X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffeqg_feqg.ma;h=1d0e4e38ff6240aacfee93fa0d18fbf64d37de34;hb=e0c91d8a4422da0b39aca790e5826dc8a617b303;hp=7a3339a88fc2fc2efcbf6c8e45c627e8f9728d2f;hpb=e23331eef5817eaa6c5e1c442d1d6bbb18650573;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/static_2/static/feqg_feqg.ma b/matita/matita/contribs/lambdadelta/static_2/static/feqg_feqg.ma index 7a3339a88..1d0e4e38f 100644 --- a/matita/matita/contribs/lambdadelta/static_2/static/feqg_feqg.ma +++ b/matita/matita/contribs/lambdadelta/static_2/static/feqg_feqg.ma @@ -28,7 +28,7 @@ qed-. lemma feqg_dec (S): (∀s1,s2. Decidable … (S s1 s2)) → - ∀G1,G2,L1,L2,T1,T2. Decidable (❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫). + ∀G1,G2,L1,L2,T1,T2. Decidable (❨G1,L1,T1❩ ≛[S] ❨G2,L2,T2❩). #S #HS #G1 #G2 #L1 #L2 #T1 #T2 elim (eq_genv_dec G1 G2) #HnG destruct [ elim (reqg_dec … HS L1 L2 T1) #HnL @@ -53,20 +53,20 @@ qed-. theorem feqg_canc_sn (S): reflexive … S → symmetric … S → Transitive … S → - ∀G,G1,L,L1,T,T1. ❪G,L,T❫ ≛[S] ❪G1,L1,T1❫ → - ∀G2,L2,T2. ❪G,L,T❫ ≛[S] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫. + ∀G,G1,L,L1,T,T1. ❨G,L,T❩ ≛[S] ❨G1,L1,T1❩ → + ∀G2,L2,T2. ❨G,L,T❩ ≛[S] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T2❩. /3 width=5 by feqg_trans, feqg_sym/ qed-. theorem feqg_canc_dx (S): reflexive … S → symmetric … S → Transitive … S → - ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ → - ∀G2,L2,T2. ❪G2,L2,T2❫ ≛[S] ❪G,L,T❫ → ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫. + ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≛[S] ❨G,L,T❩ → + ∀G2,L2,T2. ❨G2,L2,T2❩ ≛[S] ❨G,L,T❩ → ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T2❩. /3 width=5 by feqg_trans, feqg_sym/ qed-. lemma feqg_reqg_trans (S) (G2) (L) (T2): reflexive … S → symmetric … S → Transitive … S → - ∀G1,L1,T1. ❪G1,L1,T1❫ ≛[S] ❪G2,L,T2❫ → - ∀L2. L ≛[S,T2] L2 → ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫. + ∀G1,L1,T1. ❨G1,L1,T1❩ ≛[S] ❨G2,L,T2❩ → + ∀L2. L ≛[S,T2] L2 → ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T2❩. #S #G2 #L #T2 #H1S #H2S #H3S #G1 #L1 #T1 #H1 #L2 #HL2 /4 width=5 by feqg_trans, feqg_intro_sn, teqg_refl/ qed-. @@ -76,7 +76,7 @@ qed-. (* Basic_2A1: uses: feqg_tneqg_repl_dx *) lemma feqg_tneqg_trans (S) (G1) (G2) (L1) (L2) (T): reflexive … S → symmetric … S → Transitive … S → - ∀T1. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T❫ → + ∀T1. ❨G1,L1,T1❩ ≛[S] ❨G2,L2,T❩ → ∀T2. (T ≛[S] T2 → ⊥) → (T1 ≛[S] T2 → ⊥). #S #G1 #G2 #L1 #L2 #T #H1S #H2S #H3S #T1 #H1 #T2 #HnT2 #HT12 elim (feqg_inv_gen_sn … H1) -H1 #_ #_ #HnT1 -G1 -G2 -L1 -L2