reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;
reserve x1,x2,x3,x4,x5,x6,x7,x8 for object;
reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve n,k for Nat;

theorem Th74:
  not M is finite implies M+`M = M
proof
  assume not M is finite;
  then M*^succ 1 = M by Th72;
  then card M = (card 2)*`card M by Th13
    .= card (succ 1*^ M) by Th13
    .= card (1*^ M+^ M) by ORDINAL2:36
    .= M+`M by ORDINAL2:39;
  hence thesis;
end;
