
theorem Th35:
  for C being para-functional category
  for a,b being Object of C st <^a,b^> <> {} for f being Morphism of a,b
  holds dom f = the_carrier_of a & rng f c= the_carrier_of b
proof
  let C be para-functional category;
  let a,b be Object of C such that
A1: <^a,b^> <> {};
  let f be Morphism of a,b;
A2: <^a,b^> c= Funcs(the_carrier_of a, the_carrier_of b) by Th33;
  f in <^a,b^> by A1;
  hence thesis by A2,FUNCT_2:92;
end;
