for m, n being Nat st m,n are_coprime holds
ex k being Nat st
( ex i0, j0 being Integer st
( k = (i0 * m) + (j0 * n) & k > 0 ) & ( for l being Nat st ex i, j being Integer st
( l = (i * m) + (j * n) & l > 0 ) holds
k <= l ) )