reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve p for Prime;

theorem Th5:
  a/b*c is natural & b <> 0 & a,b are_coprime implies
   ex d being Nat st c = b*d
  proof
    assume a/b*c is natural;
    then reconsider n = a/b*c as Nat;
    assume that
A1: b <> 0 and
A2: a,b are_coprime;
    n*b = a/b*b*c
    .= a*c by A1,XCMPLX_1:87;
    then b divides a*c;
    then b divides c by A2,EULER_1:13;
    hence thesis;
  end;
