
theorem Th45:
  for C1,C2 being 1-sorted, M being BimapStr over C1,C2
  st M is Contravariant onto holds M is coreflexive
proof
  let C1,C2 be 1-sorted;
  let M be BimapStr over C1,C2;
  assume
A1: M is Contravariant onto;
  then the ObjectMap of M is Contravariant;
  then consider f being Function of the carrier of C1, the carrier of C2
  such that
A2: the ObjectMap of M = ~[:f,f:];
  the ObjectMap of M is onto by A1;
  then [:f,f:] is onto by A2,Th13;
  then
A3: f is onto by Th4;
  (the ObjectMap of M).:id the carrier of C1
  = [:f,f:].:id the carrier of C1 by A2,Th3;
  hence
  id the carrier of C2 c= (the ObjectMap of M).:id the carrier of C1
  by A3,Th11;
end;
