X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flpr_fquq.ma;h=43589b7c581d7922d59e60fa565bccaf6215f043;hb=3bf7a0b4185dbffe5b822c907956acdbe2d1c559;hp=6c9f743cbd8e6c4c2ac6dab6c3ef41024d3e93fc;hpb=ca7327c20c6031829fade8bb84a3a1bb66113f54;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma index 6c9f743cb..43589b7c5 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma @@ -22,9 +22,9 @@ include "basic_2/rt_transition/lpr.ma". (* Properties with extended structural successor for closures ***************) -lemma fqu_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → - ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 → - ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L1❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂[b] ❪G2,L2,U2❫. +lemma fqu_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂[b] ❨G2,L2,T2❩ → + ∀U2. ❨G2,L2❩ ⊢ T2 ➡[h,0] U2 → + ∃∃L,U1. ❨G1,L1❩ ⊢ ➡[h,0] L & ❨G1,L1❩ ⊢ T1 ➡[h,0] U1 & ❨G1,L,U1❩ ⬂[b] ❨G2,L2,U2❩. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [ /3 width=5 by lpr_pair, fqu_lref_O, ex3_2_intro/ | /3 width=5 by cpr_pair_sn, fqu_pair_sn, ex3_2_intro/ @@ -37,9 +37,9 @@ lemma fqu_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G ] qed-. -lemma fqu_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → - ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 → - ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂[b] ❪G2,L2,U2❫. +lemma fqu_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂[b] ❨G2,L2,T2❩ → + ∀U2. ❨G2,L2❩ ⊢ T2 ➡[h,0] U2 → + ∃∃L,U1. ❨G1,L1❩ ⊢ ➡[h,0] L & ❨G1,L❩ ⊢ T1 ➡[h,0] U1 & ❨G1,L,U1❩ ⬂[b] ❨G2,L2,U2❩. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [ /3 width=5 by lpr_pair, fqu_lref_O, ex3_2_intro/ | /3 width=5 by cpr_pair_sn, fqu_pair_sn, ex3_2_intro/ @@ -52,9 +52,9 @@ lemma fqu_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G ] qed-. -lemma fqu_lpr_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → - ∀K2. ❪G2,L2❫ ⊢ ➡[h,0] K2 → - ∃∃K1,T. ❪G1,L1❫ ⊢ ➡[h,0] K1 & ❪G1,L1❫ ⊢ T1 ➡[h,0] T & ❪G1,K1,T❫ ⬂[b] ❪G2,K2,T2❫. +lemma fqu_lpr_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂[b] ❨G2,L2,T2❩ → + ∀K2. ❨G2,L2❩ ⊢ ➡[h,0] K2 → + ∃∃K1,T. ❨G1,L1❩ ⊢ ➡[h,0] K1 & ❨G1,L1❩ ⊢ T1 ➡[h,0] T & ❨G1,K1,T❩ ⬂[b] ❨G2,K2,T2❩. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [ /3 width=5 by lpr_bind_refl_dx, fqu_lref_O, ex3_2_intro/ | /3 width=5 by cpr_pair_sn, fqu_pair_sn, ex3_2_intro/ @@ -71,9 +71,9 @@ qed-. (* Note: does not hold in Basic_2A1 because it requires cpm *) (* Note: L1 = K0.ⓛV0 and T1 = #0 require n = 1 *) -lemma lpr_fqu_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → - ∀K1. ❪G1,K1❫ ⊢ ➡[h,0] L1 → - ∃∃n,K2,T. ❪G1,K1❫ ⊢ T1 ➡[h,n] T & ❪G1,K1,T❫ ⬂[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ➡[h,0] L2 & n ≤ 1. +lemma lpr_fqu_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂[b] ❨G2,L2,T2❩ → + ∀K1. ❨G1,K1❩ ⊢ ➡[h,0] L1 → + ∃∃n,K2,T. ❨G1,K1❩ ⊢ T1 ➡[h,n] T & ❨G1,K1,T❩ ⬂[b] ❨G2,K2,T2❩ & ❨G2,K2❩ ⊢ ➡[h,0] L2 & n ≤ 1. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 [ * #G #K #V #K1 #H elim (lpr_inv_pair_dx … H) -H #K0 #V0 #HK0 #HV0 #H destruct @@ -91,36 +91,36 @@ qed-. (* Properties with extended optional structural successor for closures ******) -lemma fquq_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ → - ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 → - ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L1❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂⸮[b] ❪G2,L2,U2❫. +lemma fquq_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩ → + ∀U2. ❨G2,L2❩ ⊢ T2 ➡[h,0] U2 → + ∃∃L,U1. ❨G1,L1❩ ⊢ ➡[h,0] L & ❨G1,L1❩ ⊢ T1 ➡[h,0] U1 & ❨G1,L,U1❩ ⬂⸮[b] ❨G2,L2,U2❩. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 cases H -H [ #HT12 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/ | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ ] qed-. -lemma fquq_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ → - ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 → - ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂⸮[b] ❪G2,L2,U2❫. +lemma fquq_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩ → + ∀U2. ❨G2,L2❩ ⊢ T2 ➡[h,0] U2 → + ∃∃L,U1. ❨G1,L1❩ ⊢ ➡[h,0] L & ❨G1,L❩ ⊢ T1 ➡[h,0] U1 & ❨G1,L,U1❩ ⬂⸮[b] ❨G2,L2,U2❩. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 cases H -H [ #HT12 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/ | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ ] qed-. -lemma fquq_lpr_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ → - ∀K2. ❪G2,L2❫ ⊢ ➡[h,0] K2 → - ∃∃K1,T. ❪G1,L1❫ ⊢ ➡[h,0] K1 & ❪G1,L1❫ ⊢ T1 ➡[h,0] T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫. +lemma fquq_lpr_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩ → + ∀K2. ❨G2,L2❩ ⊢ ➡[h,0] K2 → + ∃∃K1,T. ❨G1,L1❩ ⊢ ➡[h,0] K1 & ❨G1,L1❩ ⊢ T1 ➡[h,0] T & ❨G1,K1,T❩ ⬂⸮[b] ❨G2,K2,T2❩. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 cases H -H [ #H12 elim (fqu_lpr_trans … H12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/ | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/ ] qed-. -lemma lpr_fquq_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ → - ∀K1. ❪G1,K1❫ ⊢ ➡[h,0] L1 → - ∃∃n,K2,T. ❪G1,K1❫ ⊢ T1 ➡[h,n] T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ➡[h,0] L2 & n ≤ 1. +lemma lpr_fquq_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩ → + ∀K1. ❨G1,K1❩ ⊢ ➡[h,0] L1 → + ∃∃n,K2,T. ❨G1,K1❩ ⊢ T1 ➡[h,n] T & ❨G1,K1,T❩ ⬂⸮[b] ❨G2,K2,T2❩ & ❨G2,K2❩ ⊢ ➡[h,0] L2 & n ≤ 1. #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 cases H -H [ #H12 elim (lpr_fqu_trans … H12 … HKL1) -L1 /3 width=7 by fqu_fquq, ex4_3_intro/ | * #H1 #H2 #H3 destruct /2 width=7 by ex4_3_intro/