reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;

theorem Th41:
  z is expression of C, s iff z in (the Sorts of Free(C, MSVars C)).s
proof
A1: dom the Sorts of Free(C, MSVars C) = the carrier of C by PARTFUN1:def 2;
  (the Sorts of Free(C, MSVars C)).s c= Union the Sorts of Free(C, MSVars C)
  by A1,CARD_5:2;
  hence thesis by Def28;
end;
