theorem
  for l being Element of NAT holds SUCC(l,STC N) = {l, NextLoc(l,STC N)}
proof
  let l be Element of NAT;
  set M = STC N;
  consider k being Nat such that
A1: l = il.(M,k) by Th6;
A2: k = locnum(l,M) by A1,Def5;
  thus SUCC(l,STC N) = {k,k+1} by A1,Th17,AMISTD_1:8
    .= {k,il.(M,k+1)} by Th17
    .= {l, NextLoc(l,STC N)} by A1,A2,Th17;
end;
