helm/software/matita/contribs/formal_topology/overlap/basic_topologies_to_o-basic_topologies.ma

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  14
  15 include "basic_topologies.ma".
  16 include "o-basic_topologies.ma".
  17 include "relations_to_o-algebra.ma".
  18
  19 definition o_basic_topology_of_basic_topology: basic_topology → Obasic_topology.
  20  intros (b); constructor 1;
  21   [ apply (POW' b) | apply (A b) | apply (J b);
  22   | apply (A_is_saturation b) | apply (J_is_reduction b) | apply (compatibility b) ]
  23 qed.
  24
  25 definition o_continuous_relation_of_continuous_relation:
  26  ∀BT1,BT2.continuous_relation BT1 BT2 →
  27   Ocontinuous_relation (o_basic_topology_of_basic_topology BT1) (o_basic_topology_of_basic_topology BT2).
  28  intros (BT1 BT2 c); constructor 1;
  29   [ apply (orelation_of_relation ?? c) | apply (reduced ?? c) | apply (saturated ?? c) ]
  30 qed.