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

theorem
  for S for U1,U2 being MSAlgebra over S for o for F being
  ManySortedFunction of U1,U2 for x being Element of Args(o,U1), f,u being
  Function st x = f & x in Args(o,U1) & u in Args(o,U2) holds u = F#x iff for n
  st n in dom f holds u.n = (F.((the_arity_of o)/.n)).(f.n) by Lm1;
