reserve S for non void non empty ManySortedSign,
  U1,U2 for MSAlgebra over S,
  o for OperSymbol of S,
  n for Nat;

theorem
  for U1,U2 being non-empty MSAlgebra over S for F be ManySortedFunction
of U1,U2 st F is_homomorphism U1,U2 ex G be ManySortedFunction of U1,Image F st
  F = G & G is_epimorphism U1,Image F
proof
  let U1,U2 be non-empty MSAlgebra over S;
  let F be ManySortedFunction of U1,U2;
  assume
A1: F is_homomorphism U1,U2;
  then reconsider G = F as ManySortedFunction of U1,Image F by Lm3;
  take G;
  thus thesis by A1,Th20;
end;
