X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Fdrops_drops.ma;h=8549cf02a7e01f280f3e71ae656986b9a1056ca3;hp=0b3279de95214bf6caea3b889a5e0fd858bd758e;hb=222044da28742b24584549ba86b1805a87def070;hpb=384b04944ac31922ee41418b106b8e19a19ba9f0 diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma index 0b3279de9..8549cf02a 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma @@ -12,7 +12,7 @@ (* *) (**************************************************************************) -include "basic_2/relocation/lifts_lifts.ma". +include "basic_2/relocation/lifts_lifts_bind.ma". include "basic_2/relocation/drops_weight.ma". (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************) @@ -20,18 +20,18 @@ include "basic_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 #I #K1 #K #V1 #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_nxx … Hf) -Hf [2,3: // ] +| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_nxx … Hf) -Hf [2,3: // ] #g #Hg #H destruct /3 width=3 by drops_inv_drop1/ -| #f1 #I #K1 #K #V1 #V #_ #HV1 #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 (after_inv_pxx … Hf) -Hf [1,3: * |*:// ] #g2 #g #Hf #H1 #H2 destruct - [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_div3/ + [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_div3/ | /4 width=3 by drops_inv_drop1, drops_drop/ ] ] @@ -41,43 +41,43 @@ qed-. (* 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 #I #K1 #K #V1 #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_nxx … Hf) -Hf +| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_nxx … Hf) -Hf /3 width=3 by drops_drop/ -| #f1 #I #K1 #K #V1 #V #_ #HV1 #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 (after_inv_pxx … Hf) -Hf [1,3: * |*: // ] #g2 #g #Hg #H1 #H2 destruct - [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_trans/ + [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_trans/ | /4 width=3 by drops_inv_drop1, drops_drop/ ] ] 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: ∀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 #V #Hf1 #IH #f2 elim (pn_split f2) * +| #f1 #I #L #K #Hf1 #IH #f2 elim (pn_split 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 - #H destruct elim (drops_inv_x_pair_xy … Hf1) + #H destruct elim (drops_inv_x_bind_xy … Hf1) | /4 width=5 by drops_inv_drop1, isuni_inv_next, eq_next/ ] -| #f1 #I #L #K #V #W #Hf1 #_ #IH #f2 elim (pn_split f2) * +| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pn_split 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/ | lapply (drops_inv_drop1 … Hf2) -Hf2 -IH -HU2 #Hg2 lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by isuni_inv_push/ -HU1 - #H destruct elim (drops_inv_x_pair_xy … Hg2) + #H destruct elim (drops_inv_x_bind_xy … Hg2) ] ] qed-. @@ -85,43 +85,49 @@ 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 (isid_after_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 (after_isid_dx 𝐈𝐝 … f) /3 width=8 by drops_conf, drops_fwd_isid/ qed-. (* Basic_2A1: includes: drop_conf_lt *) -lemma drops_conf_skip1: ∀b2,f,L,L2. ⬇*[b2, f] L ≡ L2 → - ∀b1,f1,I,K1,V1. ⬇*[b1, f1] L ≡ K1.ⓑ{I}V1 → - ∀f2. f1 ⊚ ↑f2 ≡ f → - ∃∃K2,V2. L2 = K2.ⓑ{I}V2 & - ⬇*[b2, f2] K1 ≡ K2 & ⬆*[f2] V2 ≡ V1. -#b2 #f #L #L2 #H2 #b1 #f1 #I #K1 #V1 #H1 #f2 #Hf lapply (drops_conf … H1 … H2 … Hf) -L -Hf +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. +#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,I,K2,V2. ⬇*[b2, f2] L ≡ K2.ⓑ{I}V2 → - ∀f. f1 ⊚ f2 ≡ ↑f → - ∃∃K1,V1. L1 = K1.ⓑ{I}V1 & - ⬇*[b1∧b2, f] K1 ≡ K2 & ⬆*[f] V2 ≡ V1. -#b1 #f1 #L1 #L #H1 #b2 #f2 #I #K2 #V2 #H2 #f #Hf +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. +#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_pair: ∀f1,f2,I1,I2,L,K,V1,V2. - ⬇*[Ⓣ,f1] L ≡ K.ⓑ{I1}V1 → ⬇*[Ⓣ,f2] L ≡ K.ⓑ{I2}V2 → - 𝐔⦃f1⦄ → 𝐔⦃f2⦄ → ∧∧ f1 ≗ f2 & I1 = I2 & V1 = V2. -#f1 #f2 #I1 #I2 #L #K #V1 #V2 #Hf1 #Hf2 #HU1 #HU2 +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. +#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 (eq_inv_nn … H ????) -H [5: |*: // ] #H12 lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0 lapply (drops_mono … H0 … Hf2) -L #H -destruct /2 width=1 by and3_intro/ +destruct /2 width=1 by conj/ +qed-. + +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-.