some work

[helm.git] / helm / software / matita / contribs / formal_topology / bin / formal_topology.ma

diff --git a/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma b/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma
index 54c5a2a0bcf2d771bd78454ce4a8c2e551b4920a..e84c0242ee8dd58a4225f9f8c10c27b2b924b73c 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma
+++ b/helm/software/matita/contribs/formal_topology/bin/formal_topology.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/formal_topologyxxx2/".
+set "baseuri" "cic:/matita/formal_topology/".
 include "logic/equality.ma".
 
 axiom S: Type.
@@ -22,8 +22,7 @@ axiom leq: S → S → Prop.
 notation "hvbox(A break ⊆ B)" with precedence 59
 for @{ 'subseteq $A $B}.
 
-interpretation "Subseteq" 'subseteq A B =
- (cic:/matita/formal_topologyxxx2/leq.con A B).
+interpretation "Subseteq" 'subseteq A B = (leq A B).
 
 axiom leq_refl: ∀A. A ⊆ A.
 axiom leq_antisym: ∀A,B. A ⊆ B → B ⊆ A → A=B.
@@ -47,8 +46,12 @@ axiom m_antimonotonia: ∀A,B. A ⊆ B → m B ⊆ m A.
 axiom m_saturazione: ∀A. A ⊆ m (m A).
 axiom m_puntofisso: ∀A. m A = m (m (m A)).
 
-lemma l1: ∀A,B. i A ⊆ B → i A ⊆ i B. intros; rewrite < i_idempotenza; auto. qed.
-lemma l2: ∀A,B. A ⊆ c B → c A ⊆ c B. intros; rewrite < c_idempotenza in ⊢ (? ? %); auto. qed.
+lemma l1: ∀A,B. i A ⊆ B → i A ⊆ i B.
+ intros; rewrite < i_idempotenza; apply (i_monotonia (i A) B H).
+qed.
+lemma l2: ∀A,B. A ⊆ c B → c A ⊆ c B.
+ intros; rewrite < c_idempotenza in ⊢ (? ? %); apply (c_monotonia A (c B) H).
+qed.
 
 axiom th1: ∀A. c (m A) ⊆ m (i A).
 axiom th2: ∀A. i (m A) ⊆ m (c A).