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