reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;

theorem
  for f being Function, a, A, b, B, c, C being set st a <> b & a <> c
  holds ( f +* (a .--> A) +* (b .--> B) +* (c .--> C) ).a = A
proof
  let f be Function, a, A, b, B, c, C be set;
  assume a <> b & a <> c;
  hence
  ( f +* (a .--> A) +* (b .--> B) +* (c .--> C) ).a = ( f +* (a .--> A) )
  .a by FUNCT_4:91
    .= A by Th93;
end;
