reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;

theorem Th58:
  for m,n being Integer holds
  n > 0 implies n gcd m > 0
proof
  let m,n be Integer;
  assume that
A1: n>0 and
A2: n gcd m <= 0;
A3: n gcd m divides n by INT_2:def 2;
  n gcd m = 0 or n gcd m < 0 by A2;
  then ex r being Integer st n = 0*r by A3,INT_1:def 3;
  hence contradiction by A1;
end;
