defpred S₁[ Nat] means ( not m is empty implies 2 |^ m is even );
A1: for k being Nat st S₁[k] holds
S₁[k + 1]

let k be Nat; :: thesis:
assume that
S₁[k] and
not k + 1 is empty ; :: thesis:
2 |^ (k + 1) = 2 * (2 |^ k) by NEWTON:6;
hence 2 |^ (k + 1) is even ; :: thesis:

end;