
theorem Th59:
  for S1,S2 being non empty ManySortedSign for A1 being MSAlgebra
over S1, A2 being MSAlgebra over S2 st A1 is Boolean & A2 is Boolean holds the
  Sorts of A1 tolerates the Sorts of A2
proof
  let S1,S2 be non empty ManySortedSign;
  let A1 be MSAlgebra over S1, A2 be MSAlgebra over S2;
  assume that
A1: A1 is Boolean and
A2: A2 is Boolean;
A3: the Sorts of A2 = (the carrier of S2) --> BOOLEAN by A2,Th57;
  the Sorts of A1 = (the carrier of S1) --> BOOLEAN by A1,Th57;
  hence thesis by A3,FUNCOP_1:87;
end;
