X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Freqx_fqus.ma;h=6f9b14b420483be25027fb6685a0048c7c529d8c;hp=462a000141d383e02a21298198a04b0d4552acb0;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma index 462a00014..6f9b14b42 100644 --- a/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma +++ b/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma @@ -21,9 +21,9 @@ include "static_2/static/reqx_reqx.ma". (* Properties with extended structural successor for closures ***************) -lemma fqu_teqx_conf: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂[b] ⦃G2,L2,T1⦄ → +lemma fqu_teqx_conf: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1❫ → ∀U2. U1 ≛ U2 → - ∃∃L,T2. ⦃G1,L1,U2⦄ ⬂[b] ⦃G2,L,T2⦄ & L2 ≛[T1] L & T1 ≛ T2. + ∃∃L,T2. ❪G1,L1,U2❫ ⬂[b] ❪G2,L,T2❫ & L2 ≛[T1] L & T1 ≛ T2. #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -G1 -G2 -L1 -L2 -U1 -T1 [ #I #G #L #W #X #H >(teqx_inv_lref1 … H) -X /2 width=5 by fqu_lref_O, ex3_2_intro/ @@ -45,18 +45,18 @@ lemma fqu_teqx_conf: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂[b] ⦃G2,L2,T1 ] qed-. -lemma teqx_fqu_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂[b] ⦃G2,L2,T1⦄ → +lemma teqx_fqu_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1❫ → ∀U2. U2 ≛ U1 → - ∃∃L,T2. ⦃G1,L1,U2⦄ ⬂[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2. + ∃∃L,T2. ❪G1,L1,U2❫ ⬂[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2. #b #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21 elim (fqu_teqx_conf … H12 U2) -H12 /3 width=5 by reqx_sym, teqx_sym, ex3_2_intro/ qed-. (* Basic_2A1: uses: lleq_fqu_trans *) -lemma reqx_fqu_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⬂[b] ⦃G2,K2,U⦄ → +lemma reqx_fqu_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂[b] ❪G2,K2,U❫ → ∀L1. L1 ≛[T] L2 → - ∃∃K1,U0. ⦃G1,L1,T⦄ ⬂[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2. + ∃∃K1,U0. ❪G1,L1,T❫ ⬂[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2. #b #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U [ #I #G #L2 #V2 #L1 #H elim (reqx_inv_zero_pair_dx … H) -H #K1 #V1 #HV1 #HV12 #H destruct @@ -80,9 +80,9 @@ qed-. (* Properties with optional structural successor for closures ***************) -lemma teqx_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂⸮[b] ⦃G2,L2,T1⦄ → +lemma teqx_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂⸮[b] ❪G2,L2,T1❫ → ∀U2. U2 ≛ U1 → - ∃∃L,T2. ⦃G1,L1,U2⦄ ⬂⸮[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2. + ∃∃L,T2. ❪G1,L1,U2❫ ⬂⸮[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2. #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -H [ #H #U2 #HU21 elim (teqx_fqu_trans … H … HU21) -U1 /3 width=5 by fqu_fquq, ex3_2_intro/ @@ -91,9 +91,9 @@ lemma teqx_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂⸮[b] ⦃G2,L2 qed-. (* Basic_2A1: was just: lleq_fquq_trans *) -lemma reqx_fquq_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⬂⸮[b] ⦃G2,K2,U⦄ → +lemma reqx_fquq_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂⸮[b] ❪G2,K2,U❫ → ∀L1. L1 ≛[T] L2 → - ∃∃K1,U0. ⦃G1,L1,T⦄ ⬂⸮[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2. + ∃∃K1,U0. ❪G1,L1,T❫ ⬂⸮[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2. #b #G1 #G2 #L2 #K2 #T #U #H elim H -H [ #H #L1 #HL12 elim (reqx_fqu_trans … H … HL12) -L2 /3 width=5 by fqu_fquq, ex3_2_intro/ | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/ @@ -103,9 +103,9 @@ qed-. (* Properties with plus-iterated structural successor for closures **********) (* Basic_2A1: was just: lleq_fqup_trans *) -lemma reqx_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⬂+[b] ⦃G2,K2,U⦄ → +lemma reqx_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂+[b] ❪G2,K2,U❫ → ∀L1. L1 ≛[T] L2 → - ∃∃K1,U0. ⦃G1,L1,T⦄ ⬂+[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2. + ∃∃K1,U0. ❪G1,L1,T❫ ⬂+[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2. #b #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U [ #G2 #K2 #U #HTU #L1 #HL12 elim (reqx_fqu_trans … HTU … HL12) -L2 /3 width=5 by fqu_fqup, ex3_2_intro/ @@ -118,9 +118,9 @@ lemma reqx_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⬂+[b] ⦃G2,K2,U⦄ ] qed-. -lemma teqx_fqup_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂+[b] ⦃G2,L2,T1⦄ → +lemma teqx_fqup_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂+[b] ❪G2,L2,T1❫ → ∀U2. U2 ≛ U1 → - ∃∃L,T2. ⦃G1,L1,U2⦄ ⬂+[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2. + ∃∃L,T2. ❪G1,L1,U2❫ ⬂+[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2. #b #G1 #G2 #L1 #L2 #U1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -U1 [ #G1 #L1 #U1 #H #U2 #HU21 elim (teqx_fqu_trans … H … HU21) -U1 /3 width=5 by fqu_fqup, ex3_2_intro/ @@ -136,9 +136,9 @@ qed-. (* Properties with star-iterated structural successor for closures **********) -lemma teqx_fqus_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂*[b] ⦃G2,L2,T1⦄ → +lemma teqx_fqus_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂*[b] ❪G2,L2,T1❫ → ∀U2. U2 ≛ U1 → - ∃∃L,T2. ⦃G1,L1,U2⦄ ⬂*[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2. + ∃∃L,T2. ❪G1,L1,U2❫ ⬂*[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2. #b #G1 #G2 #L1 #L2 #U1 #T1 #H #U2 #HU21 elim(fqus_inv_fqup … H) -H [ #H elim (teqx_fqup_trans … H … HU21) -U1 /3 width=5 by fqup_fqus, ex3_2_intro/ | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/ @@ -146,9 +146,9 @@ lemma teqx_fqus_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂*[b] ⦃G2,L2,T qed-. (* Basic_2A1: was just: lleq_fqus_trans *) -lemma reqx_fqus_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⬂*[b] ⦃G2,K2,U⦄ → +lemma reqx_fqus_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂*[b] ❪G2,K2,U❫ → ∀L1. L1 ≛[T] L2 → - ∃∃K1,U0. ⦃G1,L1,T⦄ ⬂*[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2. + ∃∃K1,U0. ❪G1,L1,T❫ ⬂*[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2. #b #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H [ #H elim (reqx_fqup_trans … H … HL12) -L2 /3 width=5 by fqup_fqus, ex3_2_intro/ | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/