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 Th23:
  s >= 1 implies s choose 1 = s
proof
A0: s is Nat by TARSKI:1;
  defpred P[Nat] means $1 choose 1 = $1;
A1: now
    let n be Nat;
    assume that
    n>=1 and
A2: P[n];
    (n+1) choose 1 = (n+1) choose (0+1) .= n + n choose 0 by A2,Th22
      .= n+1 by Th19;
    hence P[n+1];
  end;
A3: P[1] by Th21;
  for n be Nat st n >= 1 holds P[n] from NAT_1:sch 8(A3,A1);
  hence thesis by A0;
end;
