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 Th33:
  l >= 1 implies k*l >= k
proof
  assume
A1: l>=1;
  for k holds k*l>=k
  proof
    defpred P[Nat] means $1*l>=$1;
A2: for k st P[k] holds P[k+1]
    proof
      let k;
A3:   (k + 1)*l = k * l + 1*l;
A4:   k+l>=k+1 by A1,XREAL_1:7;
      assume k*l>=k;
      then (k+1)*l>=k+l by A3,XREAL_1:7;
      hence (k+1)*l>=k+1 by A4,XXREAL_0:2;
    end;
A5: P[0];
    thus for k holds P[k] from NAT_1:sch 2(A5,A2);
  end;
  hence thesis;
end;
