let n be Nat; :: thesis: n '*' (1. F_Complex) = n
defpred S₁[ Nat] means $1 '*' (1. F_Complex) = $1;
0 '*' (1. F_Complex) = 0. F_Complex by Th58;
then A1: S₁[ 0 ] by COMPLFLD:def 1;

A2: now :: thesis: for k being Nat st S₁[k] holds
S₁[k + 1]

let k be Nat; :: thesis: ( S₁[k] implies S₁[k + 1] )
assume A3: S₁[k] ; :: thesis: S₁[k + 1]
reconsider kk = k as Nat ;
(kk + 1) '*' (1. F_Complex) = (kk '*' (1. F_Complex)) + (1. F_Complex) by Lm5
.= kk + 1 by A3, COMPLFLD:def 1 ;
hence S₁[k + 1] ; :: thesis: verum

end;

for k being Nat holds S₁[k] from NAT_1:sch 2(A1, A2);
hence n '*' (1. F_Complex) = n ; :: thesis: verum