X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_vector.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_vector.ma;h=0000000000000000000000000000000000000000;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hp=8e234a5c1039d241987b7322ccbc7201f6690427;hpb=222044da28742b24584549ba86b1805a87def070;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma deleted file mode 100644 index 8e234a5c1..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma +++ /dev/null @@ -1,137 +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 "basic_2/syntax/term_vector.ma". -include "basic_2/relocation/lifts.ma". - -(* GENERIC RELOCATION FOR TERM VECTORS *************************************) - -(* Basic_2A1: includes: liftv_nil liftv_cons *) -inductive liftsv (f:rtmap): relation (list term) ≝ -| liftsv_nil : liftsv f (Ⓔ) (Ⓔ) -| liftsv_cons: ∀T1s,T2s,T1,T2. - ⬆*[f] T1 ≘ T2 → liftsv f T1s T2s → - liftsv f (T1 ⨮ T1s) (T2 ⨮ T2s) -. - -interpretation "uniform relocation (term vector)" - 'RLiftStar i T1s T2s = (liftsv (uni i) T1s T2s). - -interpretation "generic relocation (term vector)" - 'RLiftStar f T1s T2s = (liftsv f T1s T2s). - -(* Basic inversion lemmas ***************************************************) - -fact liftsv_inv_nil1_aux: ∀f,X,Y. ⬆*[f] X ≘ Y → X = Ⓔ → Y = Ⓔ. -#f #X #Y * -X -Y // -#T1s #T2s #T1 #T2 #_ #_ #H destruct -qed-. - -(* Basic_2A1: includes: liftv_inv_nil1 *) -lemma liftsv_inv_nil1: ∀f,Y. ⬆*[f] Ⓔ ≘ Y → Y = Ⓔ. -/2 width=5 by liftsv_inv_nil1_aux/ qed-. - -fact liftsv_inv_cons1_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≘ Y → - ∀T1,T1s. X = T1 ⨮ T1s → - ∃∃T2,T2s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s & - Y = T2 ⨮ T2s. -#f #X #Y * -X -Y -[ #U1 #U1s #H destruct -| #T1s #T2s #T1 #T2 #HT12 #HT12s #U1 #U1s #H destruct /2 width=5 by ex3_2_intro/ -] -qed-. - -(* Basic_2A1: includes: liftv_inv_cons1 *) -lemma liftsv_inv_cons1: ∀f:rtmap. ∀T1,T1s,Y. ⬆*[f] T1 ⨮ T1s ≘ Y → - ∃∃T2,T2s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s & - Y = T2 ⨮ T2s. -/2 width=3 by liftsv_inv_cons1_aux/ qed-. - -fact liftsv_inv_nil2_aux: ∀f,X,Y. ⬆*[f] X ≘ Y → Y = Ⓔ → X = Ⓔ. -#f #X #Y * -X -Y // -#T1s #T2s #T1 #T2 #_ #_ #H destruct -qed-. - -lemma liftsv_inv_nil2: ∀f,X. ⬆*[f] X ≘ Ⓔ → X = Ⓔ. -/2 width=5 by liftsv_inv_nil2_aux/ qed-. - -fact liftsv_inv_cons2_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≘ Y → - ∀T2,T2s. Y = T2 ⨮ T2s → - ∃∃T1,T1s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s & - X = T1 ⨮ T1s. -#f #X #Y * -X -Y -[ #U2 #U2s #H destruct -| #T1s #T2s #T1 #T2 #HT12 #HT12s #U2 #U2s #H destruct /2 width=5 by ex3_2_intro/ -] -qed-. - -lemma liftsv_inv_cons2: ∀f:rtmap. ∀X,T2,T2s. ⬆*[f] X ≘ T2 ⨮ T2s → - ∃∃T1,T1s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s & - X = T1 ⨮ T1s. -/2 width=3 by liftsv_inv_cons2_aux/ qed-. - -(* Basic_1: was: lifts1_flat (left to right) *) -lemma lifts_inv_applv1: ∀f:rtmap. ∀V1s,U1,T2. ⬆*[f] Ⓐ V1s.U1 ≘ T2 → - ∃∃V2s,U2. ⬆*[f] V1s ≘ V2s & ⬆*[f] U1 ≘ U2 & - T2 = Ⓐ V2s.U2. -#f #V1s elim V1s -V1s -[ /3 width=5 by ex3_2_intro, liftsv_nil/ -| #V1 #V1s #IHV1s #T1 #X #H elim (lifts_inv_flat1 … H) -H - #V2 #Y #HV12 #HY #H destruct elim (IHV1s … HY) -IHV1s -HY - #V2s #T2 #HV12s #HT12 #H destruct /3 width=5 by ex3_2_intro, liftsv_cons/ -] -qed-. - -lemma lifts_inv_applv2: ∀f:rtmap. ∀V2s,U2,T1. ⬆*[f] T1 ≘ Ⓐ V2s.U2 → - ∃∃V1s,U1. ⬆*[f] V1s ≘ V2s & ⬆*[f] U1 ≘ U2 & - T1 = Ⓐ V1s.U1. -#f #V2s elim V2s -V2s -[ /3 width=5 by ex3_2_intro, liftsv_nil/ -| #V2 #V2s #IHV2s #T2 #X #H elim (lifts_inv_flat2 … H) -H - #V1 #Y #HV12 #HY #H destruct elim (IHV2s … HY) -IHV2s -HY - #V1s #T1 #HV12s #HT12 #H destruct /3 width=5 by ex3_2_intro, liftsv_cons/ -] -qed-. - -(* Basic properties *********************************************************) - -(* Basic_2A1: includes: liftv_total *) -lemma liftsv_total: ∀f. ∀T1s:list term. ∃T2s. ⬆*[f] T1s ≘ T2s. -#f #T1s elim T1s -T1s -[ /2 width=2 by liftsv_nil, ex_intro/ -| #T1 #T1s * #T2s #HT12s - elim (lifts_total T1 f) /3 width=2 by liftsv_cons, ex_intro/ -] -qed-. - -(* Basic_1: was: lifts1_flat (right to left) *) -lemma lifts_applv: ∀f:rtmap. ∀V1s,V2s. ⬆*[f] V1s ≘ V2s → - ∀T1,T2. ⬆*[f] T1 ≘ T2 → - ⬆*[f] Ⓐ V1s.T1 ≘ Ⓐ V2s.T2. -#f #V1s #V2s #H elim H -V1s -V2s /3 width=1 by lifts_flat/ -qed. - -lemma liftsv_split_trans: ∀f,T1s,T2s. ⬆*[f] T1s ≘ T2s → - ∀f1,f2. f2 ⊚ f1 ≘ f → - ∃∃Ts. ⬆*[f1] T1s ≘ Ts & ⬆*[f2] Ts ≘ T2s. -#f #T1s #T2s #H elim H -T1s -T2s -[ /2 width=3 by liftsv_nil, ex2_intro/ -| #T1s #T2s #T1 #T2 #HT12 #_ #IH #f1 #f2 #Hf - elim (IH … Hf) -IH - elim (lifts_split_trans … HT12 … Hf) -HT12 -Hf - /3 width=5 by liftsv_cons, ex2_intro/ -] -qed-. - -(* Basic_1: removed theorems 2: lifts1_nil lifts1_cons *)