some notation for map_arrows2

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma
index ce6c6f110ac571e7483bd9d51151eac80974783b..4cbca05303ec7d6bd03389a94d4da28d182cd0d4 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma
@@ -18,19 +18,12 @@ include "relations_to_o-algebra.ma".
 
 (* These are only conversions :-) *)
 
-definition o_operator_of_operator:
- ∀C:REL. (Ω \sup C => Ω \sup C) → (SUBSETS C ⇒ SUBSETS C).
- intros;apply t;
-qed.
+definition o_operator_of_operator: ∀C:REL. (Ω^C ⇒_1 Ω^C) → ((POW C) ⇒_1 (POW C)) ≝ λC,t.t.
 
-definition is_o_saturation_of_is_saturation:
- ∀C:REL.∀R: unary_morphism1 (Ω \sup C) (Ω \sup C).
-  is_saturation ? R → is_o_saturation ? (o_operator_of_operator ? R).
- intros; apply i;
-qed.
+definition is_o_saturation_of_is_saturation: 
+  ∀C:REL.∀R: Ω^C ⇒_1 Ω^C. is_saturation ? R → is_o_saturation ? (o_operator_of_operator ? R).
+intros (C R i); apply i; qed.
 
-definition is_o_reduction_of_is_reduction:
- ∀C:REL.∀R: unary_morphism1 (Ω \sup C) (Ω \sup C).
-  is_reduction ? R → is_o_reduction ? (o_operator_of_operator ? R).
- intros; apply i;
-qed.
\ No newline at end of file
+definition is_o_reduction_of_is_reduction: 
+  ∀C:REL.∀R: Ω^C ⇒_1 Ω^C.is_reduction ? R → is_o_reduction ? (o_operator_of_operator ? R).
+intros (C R i); apply i; qed.