notation made half decent

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / saturations.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/saturations.ma
index b78952fdb4c6f2a0a50f394e1c47990a2742f751..cc0db526c340daecc942529fce614cc12edfa433 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/saturations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/saturations.ma
@@ -14,13 +14,11 @@
 
 include "relations.ma".
 
-definition is_saturation: ∀C:REL. unary_morphism1 (Ω \sup C) (Ω \sup C) → CProp1 ≝
- λC:REL.λA:unary_morphism1 (Ω \sup C) (Ω \sup C).
-  ∀U,V. (U ⊆ A V) = (A U ⊆ A V).
+definition is_saturation: ∀C:REL. Ω^C ⇒_1 Ω^C → CProp1 ≝
+ λC:REL.λA:Ω^C ⇒_1 Ω^C. ∀U,V. (U ⊆ A V) =_1 (A U ⊆ A V).
 
-definition is_reduction: ∀C:REL. unary_morphism1 (Ω \sup C) (Ω \sup C) → CProp1 ≝
- λC:REL.λJ:unary_morphism1 (Ω \sup C) (Ω \sup C).
-  ∀U,V. (J U ⊆ V) = (J U ⊆ J V).
+definition is_reduction: ∀C:REL. Ω^C ⇒_1 Ω^C → CProp1 ≝
+ λC:REL.λJ: Ω^C ⇒_1 Ω^C. ∀U,V. (J U ⊆ V) =_1 (J U ⊆ J V).
 
 theorem saturation_expansive: ∀C,A. is_saturation C A → ∀U. U ⊆ A U.
  intros; apply (fi ?? (i ??)); apply subseteq_refl.