 reserve x for Real,
    p,k,l,m,n,s,h,i,j,k1,t,t1 for Nat,
    X for Subset of REAL;

theorem
  for i,j being natural Number holds i * j = 1 implies i = 1
proof
  let i,j be natural Number;
  assume
A1: i * j = 1;
  then i <> 0;
  then consider m such that
A2: i = m + 1 by Th6;
  j <> 0 by A1;
  then consider l such that
A3: j = l + 1 by Th6;
A4: m * l + m + l + 1 = 0 + 1 by A1,A2,A3;
  then m * l + m = 0;
  hence thesis by A2,A4;
end;
