reserve i for object;
reserve S for non empty ManySortedSign;
reserve D for non empty set,
  n for Nat;
reserve MS for segmental non void 1-element ManySortedSign,
  A for non-empty MSAlgebra over MS,
  h for PartFunc of (the_sort_of A)*,(the_sort_of A) ,
  x,y for FinSequence of the_sort_of A;

theorem
  for A being Universal_Algebra for f being Function of dom signature A,
  {0}* for z being Element of {0} st f = (*-->0)*signature A holds MSSign A =
  ManySortedSign(#{0},dom signature A,f,dom signature(A)-->z#)
proof
  let A be Universal_Algebra;
  let f be Function of dom signature A, {0}*;
  let z be Element of {0};
A1: the carrier' of MSSign A = dom signature A & the Arity of MSSign A = (
  *-->0) *signature A by Def8;
  z = 0 & the carrier of MSSign A = {0} by Def8,TARSKI:def 1;
  hence thesis by A1,Def8;
end;
