reserve S for OrderSortedSign;
reserve S for OrderSortedSign,
  X for ManySortedSet of S,
  o for OperSymbol of S ,
  b for Element of ([:the carrier' of S,{the carrier of S}:] \/ Union (coprod X
  ))*;
reserve x for set;

theorem Th43:
  for S be locally_directed regular monotone OrderSortedSign, X
be non-empty ManySortedSet of S, t1 be Element of TS DTConOSA(X) holds (PTMin X
  ).((PTMin X).t1) = (PTMin X).t1
proof
  let S be locally_directed regular monotone OrderSortedSign, X be non-empty
  ManySortedSet of S, t1 be Element of TS DTConOSA(X);
  (PTMin X).t1 in OSClass(PTCongruence(X),t1) by Th40;
  hence thesis by Th42;
end;
