X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flexs_lexs.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flexs_lexs.ma;h=0000000000000000000000000000000000000000;hb=222044da28742b24584549ba86b1805a87def070;hp=753b43b2efdc671f3325d2d7228734e7e685d0c0;hpb=5c186c72f508da0849058afeecc6877cd9ed6303;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma deleted file mode 100644 index 753b43b2e..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma +++ /dev/null @@ -1,119 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "ground_2/relocation/rtmap_sand.ma". -include "basic_2/relocation/drops.ma". - -(* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****) - -(* Main properties **********************************************************) - -theorem lexs_trans_gen (RN1) (RP1) (RN2) (RP2) (RN) (RP): - ∀L1,f. - (∀g,I,K,n. ⬇*[n] L1 ≘ K.ⓘ{I} → ↑g = ⫱*[n] f → lexs_transitive RN1 RN2 RN RN1 RP1 g K I) → - (∀g,I,K,n. ⬇*[n] L1 ≘ K.ⓘ{I} → ⫯g = ⫱*[n] f → lexs_transitive RP1 RP2 RP RN1 RP1 g K I) → - ∀L0. L1 ⪤*[RN1, RP1, f] L0 → - ∀L2. L0 ⪤*[RN2, RP2, f] L2 → - L1 ⪤*[RN, RP, f] L2. -#RN1 #RP1 #RN2 #RP2 #RN #RP #L1 elim L1 -L1 -[ #f #_ #_ #L0 #H1 #L2 #H2 - lapply (lexs_inv_atom1 … H1) -H1 #H destruct - lapply (lexs_inv_atom1 … H2) -H2 #H destruct - /2 width=1 by lexs_atom/ -| #K1 #I1 #IH #f elim (pn_split f) * #g #H destruct - #HN #HP #L0 #H1 #L2 #H2 - [ elim (lexs_inv_push1 … H1) -H1 #I0 #K0 #HK10 #HI10 #H destruct - elim (lexs_inv_push1 … H2) -H2 #I2 #K2 #HK02 #HI02 #H destruct - lapply (HP … 0 … HI10 … HK10 … HI02) -HI10 -HI02 /2 width=2 by drops_refl/ #HI12 - lapply (IH … HK10 … HK02) -IH -K0 /3 width=3 by lexs_push, drops_drop/ - | elim (lexs_inv_next1 … H1) -H1 #I0 #K0 #HK10 #HI10 #H destruct - elim (lexs_inv_next1 … H2) -H2 #I2 #K2 #HK02 #HI02 #H destruct - lapply (HN … 0 … HI10 … HK10 … HI02) -HI10 -HI02 /2 width=2 by drops_refl/ #HI12 - lapply (IH … HK10 … HK02) -IH -K0 /3 width=3 by lexs_next, drops_drop/ - ] -] -qed-. - -theorem lexs_trans (RN) (RP) (f): (∀g,I,K. lexs_transitive RN RN RN RN RP g K I) → - (∀g,I,K. lexs_transitive RP RP RP RN RP g K I) → - Transitive … (lexs RN RP f). -/2 width=9 by lexs_trans_gen/ qed-. - -theorem lexs_trans_id_cfull: ∀R1,R2,R3,L1,L,f. L1 ⪤*[R1, cfull, f] L → 𝐈⦃f⦄ → - ∀L2. L ⪤*[R2, cfull, f] L2 → L1 ⪤*[R3, cfull, f] L2. -#R1 #R2 #R3 #L1 #L #f #H elim H -L1 -L -f -[ #f #Hf #L2 #H >(lexs_inv_atom1 … H) -L2 // ] -#f #I1 #I #K1 #K #HK1 #_ #IH #Hf #L2 #H -[ elim (isid_inv_next … Hf) | lapply (isid_inv_push … Hf ??) ] -Hf [5: |*: // ] #Hf -elim (lexs_inv_push1 … H) -H #I2 #K2 #HK2 #_ #H destruct -/3 width=1 by lexs_push/ -qed-. - -theorem lexs_conf (RN1) (RP1) (RN2) (RP2): - ∀L,f. - (∀g,I,K,n. ⬇*[n] L ≘ K.ⓘ{I} → ↑g = ⫱*[n] f → R_pw_confluent2_lexs RN1 RN2 RN1 RP1 RN2 RP2 g K I) → - (∀g,I,K,n. ⬇*[n] L ≘ K.ⓘ{I} → ⫯g = ⫱*[n] f → R_pw_confluent2_lexs RP1 RP2 RN1 RP1 RN2 RP2 g K I) → - pw_confluent2 … (lexs RN1 RP1 f) (lexs RN2 RP2 f) L. -#RN1 #RP1 #RN2 #RP2 #L elim L -L -[ #f #_ #_ #L1 #H1 #L2 #H2 >(lexs_inv_atom1 … H1) >(lexs_inv_atom1 … H2) -H2 -H1 - /2 width=3 by lexs_atom, ex2_intro/ -| #L #I0 #IH #f elim (pn_split f) * #g #H destruct - #HN #HP #Y1 #H1 #Y2 #H2 - [ elim (lexs_inv_push1 … H1) -H1 #I1 #L1 #HL1 #HI01 #H destruct - elim (lexs_inv_push1 … H2) -H2 #I2 #L2 #HL2 #HI02 #H destruct - elim (HP … 0 … HI01 … HI02 … HL1 … HL2) -HI01 -HI02 /2 width=2 by drops_refl/ #I #HI1 #HI2 - elim (IH … HL1 … HL2) -IH -HL1 -HL2 /3 width=5 by drops_drop, lexs_push, ex2_intro/ - | elim (lexs_inv_next1 … H1) -H1 #I1 #L1 #HL1 #HI01 #H destruct - elim (lexs_inv_next1 … H2) -H2 #I2 #L2 #HL2 #HI02 #H destruct - elim (HN … 0 … HI01 … HI02 … HL1 … HL2) -HI01 -HI02 /2 width=2 by drops_refl/ #I #HI1 #HI2 - elim (IH … HL1 … HL2) -IH -HL1 -HL2 /3 width=5 by drops_drop, lexs_next, ex2_intro/ - ] -] -qed-. - -theorem lexs_canc_sn: ∀RN,RP,f. Transitive … (lexs RN RP f) → - symmetric … (lexs RN RP f) → - left_cancellable … (lexs RN RP f). -/3 width=3 by/ qed-. - -theorem lexs_canc_dx: ∀RN,RP,f. Transitive … (lexs RN RP f) → - symmetric … (lexs RN RP f) → - right_cancellable … (lexs RN RP f). -/3 width=3 by/ qed-. - -lemma lexs_meet: ∀RN,RP,L1,L2. - ∀f1. L1 ⪤*[RN, RP, f1] L2 → - ∀f2. L1 ⪤*[RN, RP, f2] L2 → - ∀f. f1 ⋒ f2 ≘ f → L1 ⪤*[RN, RP, f] L2. -#RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 // -#f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H #f #Hf -elim (pn_split f2) * #g2 #H2 destruct -try elim (lexs_inv_push … H) try elim (lexs_inv_next … H) -H -[ elim (sand_inv_npx … Hf) | elim (sand_inv_nnx … Hf) -| elim (sand_inv_ppx … Hf) | elim (sand_inv_pnx … Hf) -] -Hf /3 width=5 by lexs_next, lexs_push/ -qed-. - -lemma lexs_join: ∀RN,RP,L1,L2. - ∀f1. L1 ⪤*[RN, RP, f1] L2 → - ∀f2. L1 ⪤*[RN, RP, f2] L2 → - ∀f. f1 ⋓ f2 ≘ f → L1 ⪤*[RN, RP, f] L2. -#RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 // -#f1 #I1 #I2 #L1 #L2 #_ #HI12 #IH #f2 #H #f #Hf -elim (pn_split f2) * #g2 #H2 destruct -try elim (lexs_inv_push … H) try elim (lexs_inv_next … H) -H -[ elim (sor_inv_npx … Hf) | elim (sor_inv_nnx … Hf) -| elim (sor_inv_ppx … Hf) | elim (sor_inv_pnx … Hf) -] -Hf /3 width=5 by lexs_next, lexs_push/ -qed-.