reserve a, I for set,
  S for non empty non void ManySortedSign;
reserve A, M for ManySortedSet of I,
  B, C for non-empty ManySortedSet of I;

theorem Th31:
  for A being non-empty MSAlgebra over S for C being MSCongruence
of A for s being SortSymbol of S for a being Element of (the Sorts of QuotMSAlg
  (A,C)).s ex x being Element of (the Sorts of A).s st a = Class(C,x)
proof
  let A be non-empty MSAlgebra over S, C be MSCongruence of A, s be SortSymbol
  of S, a be Element of (the Sorts of QuotMSAlg (A,C)).s;
  a in (Class C).s;
  then a in Class (C.s) by MSUALG_4:def 6;
  then consider t being object such that
A1: t in (the Sorts of A).s and
A2: a = Class(C.s,t) by EQREL_1:def 3;
  reconsider t as Element of (the Sorts of A).s by A1;
  take t;
  thus thesis by A2;
end;
