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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
index 9ed4a0b59..1fecc55e4 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
@@ -21,26 +21,28 @@ include "basic_2/rt_computation/csx_csx.ma".
 (* Properties with unbound context-sensitive rt-computation for terms *******)
 
 (* Basic_1: was just: sn3_intro *)
-lemma csx_intro_cpxs: ∀h,G,L,T1.
-                      (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T2❫) →
-                      ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫.
+lemma csx_intro_cpxs (h) (G) (L):
+      ∀T1. (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒[h] T2) →
+      ❪G,L❫ ⊢ ⬈*𝐒[h] T1.
 /4 width=1 by cpx_cpxs, csx_intro/ qed-.
 
 (* Basic_1: was just: sn3_pr3_trans *)
-lemma csx_cpxs_trans: ∀h,G,L,T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
-                      ∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T2❫.
+lemma csx_cpxs_trans (h) (G) (L):
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
+      ∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → ❪G,L❫ ⊢ ⬈*𝐒[h] T2.
 #h #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2
 /2 width=3 by csx_cpx_trans/
 qed-.
 
 (* Eliminators with unbound context-sensitive rt-computation for terms ******)
 
-lemma csx_ind_cpxs_teqx: ∀h,G,L. ∀Q:predicate term.
-                         (∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
-                               (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
-                         ) →
-                         ∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
-                         ∀T0. ❪G,L❫ ⊢ T1 ⬈*[h] T0 → ∀T2. T0 ≛ T2 → Q T2.
+lemma csx_ind_cpxs_teqx (h) (G) (L):
+      ∀Q:predicate term.
+      (∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
+      ∀T0. ❪G,L❫ ⊢ T1 ⬈*[h] T0 → ∀T2. T0 ≛ T2 → Q T2.
 #h #G #L #Q #IH #T1 #H @(csx_ind … H) -T1
 #T1 #HT1 #IH1 #T0 #HT10 #T2 #HT02
 @IH -IH /3 width=3 by csx_cpxs_trans, csx_teqx_trans/ -HT1 #V2 #HTV2 #HnTV2
@@ -59,11 +61,11 @@ elim (teqx_dec T1 T0) #H
 qed-.
 
 (* Basic_2A1: was: csx_ind_alt *)
-lemma csx_ind_cpxs: ∀h,G,L. ∀Q:predicate term.
-                    (∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
-                          (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
-                    ) →
-                    ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ →  Q T.
+lemma csx_ind_cpxs (h) (G) (L) (Q:predicate …):
+      (∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → Q T.
 #h #G #L #Q #IH #T #HT
 @(csx_ind_cpxs_teqx … IH … HT) -IH -HT // (**) (* full auto fails *)
 qed-.