reserve S for non empty non void ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S,
  A for non-empty MSAlgebra over S,
  X for non empty Subset of S-Terms V,
  t for Element of X;
reserve S for non empty non void ManySortedSign,
  A for non-empty finite-yielding MSAlgebra over S,
  V for Variables of A,
  X for SetWithCompoundTerm of S,V;
reserve G1, G2 for Circuit-like non void non empty ManySortedSign,
  f, g for Function,
  C1 for non-empty Circuit of G1,
  C2 for non-empty Circuit of G2;

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;
