reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;
reserve C for Cocartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem Th66:
  [$in1(a,b),in2(a,b)$] = id(a+b)
proof
A1: Hom(b,a+b) <> {} by Th61;
  then
A2: (id(a+b))*in2(a,b) = in2(a,b) by CAT_1:28;
A3: Hom(a,a+b) <> {} by Th61;
  then (id(a+b))*in1(a,b) = in1(a,b) by CAT_1:28;
  hence thesis by A3,A1,A2,Def28;
end;
