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;

theorem Th36:
  for S1, S2 being non empty ManySortedSign for f, g being Function
  for C1 being non-empty MSAlgebra over S1
  for C2 being non-empty MSAlgebra over S2 st C1, C2 are_similar_wrt f, g
  holds S1, S2 are_equivalent_wrt f, g
proof
  let S1, S2 be non empty ManySortedSign;
  let f,g be Function;
  let C1 be non-empty MSAlgebra over S1;
  let C2 be non-empty MSAlgebra over S2;
  assume that
A1: f is one-to-one and
A2: g is one-to-one and
A3: f, g form_morphism_between S1, S2 and the Sorts of C1 = (the Sorts of C2)*f
  and the Charact of C1 = (the Charact of C2)*g
  and f" is one-to-one
  and g" is one-to-one and
A4: f", g" form_morphism_between S2, S1;
  thus thesis by A1,A2,A3,A4;
end;
