
theorem
  for S1,S2 being non empty ManySortedSign for A,B being MSAlgebra over
  S2 st the MSAlgebra of A = the MSAlgebra of B for f,g being Function st f,g
  form_morphism_between S1,S2 holds A|(S1,f,g) = B|(S1,f,g)
proof
  let S1,S2 be non empty ManySortedSign;
  let A,B be MSAlgebra over S2 such that
A1: the MSAlgebra of A = the MSAlgebra of B;
  let f,g be Function;
  assume
A2: f,g form_morphism_between S1,S2;
  then
  the Sorts of A|(S1,f,g) = (the Sorts of A)*f & the Charact of A|(S1,f,g)
  = ( the Charact of A)*g by Def3;
  hence thesis by A1,A2,Def3;
end;
