reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th63:
  for i,j being Integer holds i mod j = 0 implies i div j = i / j
proof
  let i,j be Integer such that
A2: i mod j = 0;
  per cases;
  suppose
A1: j <> 0;
  i = (i div j) * j + (i mod j) by A1,INT_1:59
  .= (i div j) * j by A2;
  hence thesis by A1,XCMPLX_1:89;
  end;
  suppose j = 0;
    hence thesis by XCMPLX_1:49;
  end;
end;
