reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th4:
  A c= B & C c= D implies A * C c= B * D
proof
  assume
A1: A c= B & C c= D;
  let x be object;
  assume x in A * C;
  then ex a,c st x = a * c & a in A & c in C;
  hence thesis by A1;
end;
