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[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_equivalence / cpcs_lprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma
index 3564a480a1ab5c769c29f6f5a8fd7227c94af943..6da444ce16f119823f85eba2942f9cbd7fb66e82 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma
@@ -19,20 +19,20 @@ include "basic_2/rt_equivalence/cpcs_cprs.ma".
 
 (* Properties with parallel r-computation for full local environments *******)
 
-lemma lpr_cpcs_trans (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 →
-                              ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌*[h] T2 → ⦃G, L1⦄ ⊢ T1 ⬌*[h] T2.
+lemma lpr_cpcs_trans (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ➡[h] L2 →
+                              ∀T1,T2. ⦃G,L2⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L1⦄ ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H
  /4 width=5 by cprs_div, lpr_cpms_trans/
 qed-.
 
-lemma lprs_cpcs_trans (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 →
-                               ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌*[h] T2 → ⦃G, L1⦄ ⊢ T1 ⬌*[h] T2.
+lemma lprs_cpcs_trans (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ➡*[h] L2 →
+                               ∀T1,T2. ⦃G,L2⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L1⦄ ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H
 /4 width=5 by cprs_div, lprs_cpms_trans/
 qed-.
 
-lemma lprs_cprs_conf (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 →
-                              ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[h] T2 → ⦃G, L2⦄ ⊢ T1 ⬌*[h] T2.
+lemma lprs_cprs_conf (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ➡*[h] L2 →
+                              ∀T1,T2. ⦃G,L1⦄ ⊢ T1 ➡*[h] T2 → ⦃G,L2⦄ ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #HT12 elim (lprs_cprs_conf_dx … HT12 … HL12) -L1
 /2 width=3 by cprs_div/
 qed-.
@@ -40,23 +40,23 @@ qed-.
 (* Basic_1: was: pc3_wcpr0_t *)
 (* Basic_1: note: pc3_wcpr0_t should be renamed *)
 (* Note: alternative proof /3 width=5 by lprs_cprs_conf, lpr_lprs/ *)
-lemma lpr_cprs_conf (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 →
-                             ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[h] T2 → ⦃G, L2⦄ ⊢ T1 ⬌*[h] T2.
+lemma lpr_cprs_conf (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ➡[h] L2 →
+                             ∀T1,T2. ⦃G,L1⦄ ⊢ T1 ➡*[h] T2 → ⦃G,L2⦄ ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #HT12 elim (cprs_lpr_conf_dx … HT12 … HL12) -L1
 /2 width=3 by cprs_div/
 qed-.
 
 (* Basic_1: was only: pc3_pr0_pr2_t *)
 (* Basic_1: note: pc3_pr0_pr2_t should be renamed *)
-lemma lpr_cpr_conf (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 →
-                            ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h] T2 → ⦃G, L2⦄ ⊢ T1 ⬌*[h] T2.
+lemma lpr_cpr_conf (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ➡[h] L2 →
+                            ∀T1,T2. ⦃G,L1⦄ ⊢ T1 ➡[h] T2 → ⦃G,L2⦄ ⊢ T1 ⬌*[h] T2.
 /3 width=5 by lpr_cprs_conf, cpm_cpms/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
 (* Note: there must be a proof suitable for lfpr *)
-lemma cpcs_inv_abst_sn (h) (G) (L): ∀p1,p2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{p1}W1.T1 ⬌*[h] ⓛ{p2}W2.T2 →
-                                    ∧∧ ⦃G, L⦄ ⊢ W1 ⬌*[h] W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬌*[h] T2 & p1 = p2.
+lemma cpcs_inv_abst_sn (h) (G) (L): ∀p1,p2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ ⓛ{p1}W1.T1 ⬌*[h] ⓛ{p2}W2.T2 →
+                                    ∧∧ ⦃G,L⦄ ⊢ W1 ⬌*[h] W2 & ⦃G,L.ⓛW1⦄ ⊢ T1 ⬌*[h] T2 & p1 = p2.
 #h #G #L #p1 #p2 #W1 #W2 #T1 #T2 #H
 elim (cpcs_inv_cprs … H) -H #T #H1 #H2
 elim (cpms_inv_abst_sn … H1) -H1 #W0 #T0 #HW10 #HT10 #H destruct
@@ -66,8 +66,8 @@ lapply (lprs_cpcs_trans … (L.ⓛW1) … HT2) /2 width=1 by lprs_pair/ -HT2 #HT
 /4 width=3 by and3_intro, cprs_div, cpcs_cprs_div, cpcs_sym/
 qed-.
 
-lemma cpcs_inv_abst_dx (h) (G) (L): ∀p1,p2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{p1}W1.T1 ⬌*[h] ⓛ{p2}W2.T2 →
-                                   ∧∧ ⦃G, L⦄ ⊢ W1 ⬌*[h] W2 & ⦃G, L.ⓛW2⦄ ⊢ T1 ⬌*[h] T2 & p1 = p2.
+lemma cpcs_inv_abst_dx (h) (G) (L): ∀p1,p2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ ⓛ{p1}W1.T1 ⬌*[h] ⓛ{p2}W2.T2 →
+                                   ∧∧ ⦃G,L⦄ ⊢ W1 ⬌*[h] W2 & ⦃G,L.ⓛW2⦄ ⊢ T1 ⬌*[h] T2 & p1 = p2.
 #h #G #L #p1 #p2 #W1 #W2 #T1 #T2 #HT12 lapply (cpcs_sym … HT12) -HT12
 #HT12 elim (cpcs_inv_abst_sn … HT12) -HT12 /3 width=1 by cpcs_sym, and3_intro/
 qed-.