X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flex.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flex.ma;h=0000000000000000000000000000000000000000;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hp=7e6aeae497657e6919a0c11dd56e1ce59573c18c;hpb=222044da28742b24584549ba86b1805a87def070;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lex.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex.ma deleted file mode 100644 index 7e6aeae49..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lex.ma +++ /dev/null @@ -1,162 +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/pull/pull_2.ma". -include "ground_2/pull/pull_4.ma". -include "ground_2/relocation/rtmap_uni.ma". -include "basic_2/notation/relations/relation_3.ma". -include "basic_2/syntax/cext2.ma". -include "basic_2/relocation/sex.ma". - -(* GENERIC EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS **************) - -definition lex (R): relation lenv ≝ - λL1,L2. ∃∃f. 𝐈⦃f⦄ & L1 ⪤[cfull, cext2 R, f] L2. - -interpretation "generic extension (local environment)" - 'Relation R L1 L2 = (lex R L1 L2). - -definition lex_confluent: relation (relation3 …) ≝ λR1,R2. - ∀L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 → - ∀L1. L0 ⪤[R1] L1 → ∀L2. L0 ⪤[R2] L2 → - ∃∃T. R2 L1 T1 T & R1 L2 T2 T. - -definition lex_transitive: relation (relation3 …) ≝ λR1,R2. - ∀L1,T1,T. R1 L1 T1 T → ∀L2. L1 ⪤[R1] L2 → - ∀T2. R2 L2 T T2 → R1 L1 T1 T2. - -(* Basic properties *********************************************************) - -(* Basic_2A1: was: lpx_sn_atom *) -lemma lex_atom (R): ⋆ ⪤[R] ⋆. -/2 width=3 by sex_atom, ex2_intro/ qed. - -lemma lex_bind (R): ∀I1,I2,K1,K2. K1 ⪤[R] K2 → cext2 R K1 I1 I2 → - K1.ⓘ{I1} ⪤[R] K2.ⓘ{I2}. -#R #I1 #I2 #K1 #K2 * #f #Hf #HK12 #HI12 -/3 width=3 by sex_push, isid_push, ex2_intro/ -qed. - -(* Basic_2A1: was: lpx_sn_refl *) -lemma lex_refl (R): c_reflexive … R → reflexive … (lex R). -/4 width=3 by sex_refl, ext2_refl, ex2_intro/ qed. - -lemma lex_co (R1) (R2): (∀L,T1,T2. R1 L T1 T2 → R2 L T1 T2) → - ∀L1,L2. L1 ⪤[R1] L2 → L1 ⪤[R2] L2. -#R1 #R2 #HR #L1 #L2 * /5 width=7 by sex_co, cext2_co, ex2_intro/ -qed-. - -(* Advanced properties ******************************************************) - -lemma lex_bind_refl_dx (R): c_reflexive … R → - ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓘ{I} ⪤[R] K2.ⓘ{I}. -/3 width=3 by ext2_refl, lex_bind/ qed. - -lemma lex_unit (R): ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓤ{I} ⪤[R] K2.ⓤ{I}. -/3 width=1 by lex_bind, ext2_unit/ qed. - -(* Basic_2A1: was: lpx_sn_pair *) -lemma lex_pair (R): ∀I,K1,K2,V1,V2. K1 ⪤[R] K2 → R K1 V1 V2 → - K1.ⓑ{I}V1 ⪤[R] K2.ⓑ{I}V2. -/3 width=1 by lex_bind, ext2_pair/ qed. - -(* Basic inversion lemmas ***************************************************) - -(* Basic_2A1: was: lpx_sn_inv_atom1: *) -lemma lex_inv_atom_sn (R): ∀L2. ⋆ ⪤[R] L2 → L2 = ⋆. -#R #L2 * #f #Hf #H >(sex_inv_atom1 … H) -L2 // -qed-. - -lemma lex_inv_bind_sn (R): ∀I1,L2,K1. K1.ⓘ{I1} ⪤[R] L2 → - ∃∃I2,K2. K1 ⪤[R] K2 & cext2 R K1 I1 I2 & L2 = K2.ⓘ{I2}. -#R #I1 #L2 #K1 * #f #Hf #H -lapply (sex_eq_repl_fwd … H (⫯f) ?) -H /2 width=1 by eq_push_inv_isid/ #H -elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct -/3 width=5 by ex2_intro, ex3_2_intro/ -qed-. - -(* Basic_2A1: was: lpx_sn_inv_atom2 *) -lemma lex_inv_atom_dx (R): ∀L1. L1 ⪤[R] ⋆ → L1 = ⋆. -#R #L1 * #f #Hf #H >(sex_inv_atom2 … H) -L1 // -qed-. - -lemma lex_inv_bind_dx (R): ∀I2,L1,K2. L1 ⪤[R] K2.ⓘ{I2} → - ∃∃I1,K1. K1 ⪤[R] K2 & cext2 R K1 I1 I2 & L1 = K1.ⓘ{I1}. -#R #I2 #L1 #K2 * #f #Hf #H -lapply (sex_eq_repl_fwd … H (⫯f) ?) -H /2 width=1 by eq_push_inv_isid/ #H -elim (sex_inv_push2 … H) -H #I1 #K1 #HK12 #HI12 #H destruct -/3 width=5 by ex3_2_intro, ex2_intro/ -qed-. - -(* Advanced inversion lemmas ************************************************) - -lemma lex_inv_unit_sn (R): ∀I,L2,K1. K1.ⓤ{I} ⪤[R] L2 → - ∃∃K2. K1 ⪤[R] K2 & L2 = K2.ⓤ{I}. -#R #I #L2 #K1 #H -elim (lex_inv_bind_sn … H) -H #Z2 #K2 #HK12 #HZ2 #H destruct -elim (ext2_inv_unit_sn … HZ2) -HZ2 -/2 width=3 by ex2_intro/ -qed-. - -(* Basic_2A1: was: lpx_sn_inv_pair1 *) -lemma lex_inv_pair_sn (R): ∀I,L2,K1,V1. K1.ⓑ{I}V1 ⪤[R] L2 → - ∃∃K2,V2. K1 ⪤[R] K2 & R K1 V1 V2 & L2 = K2.ⓑ{I}V2. -#R #I #L2 #K1 #V1 #H -elim (lex_inv_bind_sn … H) -H #Z2 #K2 #HK12 #HZ2 #H destruct -elim (ext2_inv_pair_sn … HZ2) -HZ2 #V2 #HV12 #H destruct -/2 width=5 by ex3_2_intro/ -qed-. - -lemma lex_inv_unit_dx (R): ∀I,L1,K2. L1 ⪤[R] K2.ⓤ{I} → - ∃∃K1. K1 ⪤[R] K2 & L1 = K1.ⓤ{I}. -#R #I #L1 #K2 #H -elim (lex_inv_bind_dx … H) -H #Z1 #K1 #HK12 #HZ1 #H destruct -elim (ext2_inv_unit_dx … HZ1) -HZ1 -/2 width=3 by ex2_intro/ -qed-. - -(* Basic_2A1: was: lpx_sn_inv_pair2 *) -lemma lex_inv_pair_dx (R): ∀I,L1,K2,V2. L1 ⪤[R] K2.ⓑ{I}V2 → - ∃∃K1,V1. K1 ⪤[R] K2 & R K1 V1 V2 & L1 = K1.ⓑ{I}V1. -#R #I #L1 #K2 #V2 #H -elim (lex_inv_bind_dx … H) -H #Z1 #K1 #HK12 #HZ1 #H destruct -elim (ext2_inv_pair_dx … HZ1) -HZ1 #V1 #HV12 #H destruct -/2 width=5 by ex3_2_intro/ -qed-. - -(* Basic_2A1: was: lpx_sn_inv_pair *) -lemma lex_inv_pair (R): ∀I1,I2,L1,L2,V1,V2. - L1.ⓑ{I1}V1 ⪤[R] L2.ⓑ{I2}V2 → - ∧∧ L1 ⪤[R] L2 & R L1 V1 V2 & I1 = I2. -#R #I1 #I2 #L1 #L2 #V1 #V2 #H elim (lex_inv_pair_sn … H) -H -#L0 #V0 #HL10 #HV10 #H destruct /2 width=1 by and3_intro/ -qed-. - -(* Basic eliminators ********************************************************) - -lemma lex_ind (R) (Q:relation2 …): - Q (⋆) (⋆) → - ( - ∀I,K1,K2. K1 ⪤[R] K2 → Q K1 K2 → Q (K1.ⓤ{I}) (K2.ⓤ{I}) - ) → ( - ∀I,K1,K2,V1,V2. K1 ⪤[R] K2 → Q K1 K2 → R K1 V1 V2 →Q (K1.ⓑ{I}V1) (K2.ⓑ{I}V2) - ) → - ∀L1,L2. L1 ⪤[R] L2 → Q L1 L2. -#R #Q #IH1 #IH2 #IH3 #L1 #L2 * #f @pull_2 #H -elim H -f -L1 -L2 // #f #I1 #I2 #K1 #K2 @pull_4 #H -[ elim (isid_inv_next … H) -| lapply (isid_inv_push … H ??) -] -H [5:|*: // ] #Hf @pull_2 #H -elim H -H /3 width=3 by ex2_intro/ -qed-.