X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Frelocation%2Fdrops_drops.ma;h=7b8bebb691e39ceda5411552b510022723f1a2b0;hb=98e786e1a6bd7b621e37ba7cd4098d4a0a6f8278;hp=4b52fd651bb8b753970ae8d8bb462099e13a4a7f;hpb=6b4da5fa47d474dcf2f203ec7f5ed36938739c9b;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma index 4b52fd651..7b8bebb69 100644 --- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma +++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma @@ -20,16 +20,16 @@ include "static_2/relocation/drops_weight.ma". (* Main properties **********************************************************) (* Basic_2A1: includes: drop_conf_ge drop_conf_be drop_conf_le *) -theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L → - ∀b2,f,L2. ⬇*[b2, f] L1 ≘ L2 → - ∀f2. f1 ⊚ f2 ≘ f → ⬇*[b2, f2] L ≘ L2. +theorem drops_conf: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L → + ∀b2,f,L2. ⇩*[b2,f] L1 ≘ L2 → + ∀f2. f1 ⊚ f2 ≘ f → ⇩*[b2,f2] L ≘ L2. #b1 #f1 #L1 #L #H elim H -f1 -L1 -L [ #f1 #_ #b2 #f #L2 #HL2 #f2 #Hf12 elim (drops_inv_atom1 … HL2) -b1 -HL2 #H #Hf destruct @drops_atom - #H elim (after_inv_isid3 … Hf12) -Hf12 /2 width=1 by/ -| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_nxx … Hf) -Hf [2,3: // ] + #H elim (pr_after_inv_isi … Hf12) -Hf12 /2 width=1 by/ +| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (pr_after_inv_next_sn … Hf) -Hf [2,3: // ] #g #Hg #H destruct /3 width=3 by drops_inv_drop1/ -| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*:// ] +| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*:// ] #g2 #g #Hf #H1 #H2 destruct [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_div3/ | /4 width=3 by drops_inv_drop1, drops_drop/ @@ -38,20 +38,20 @@ theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L → qed-. (* Basic_1: was: drop1_trans *) -(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm +(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm drops_drop_trans *) -theorem drops_trans: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L → - ∀b2,f2,L2. ⬇*[b2, f2] L ≘ L2 → - ∀f. f1 ⊚ f2 ≘ f → ⬇*[b1∧b2, f] L1 ≘ L2. +theorem drops_trans: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L → + ∀b2,f2,L2. ⇩*[b2,f2] L ≘ L2 → + ∀f. f1 ⊚ f2 ≘ f → ⇩*[b1∧b2,f] L1 ≘ L2. #b1 #f1 #L1 #L #H elim H -f1 -L1 -L [ #f1 #Hf1 #b2 #f2 #L2 #HL2 #f #Hf elim (drops_inv_atom1 … HL2) -HL2 #H #Hf2 destruct @drops_atom #H elim (andb_inv_true_dx … H) -H - #H1 #H2 lapply (after_isid_inv_sn … Hf ?) -Hf - /3 width=3 by isid_eq_repl_back/ -| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_nxx … Hf) -Hf + #H1 #H2 lapply (pr_after_isi_inv_sn … Hf ?) -Hf + /3 width=3 by pr_isi_eq_repl_back/ +| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (pr_after_inv_next_sn … Hf) -Hf /3 width=3 by drops_drop/ -| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*: // ] +| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f2 #L2 #HL2 #f #Hf elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*: // ] #g2 #g #Hg #H1 #H2 destruct [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_trans/ | /4 width=3 by drops_inv_drop1, drops_drop/ @@ -59,24 +59,25 @@ theorem drops_trans: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L → ] qed-. -theorem drops_conf_div: ∀f1,L,K. ⬇*[Ⓣ,f1] L ≘ K → ∀f2. ⬇*[Ⓣ,f2] L ≘ K → - 𝐔⦃f1⦄ → 𝐔⦃f2⦄ → f1 ≡ f2. +theorem drops_conf_div_isuni: + ∀f1,L,K. ⇩*[Ⓣ,f1] L ≘ K → ∀f2. ⇩*[Ⓣ,f2] L ≘ K → + 𝐔❪f1❫ → 𝐔❪f2❫ → f1 ≡ f2. #f1 #L #K #H elim H -f1 -L -K [ #f1 #Hf1 #f2 #Hf2 elim (drops_inv_atom1 … Hf2) -Hf2 - /3 width=1 by isid_inv_eq_repl/ -| #f1 #I #L #K #Hf1 #IH #f2 elim (pn_split f2) * + /3 width=1 by pr_isi_inv_eq_repl/ +| #f1 #I #L #K #Hf1 #IH #f2 elim (pr_map_split_tl f2) * #g2 #H2 #Hf2 #HU1 #HU2 destruct [ elim (drops_inv_skip1 … Hf2) -IH -HU1 -Hf2 #Y2 #X2 #HY2 #_ #H destruct - lapply (drops_fwd_isid … HY2 ?) -HY2 /2 width=3 by isuni_inv_push/ -HU2 + lapply (drops_fwd_isid … HY2 ?) -HY2 /2 width=3 by pr_isu_inv_push/ -HU2 #H destruct elim (drops_inv_x_bind_xy … Hf1) - | /4 width=5 by drops_inv_drop1, isuni_inv_next, eq_next/ + | /4 width=5 by drops_inv_drop1, pr_isu_inv_next, pr_eq_next/ ] -| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pn_split f2) * +| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pr_map_split_tl f2) * #g2 #H2 #Hf2 #HU1 #HU2 destruct [ elim (drops_inv_skip1 … Hf2) -Hf2 #Y2 #X2 #HY2 #_ #H destruct -Hf1 - /4 width=5 by isuni_fwd_push, eq_push/ + /4 width=5 by pr_isu_fwd_push, pr_eq_push/ | lapply (drops_inv_drop1 … Hf2) -Hf2 -IH -HU2 #Hg2 - lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by isuni_inv_push/ -HU1 + lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by pr_isu_inv_push/ -HU1 #H destruct elim (drops_inv_x_bind_xy … Hg2) ] ] @@ -85,19 +86,19 @@ qed-. (* Advanced properties ******************************************************) (* Basic_2A1: includes: drop_mono *) -lemma drops_mono: ∀b1,f,L,L1. ⬇*[b1, f] L ≘ L1 → - ∀b2,L2. ⬇*[b2, f] L ≘ L2 → L1 = L2. -#b1 #f #L #L1 lapply (after_isid_dx 𝐈𝐝 … f) +lemma drops_mono: ∀b1,f,L,L1. ⇩*[b1,f] L ≘ L1 → + ∀b2,L2. ⇩*[b2,f] L ≘ L2 → L1 = L2. +#b1 #f #L #L1 lapply (pr_after_isi_dx 𝐢 … f) /3 width=8 by drops_conf, drops_fwd_isid/ qed-. -lemma drops_inv_uni: ∀L,i. ⬇*[Ⓕ, 𝐔❴i❵] L ≘ ⋆ → ∀I,K. ⬇*[i] L ≘ K.ⓘ{I} → ⊥. +lemma drops_inv_uni: ∀L,i. ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆ → ∀I,K. ⇩[i] L ≘ K.ⓘ[I] → ⊥. #L #i #H1 #I #K #H2 lapply (drops_F … H2) -H2 #H2 lapply (drops_mono … H2 … H1) -L -i #H destruct qed-. -lemma drops_ldec_dec: ∀L,i. Decidable (∃∃K,W. ⬇*[i] L ≘ K.ⓛW). +lemma drops_ldec_dec: ∀L,i. Decidable (∃∃K,W. ⇩[i] L ≘ K.ⓛW). #L #i elim (drops_F_uni L i) [| * * [ #I #K1 | * #W1 #K1 ] ] [4: /3 width=3 by ex1_2_intro, or_introl/ |*: #H1L @or_intror * #K2 #W2 #H2L @@ -106,34 +107,35 @@ lemma drops_ldec_dec: ∀L,i. Decidable (∃∃K,W. ⬇*[i] L ≘ K.ⓛW). qed-. (* Basic_2A1: includes: drop_conf_lt *) -lemma drops_conf_skip1: ∀b2,f,L,L2. ⬇*[b2, f] L ≘ L2 → - ∀b1,f1,I1,K1. ⬇*[b1, f1] L ≘ K1.ⓘ{I1} → +lemma drops_conf_skip1: ∀b2,f,L,L2. ⇩*[b2,f] L ≘ L2 → + ∀b1,f1,I1,K1. ⇩*[b1,f1] L ≘ K1.ⓘ[I1] → ∀f2. f1 ⊚ ⫯f2 ≘ f → - ∃∃I2,K2. L2 = K2.ⓘ{I2} & - ⬇*[b2, f2] K1 ≘ K2 & ⬆*[f2] I2 ≘ I1. + ∃∃I2,K2. L2 = K2.ⓘ[I2] & + ⇩*[b2,f2] K1 ≘ K2 & ⇧*[f2] I2 ≘ I1. #b2 #f #L #L2 #H2 #b1 #f1 #I1 #K1 #H1 #f2 #Hf lapply (drops_conf … H1 … H2 … Hf) -L -Hf #H elim (drops_inv_skip1 … H) -H /2 width=5 by ex3_2_intro/ qed-. (* Basic_2A1: includes: drop_trans_lt *) -lemma drops_trans_skip2: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L → - ∀b2,f2,I2,K2. ⬇*[b2, f2] L ≘ K2.ⓘ{I2} → +lemma drops_trans_skip2: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L → + ∀b2,f2,I2,K2. ⇩*[b2,f2] L ≘ K2.ⓘ[I2] → ∀f. f1 ⊚ f2 ≘ ⫯f → - ∃∃I1,K1. L1 = K1.ⓘ{I1} & - ⬇*[b1∧b2, f] K1 ≘ K2 & ⬆*[f] I2 ≘ I1. + ∃∃I1,K1. L1 = K1.ⓘ[I1] & + ⇩*[b1∧b2,f] K1 ≘ K2 & ⇧*[f] I2 ≘ I1. #b1 #f1 #L1 #L #H1 #b2 #f2 #I2 #K2 #H2 #f #Hf lapply (drops_trans … H1 … H2 … Hf) -L -Hf #H elim (drops_inv_skip2 … H) -H /2 width=5 by ex3_2_intro/ qed-. (* Basic_2A1: includes: drops_conf_div *) -lemma drops_conf_div_bind: ∀f1,f2,I1,I2,L,K. - ⬇*[Ⓣ, f1] L ≘ K.ⓘ{I1} → ⬇*[Ⓣ, f2] L ≘ K.ⓘ{I2} → - 𝐔⦃f1⦄ → 𝐔⦃f2⦄ → f1 ≡ f2 ∧ I1 = I2. +lemma drops_conf_div_bind_isuni: + ∀f1,f2,I1,I2,L,K. + ⇩*[Ⓣ,f1] L ≘ K.ⓘ[I1] → ⇩*[Ⓣ,f2] L ≘ K.ⓘ[I2] → + 𝐔❪f1❫ → 𝐔❪f2❫ → f1 ≡ f2 ∧ I1 = I2. #f1 #f2 #I1 #I2 #L #K #Hf1 #Hf2 #HU1 #HU2 lapply (drops_isuni_fwd_drop2 … Hf1) // #H1 lapply (drops_isuni_fwd_drop2 … Hf2) // #H2 -lapply (drops_conf_div … H1 … H2 ??) /2 width=3 by isuni_next/ -H1 -H2 -HU1 -HU2 #H +lapply (drops_conf_div_isuni … H1 … H2 ??) /2 width=3 by pr_isu_next/ -H1 -H2 -HU1 -HU2 #H lapply (eq_inv_nn … H ????) -H [5: |*: // ] #H12 lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0 lapply (drops_mono … H0 … Hf2) -L #H