X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flpr_fquq.ma;h=031de39f82e155b30d7a92099069cfaf3669b5f8;hp=e1256efc58a5db1ad1487e72d92e05f41958437e;hb=f308429a0fde273605a2330efc63268b4ac36c99;hpb=87f57ddc367303c33e19c83cd8989cd561f3185b 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 e1256efc5..031de39f8 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] U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] 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] U2 → + ∃∃L,U1. ⦃G1,L1⦄ ⊢ ➡[h] L & ⦃G1,L1⦄ ⊢ T1 ➡[h] 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] ] 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] U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h] L & ⦃G1, L⦄ ⊢ T1 ➡[h] 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] U2 → + ∃∃L,U1. ⦃G1,L1⦄ ⊢ ➡[h] L & ⦃G1,L⦄ ⊢ T1 ➡[h] 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] ] qed-. -lemma fqu_lpr_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → - ∀K2. ⦃G2, L2⦄ ⊢ ➡[h] K2 → - ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h] 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] K2 → + ∃∃K1,T. ⦃G1,L1⦄ ⊢ ➡[h] K1 & ⦃G1,L1⦄ ⊢ T1 ➡[h] 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] L1 → - ∃∃n,K2,T. ⦃G1, K1⦄ ⊢ T1 ➡[n, h] T & ⦃G1, K1, T⦄ ⊐[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h] 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] L1 → + ∃∃n,K2,T. ⦃G1,K1⦄ ⊢ T1 ➡[n,h] T & ⦃G1,K1,T⦄ ⊐[b] ⦃G2,K2,T2⦄ & ⦃G2,K2⦄ ⊢ ➡[h] 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] U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] 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] U2 → + ∃∃L,U1. ⦃G1,L1⦄ ⊢ ➡[h] L & ⦃G1,L1⦄ ⊢ T1 ➡[h] 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] U2 → - ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h] L & ⦃G1, L⦄ ⊢ T1 ➡[h] 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] U2 → + ∃∃L,U1. ⦃G1,L1⦄ ⊢ ➡[h] L & ⦃G1,L⦄ ⊢ T1 ➡[h] 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] K2 → - ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h] 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] K2 → + ∃∃K1,T. ⦃G1,L1⦄ ⊢ ➡[h] K1 & ⦃G1,L1⦄ ⊢ T1 ➡[h] 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] L1 → - ∃∃n,K2,T. ⦃G1, K1⦄ ⊢ T1 ➡[n, h] T & ⦃G1, K1, T⦄ ⊐⸮[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h] 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] L1 → + ∃∃n,K2,T. ⦃G1,K1⦄ ⊢ T1 ➡[n,h] T & ⦃G1,K1,T⦄ ⊐⸮[b] ⦃G2,K2,T2⦄ & ⦃G2,K2⦄ ⊢ ➡[h] 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/