X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbs_feqg.ma;h=3d39cebebb0ebf851e9443523360e691ede1cc0e;hb=b0c6bbd5db69489a5ebd1b36de6685fa6de441b3;hp=6c92352e45ec8218c5b1de3cc52eb793acdf4c90;hpb=e23331eef5817eaa6c5e1c442d1d6bbb18650573;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_feqg.ma index 6c92352e4..3d39cebeb 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_feqg.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_feqg.ma @@ -23,31 +23,31 @@ include "basic_2/rt_computation/fpbs_fqup.ma". (* Basic_2A1: uses: lleq_fpbs fleq_fpbs *) lemma feqg_fpbs (S) (G1) (G2) (L1) (L2) (T1) (T2): reflexive … S → symmetric … S → - ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫. + ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩. /3 width=5 by fpb_fpbs, feqg_fpb/ qed. (* Basic_2A1: uses: fpbs_lleq_trans *) lemma fpbs_feqg_trans (S) (G) (L) (T): reflexive … S → symmetric … S → - ∀G1,L1,T1. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ → - ∀G2,L2,T2. ❪G,L,T❫ ≛[S] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫. + ∀G1,L1,T1. ❨G1,L1,T1❩ ≥ ❨G,L,T❩ → + ∀G2,L2,T2. ❨G,L,T❩ ≛[S] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩. /3 width=9 by fpbs_strap1, feqg_fpb/ qed-. (* Basic_2A1: uses: lleq_fpbs_trans *) lemma feqg_fpbs_trans (S) (G) (L) (T): reflexive … S → symmetric … S → - ∀G2,L2,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → - ∀G1,L1,T1. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫. + ∀G2,L2,T2. ❨G,L,T❩ ≥ ❨G2,L2,T2❩ → + ∀G1,L1,T1. ❨G1,L1,T1❩ ≛[S] ❨G,L,T❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩. /3 width=5 by fpbs_strap2, feqg_fpb/ qed-. lemma teqg_fpbs_trans (S) (T): reflexive … S → symmetric … S → ∀T1. T1 ≛[S] T → - ∀G1,G2,L1,L2,T2. ❪G1,L1,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫. + ∀G1,G2,L1,L2,T2. ❨G1,L1,T❩ ≥ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩. /3 width=8 by feqg_fpbs_trans, teqg_feqg/ qed-. lemma fpbs_teqg_trans (S) (T): reflexive … S → symmetric … S → - ∀G1,G2,L1,L2,T1. ❪G1,L1,T1❫ ≥ ❪G2,L2,T❫ → - ∀T2. T ≛[S] T2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫. + ∀G1,G2,L1,L2,T1. ❨G1,L1,T1❩ ≥ ❨G2,L2,T❩ → + ∀T2. T ≛[S] T2 → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩. /3 width=8 by fpbs_feqg_trans, teqg_feqg/ qed-.