intro, or_intror, or_introl/ qed-. -lemma lfxs_pair_sn_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) → - lexs_frees_confluent … (cext2 R1) cfull → - ∀L1,L2,V. L1 ⪤*[R1, V] L2 → ∀I,T. - ∃∃L. L1 ⪤*[R1, ②{I}V.T] L & L ⪤*[R2, V] L2. -#R1 #R2 #HR1 #HR2 #HR #L1 #L2 #V * #f #Hf #HL12 * [ #p ] #I #T -[ elim (frees_total L1 (ⓑ{p,I}V.T)) #g #Hg - elim (frees_inv_bind … Hg) #y1 #y2 #H #_ #Hy -| elim (frees_total L1 (ⓕ{I}V.T)) #g #Hg - elim (frees_inv_flat … Hg) #y1 #y2 #H #_ #Hy -] -lapply(frees_mono … H … Hf) -H #H1 -lapply (sor_eq_repl_back1 … Hy … H1) -y1 #Hy -lapply (sor_inv_sle_sn … Hy) -y2 #Hfg -elim (lexs_sle_split (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2 -lapply (sle_lexs_trans … HL1 … Hfg) // #H -elim (HR … Hf … H) -HR -Hf -H -/4 width=7 by sle_lexs_trans, ex2_intro/ -qed-. - -lemma lfxs_flat_dx_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) → - lexs_frees_confluent … (cext2 R1) cfull → - ∀L1,L2,T. L1 ⪤*[R1, T] L2 → ∀I,V. - ∃∃L. L1 ⪤*[R1, ⓕ{I}V.T] L & L ⪤*[R2, T] L2. -#R1 #R2 #HR1 #HR2 #HR #L1 #L2 #T * #f #Hf #HL12 #I #V -elim (frees_total L1 (ⓕ{I}V.T)) #g #Hg -elim (frees_inv_flat … Hg) #y1 #y2 #_ #H #Hy -lapply(frees_mono … H … Hf) -H #H2 -lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy -lapply (sor_inv_sle_dx … Hy) -y1 #Hfg -elim (lexs_sle_split (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2 -lapply (sle_lexs_trans … HL1 … Hfg) // #H -elim (HR … Hf … H) -HR -Hf -H -/4 width=7 by sle_lexs_trans, ex2_intro/ -qed-. - -lemma lfxs_bind_dx_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) → - lexs_frees_confluent … (cext2 R1) cfull → - ∀I,L1,L2,V1,T. L1.ⓑ{I}V1 ⪤*[R1, T] L2 → ∀p. - ∃∃L,V. L1 ⪤*[R1, ⓑ{p,I}V1.T] L & L.ⓑ{I}V ⪤*[R2, T] L2 & R1 L1 V1 V. -#R1 #R2 #HR1 #HR2 #HR #I #L1 #L2 #V1 #T * #f #Hf #HL12 #p -elim (frees_total L1 (ⓑ{p,I}V1.T)) #g #Hg -elim (frees_inv_bind … Hg) #y1 #y2 #_ #H #Hy -lapply(frees_mono … H … Hf) -H #H2 -lapply (tl_eq_repl … H2) -H2 #H2 -lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy -lapply (sor_inv_sle_dx … Hy) -y1 #Hfg -lapply (sle_inv_tl_sn … Hfg) -Hfg #Hfg -elim (lexs_sle_split (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #Y #H #HL2 -lapply (sle_lexs_trans … H … Hfg) // #H0 -elim (lexs_inv_next1 … H) -H #Z #L #HL1 #H -elim (ext2_inv_pair_sn … H) -H #V #HV #H1 #H2 destruct -elim (HR … Hf … H0) -HR -Hf -H0 -/4 width=7 by sle_lexs_trans, ex3_2_intro, ex2_intro/ -qed-. - (* Main properties **********************************************************) (* Basic_2A1: uses: llpx_sn_bind llpx_sn_bind_O *) @@ -116,35 +63,6 @@ lapply (lexs_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2)) /3 width=7 by frees_fwd_isfin, frees_bind_void, lexs_join, isfin_tl, ex2_intro/ qed. -theorem lfxs_conf: ∀R1,R2. - lexs_frees_confluent (cext2 R1) cfull → - lexs_frees_confluent (cext2 R2) cfull → - R_confluent2_lfxs R1 R2 R1 R2 → - ∀T. confluent2 … (lfxs R1 T) (lfxs R2 T). -#R1 #R2 #HR1 #HR2 #HR12 #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02 -lapply (frees_mono … Hf1 … Hf) -Hf1 #Hf12 -lapply (lexs_eq_repl_back … HL01 … Hf12) -f1 #HL01 -elim (lexs_conf … HL01 … HL02) /2 width=3 by ex2_intro/ [ | -HL01 -HL02 ] -[ #L #HL1 #HL2 - elim (HR1 … Hf … HL01) -HL01 #f1 #Hf1 #H1 - elim (HR2 … Hf … HL02) -HL02 #f2 #Hf2 #H2 - lapply (sle_lexs_trans … HL1 … H1) // -HL1 -H1 #HL1 - lapply (sle_lexs_trans … HL2 … H2) // -HL2 -H2 #HL2 - /3 width=5 by ex2_intro/ -| #g * #I0 [2: #V0 ] #K0 #n #HLK0 #Hgf #Z1 #H1 #Z2 #H2 #K1 #HK01 #K2 #HK02 - [ elim (ext2_inv_pair_sn … H1) -H1 #V1 #HV01 #H destruct - elim (ext2_inv_pair_sn … H2) -H2 #V2 #HV02 #H destruct - elim (frees_inv_drops_next … Hf … HLK0 … Hgf) -Hf -HLK0 -Hgf #g0 #Hg0 #H0 - lapply (sle_lexs_trans … HK01 … H0) // -HK01 #HK01 - lapply (sle_lexs_trans … HK02 … H0) // -HK02 #HK02 - elim (HR12 … HV01 … HV02 K1 … K2) /3 width=3 by ext2_pair, ex2_intro/ - | lapply (ext2_inv_unit_sn … H1) -H1 #H destruct - lapply (ext2_inv_unit_sn … H2) -H2 #H destruct - /3 width=3 by ext2_unit, ex2_intro/ - ] -] -qed-. - (* Negated inversion lemmas *************************************************) (* Basic_2A1: uses: nllpx_sn_inv_bind nllpx_sn_inv_bind_O *)