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[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpr_fquq.ma

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 e1256efc58a5db1ad1487e72d92e05f41958437e..031de39f82e155b30d7a92099069cfaf3669b5f8 100644 (file)
--- 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/