let n be Nat; :: thesis: n <= Triangle n
defpred S₁[ Nat] means $1 <= Triangle $1;
A1: S₁[ 0 ] ;
A2: for k being Nat st S₁[k] holds
S₁[k + 1]

proof

let k be Nat; :: thesis: ( S₁[k] implies S₁[k + 1] )
assume S₁[k] ; :: thesis: S₁[k + 1]
Triangle (k + 1) = (Triangle k) + (k + 1) by Th10;
hence S₁[k + 1] by NAT_1:11; :: thesis: verum

end;

for n being Nat holds S₁[n] from NAT_1:sch 2(A1, A2);
hence n <= Triangle n ; :: thesis: verum