theorem
  for G being Circuit-like non void non empty ManySortedSign
  for C being non-empty Circuit of G st X, A specifies C
  for f being SortMap of X, A, C
  for s being State of C, t being Term of S,V st t in Subtrees X
  holds Following(s, 1+height dom t) is_stable_at f.t &
  for s9 being State of X-Circuit A st s9 = s*f
  for h being CompatibleValuation of s9
  holds Following(s, 1+height dom t).(f.t) = t@(h, A)
proof
  let G be Circuit-like non void non empty ManySortedSign;
  let C be non-empty Circuit of G;
  assume X, A specifies C;
  then C calculates X, A by Th58;
  hence thesis by Th59;
end;
