let i be Nat; :: thesis: 0 <= i
defpred S₁[ Nat] means 0 <= $1;
A1: S₁[ 0 ] ;
A2: for n being Nat st S₁[n] holds
S₁[n + 1] ;
for k being Nat holds S₁[k] from NAT_1:sch 2(A1, A2);
hence 0 <= i ; :: thesis: verum