reserve x,y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve f for RingMorphismStr;
reserve G,H,G1,G2,G3,G4 for Ring;
reserve F for RingMorphism;

theorem
  for F being strict RingMorphism ex G,H st ex f being Function of G,H
  st F is Morphism of G,H & F = RingMorphismStr(#G,H,f#) & f is linear
proof
  let F be strict RingMorphism;
  consider G,H such that
A1: G <= H and
  dom(F) = G and
  cod(F) = H and
A2: F is Morphism of G,H by Lm6;
  reconsider F9 = F as Morphism of G,H by A2;
  consider f being Function of G,H such that
A3: F9 = RingMorphismStr(#G,H,f#) & f is linear by A1,Lm7;
  take G,H,f;
  thus thesis by A3;
end;
