Some renaming to avoid confusion between saturations and o_saturations.

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
index bd4e187777fb9635dc3349b9a32a6ffb2596deec..a1c83e70969009a9aabbd3338cdc6a612a30837f 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
@@ -15,29 +15,29 @@
 include "o-algebra.ma".
 
 alias symbol "eq" = "setoid1 eq".
-definition is_saturation: ∀C:OA. unary_morphism1 C C → CProp1 ≝
+definition is_o_saturation: ∀C:OA. unary_morphism1 C C → CProp1 ≝
  λC:OA.λA:unary_morphism1 C C.
   ∀U,V. (U ≤ A V) = (A U ≤ A V).
 
-definition is_reduction: ∀C:OA. unary_morphism1 C C → CProp1 ≝
+definition is_o_reduction: ∀C:OA. unary_morphism1 C C → CProp1 ≝
  λC:OA.λJ:unary_morphism1 C C.
     ∀U,V. (J U ≤ V) = (J U ≤ J V).
 
-theorem saturation_expansive: ∀C,A. is_saturation C A → ∀U. U ≤ A U.
+theorem o_saturation_expansive: ∀C,A. is_o_saturation C A → ∀U. U ≤ A U.
  intros; apply (fi ?? (i ??)); apply (oa_leq_refl C).
 qed.
 
-theorem saturation_monotone:
- ∀C,A. is_saturation C A →
+theorem o_saturation_monotone:
+ ∀C,A. is_o_saturation C A →
   ∀U,V. U ≤ V → A U ≤ A V.
  intros; apply (if ?? (i ??)); apply (oa_leq_trans C);
-  [apply V|3: apply saturation_expansive ]
+  [apply V|3: apply o_saturation_expansive ]
  assumption.
 qed.
 
-theorem saturation_idempotent: ∀C,A. is_saturation C A → ∀U. 
+theorem o_saturation_idempotent: ∀C,A. is_o_saturation C A → ∀U. 
  eq1 C (A (A U)) (A U).
  intros; apply (oa_leq_antisym C);
   [ apply (if ?? (i (A U) U)); apply (oa_leq_refl C).
-  | apply saturation_expansive; assumption]
-qed.
\ No newline at end of file
+  | apply o_saturation_expansive; assumption]
+qed.