X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Fseq.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Fseq.ma;h=0000000000000000000000000000000000000000;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hp=8b833f570a220f4038a36f246bb4e18262d08803;hpb=222044da28742b24584549ba86b1805a87def070;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/seq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/seq.ma deleted file mode 100644 index 8b833f570..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/seq.ma +++ /dev/null @@ -1,103 +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/notation/relations/ideqsn_3.ma". -include "basic_2/syntax/ceq_ext.ma". -include "basic_2/relocation/sex.ma". - -(* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************) - -(* Basic_2A1: includes: lreq_atom lreq_zero lreq_pair lreq_succ *) -definition seq: relation3 rtmap lenv lenv ≝ sex ceq_ext cfull. - -interpretation - "syntactic equivalence on selected entries (local environment)" - 'IdEqSn f L1 L2 = (seq f L1 L2). - -(* Basic properties *********************************************************) - -lemma seq_eq_repl_back: ∀L1,L2. eq_repl_back … (λf. L1 ≡[f] L2). -/2 width=3 by sex_eq_repl_back/ qed-. - -lemma seq_eq_repl_fwd: ∀L1,L2. eq_repl_fwd … (λf. L1 ≡[f] L2). -/2 width=3 by sex_eq_repl_fwd/ qed-. - -lemma sle_seq_trans: ∀f2,L1,L2. L1 ≡[f2] L2 → - ∀f1. f1 ⊆ f2 → L1 ≡[f1] L2. -/2 width=3 by sle_sex_trans/ qed-. - -(* Basic_2A1: includes: lreq_refl *) -lemma seq_refl: ∀f. reflexive … (seq f). -/2 width=1 by sex_refl/ qed. - -(* Basic_2A1: includes: lreq_sym *) -lemma seq_sym: ∀f. symmetric … (seq f). -/3 width=2 by sex_sym, cext2_sym/ qed-. - -(* Basic inversion lemmas ***************************************************) - -(* Basic_2A1: includes: lreq_inv_atom1 *) -lemma seq_inv_atom1: ∀f,Y. ⋆ ≡[f] Y → Y = ⋆. -/2 width=4 by sex_inv_atom1/ qed-. - -(* Basic_2A1: includes: lreq_inv_pair1 *) -lemma seq_inv_next1: ∀g,J,K1,Y. K1.ⓘ{J} ≡[↑g] Y → - ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓘ{J}. -#g #J #K1 #Y #H -elim (sex_inv_next1 … H) -H #Z #K2 #HK12 #H1 #H2 destruct -<(ceq_ext_inv_eq … H1) -Z /2 width=3 by ex2_intro/ -qed-. - -(* Basic_2A1: includes: lreq_inv_zero1 lreq_inv_succ1 *) -lemma seq_inv_push1: ∀g,J1,K1,Y. K1.ⓘ{J1} ≡[⫯g] Y → - ∃∃J2,K2. K1 ≡[g] K2 & Y = K2.ⓘ{J2}. -#g #J1 #K1 #Y #H elim (sex_inv_push1 … H) -H /2 width=4 by ex2_2_intro/ -qed-. - -(* Basic_2A1: includes: lreq_inv_atom2 *) -lemma seq_inv_atom2: ∀f,X. X ≡[f] ⋆ → X = ⋆. -/2 width=4 by sex_inv_atom2/ qed-. - -(* Basic_2A1: includes: lreq_inv_pair2 *) -lemma seq_inv_next2: ∀g,J,X,K2. X ≡[↑g] K2.ⓘ{J} → - ∃∃K1. K1 ≡[g] K2 & X = K1.ⓘ{J}. -#g #J #X #K2 #H -elim (sex_inv_next2 … H) -H #Z #K1 #HK12 #H1 #H2 destruct -<(ceq_ext_inv_eq … H1) -J /2 width=3 by ex2_intro/ -qed-. - -(* Basic_2A1: includes: lreq_inv_zero2 lreq_inv_succ2 *) -lemma seq_inv_push2: ∀g,J2,X,K2. X ≡[⫯g] K2.ⓘ{J2} → - ∃∃J1,K1. K1 ≡[g] K2 & X = K1.ⓘ{J1}. -#g #J2 #X #K2 #H elim (sex_inv_push2 … H) -H /2 width=4 by ex2_2_intro/ -qed-. - -(* Basic_2A1: includes: lreq_inv_pair *) -lemma seq_inv_next: ∀f,I1,I2,L1,L2. L1.ⓘ{I1} ≡[↑f] L2.ⓘ{I2} → - ∧∧ L1 ≡[f] L2 & I1 = I2. -#f #I1 #I2 #L1 #L2 #H elim (sex_inv_next … H) -H -/3 width=3 by ceq_ext_inv_eq, conj/ -qed-. - -(* Basic_2A1: includes: lreq_inv_succ *) -lemma seq_inv_push: ∀f,I1,I2,L1,L2. L1.ⓘ{I1} ≡[⫯f] L2.ⓘ{I2} → L1 ≡[f] L2. -#f #I1 #I2 #L1 #L2 #H elim (sex_inv_push … H) -H /2 width=1 by conj/ -qed-. - -lemma seq_inv_tl: ∀f,I,L1,L2. L1 ≡[⫱f] L2 → L1.ⓘ{I} ≡[f] L2.ⓘ{I}. -/2 width=1 by sex_inv_tl/ qed-. - -(* Basic_2A1: removed theorems 5: - lreq_pair_lt lreq_succ_lt lreq_pair_O_Y lreq_O2 lreq_inv_O_Y -*)