reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem Th12:
  (a <> 0 or b <> 0) & c <> 0 &
  a,b,c are_mutually_coprime & a divides n & b divides n & c divides n
  implies a*b*c divides n
  proof
    assume that
A1: (a <> 0 or b <> 0) & c <> 0 and
A2: a,b,c are_mutually_coprime and
A3: a divides n & b divides n;
    a*b divides n by A2,A3,PEPIN:4;
    hence thesis by A1,A2,PEPIN:4,EULER_1:14;
  end;
