
theorem Th27:
  for S1,S2 being non void non empty ManySortedSign for A1 being
non-empty MSAlgebra over S1, A2 being non-empty MSAlgebra over S2 st the Sorts
  of A1 tolerates the Sorts of A2 for o being OperSymbol of S1+*S2, o2 being
  OperSymbol of S2 st o = o2 holds Den(o, A1+*A2) = Den(o2, A2)
proof
  let S1,S2 be non void non empty ManySortedSign;
  let A1 be non-empty MSAlgebra over S1, A2 be non-empty MSAlgebra over S2;
A1: dom the Charact of A2 = the carrier' of S2 by PARTFUN1:def 2;
  assume the Sorts of A1 tolerates the Sorts of A2;
  then
A2: the Charact of A1+*A2 = (the Charact of A1)+*the Charact of A2 by Def4;
  let o be OperSymbol of S1+*S2, o2 be OperSymbol of S2;
  assume o = o2;
  hence thesis by A2,A1,FUNCT_4:13;
end;
