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 Th60:
  for G being Circuit-like non void non empty ManySortedSign
  for C being non-empty Circuit of G st C calculates X, A
  for t being Term of S,V st t in Subtrees X ex v being Vertex of G st
  for s being State of C holds Following(s, 1+height dom t) is_stable_at v &
  ex f being SortMap of X, A, C st
  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).v = t@(h, A)
proof
  let G be Circuit-like non void non empty ManySortedSign;
  let C be non-empty Circuit of G;
  assume
A1: C calculates X, A;
  then consider f, g such that
A2: f, g form_embedding_of X-Circuit A, C and
A3: f preserves_inputs_of X-CircuitStr, G;
  reconsider f as SortMap of X, A, C by A1,A2,A3,Def17;
  let t be Term of S,V such that
A4: t in Subtrees X;
A5: f, g form_morphism_between X-CircuitStr, G by A2;
  reconsider t9 = t as Vertex of X-CircuitStr by A4;
  reconsider v = f.t9 as Vertex of G by A5,Th30;
  take v;
  let s be State of C;
  thus Following(s, 1+height dom t) is_stable_at v by A1,Th59;
  take f;
  thus thesis by A1,Th59;
end;
