reserve S for non empty non void ManySortedSign,
  A for MSAlgebra over S;
reserve A for non-empty MSAlgebra over S;
reserve S for non empty non void ManySortedSign,
  A for non-empty MSAlgebra over S,
  R for ManySortedRelation of the Sorts of A;

theorem Th37:
  InvCl StabCl R = TRS R
proof
A1: StabCl R c= InvCl StabCl R by Def11;
  R c= TRS R by Def13;
  then StabCl R c= TRS R by Def12;
  then
A2: InvCl StabCl R c= TRS R by Def11;
A3: InvCl StabCl R is invariant stable ManySortedRelation of A by Th30;
  R c= StabCl R by Def12;
  then R c= InvCl StabCl R by A1,PBOOLE:13;
  then TRS R c= InvCl StabCl R by A3,Def13;
  hence thesis by A2,PBOOLE:146;
end;
