reserve a,b,c,k,l,m,n for Nat,
  i,j,x,y for Integer;

theorem Th5:
  a gcd b = 1 implies for c holds a*c gcd b*c = c
proof
  assume
A1: a gcd b = 1;
  let m;
  reconsider a9 = a, b9 = b as Integer;
  a9,b9 are_coprime by A1,INT_2:def 3;
  hence a*m gcd b*m = |.|.m.|.| by INT_2:24
    .= m by ABSVALUE:def 1;
end;
