update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma
index dfbcf7e487e76635ecf64acd42010ef56c7ebc45..2f2544ad847e87e9a78c605e7b2be8f3b0a8ebcb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma
@@ -21,40 +21,45 @@ include "basic_2/rt_computation/csx_gcr.ma".
 
 (* Main properties with atomic arity assignment *****************************)
 
-theorem aaa_csx: ∀h,G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+theorem aaa_csx (h) (G) (L):
+        ∀T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*𝐒[h] T.
 #h #G #L #T #A #H
 @(gcr_aaa … (csx_gcp h) (csx_gcr h) … H)
 qed.
 
 (* Advanced eliminators *****************************************************)
 
-fact aaa_ind_csx_aux: ∀h,G,L,A. ∀Q:predicate term.
-                      (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A →
-                            (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
-                      ) →
-                      ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ T ⁝ A →  Q T.
+fact aaa_ind_csx_aux (h) (G) (L):
+     ∀A. ∀Q:predicate term.
+     (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+       (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+     ) →
+     ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
 #h #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
 qed-.
 
-lemma aaa_ind_csx: ∀h,G,L,A. ∀Q:predicate term.
-                   (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A →
-                         (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
-                   ) →
-                   ∀T. ⦃G,L⦄ ⊢ T ⁝ A → Q T.
+lemma aaa_ind_csx (h) (G) (L):
+      ∀A. ∀Q:predicate term.
+      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
 
-fact aaa_ind_csx_cpxs_aux: ∀h,G,L,A. ∀Q:predicate term.
-                           (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A →
-                                 (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
-                           ) →
-                           ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ T ⁝ A →  Q T.
+fact aaa_ind_csx_cpxs_aux (h) (G) (L):
+     ∀A. ∀Q:predicate term.
+     (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+       (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+     ) →
+     ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
 #h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
 qed-.
 
 (* Basic_2A1: was: aaa_ind_csx_alt *)
-lemma aaa_ind_csx_cpxs: ∀h,G,L,A. ∀Q:predicate term.
-                        (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A →
-                              (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
-                        ) →
-                        ∀T. ⦃G,L⦄ ⊢ T ⁝ A → Q T.
+lemma aaa_ind_csx_cpxs (h) (G) (L):
+      ∀A. ∀Q:predicate term.
+      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+     ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
 /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.