X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Frelocation%2Flex.ma;h=6ca29e5868097f6c078670cc0dc2c1dc2c976df6;hp=cc4bf1797629af644cf4211aee7360f683475da7;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma index cc4bf1797..6ca29e586 100644 --- a/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma +++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lex.ma @@ -21,7 +21,7 @@ include "static_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. + λL1,L2. ∃∃f. 𝐈❪f❫ & L1 ⪤[cfull,cext2 R,f] L2. interpretation "generic extension (local environment)" 'Relation R L1 L2 = (lex R L1 L2). @@ -42,7 +42,7 @@ 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}. + 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. @@ -59,15 +59,15 @@ qed-. (* Advanced properties ******************************************************) lemma lex_bind_refl_dx (R): c_reflexive … R → - ∀I,K1,K2. K1 ⪤[R] K2 → K1.ⓘ{I} ⪤[R] K2.ⓘ{I}. + ∀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}. +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. + K1.ⓑ[I]V1 ⪤[R] K2.ⓑ[I]V2. /3 width=1 by lex_bind, ext2_pair/ qed. (* Basic inversion lemmas ***************************************************) @@ -77,8 +77,8 @@ 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}. +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 @@ -90,8 +90,8 @@ 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}. +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 @@ -100,8 +100,8 @@ qed-. (* Advanced inversion lemmas ************************************************) -lemma lex_inv_unit_sn (R): ∀I,L2,K1. K1.ⓤ{I} ⪤[R] L2 → - ∃∃K2. K1 ⪤[R] K2 & L2 = K2.ⓤ{I}. +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 @@ -109,16 +109,16 @@ elim (ext2_inv_unit_sn … HZ2) -HZ2 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. +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}. +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 @@ -126,8 +126,8 @@ elim (ext2_inv_unit_dx … HZ1) -HZ1 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. +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 @@ -136,7 +136,7 @@ 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.ⓑ[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/ @@ -147,9 +147,9 @@ qed-. lemma lex_ind (R) (Q:relation2 …): Q (⋆) (⋆) → ( - ∀I,K1,K2. K1 ⪤[R] K2 → Q K1 K2 → Q (K1.ⓤ{I}) (K2.ⓤ{I}) + ∀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) + ∀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