reserve X for set;

theorem Th68:
  for a,b,c being Nat
  st b<>0 & b divides c & a*b,c are_coprime
  holds b=1
proof
  let a,b,c be Nat;
  assume b<>0;
  assume A1: b divides c;
  assume A2: a*b,c are_coprime;
  b divides a*b by INT_1:def 3;
  then b divides (a*b gcd c) by A1,INT_2:22;
  then b divides 1 by A2, INT_2:def 3;
  hence b=1 by INT_2:13;
end;
