Goal:
  
  A : Type
  cmp : A -> A -> comparison
  Hc : forall (c : comparison) (x y z : A),
       cmp x y = c -> cmp y z = c -> cmp x z = c
  He : forall x y : A, cmp x y = Eq -> x = y
  c : comparison
  x : A
  q' : comparison
  q'' : comparison
  Hqs : forall c0 : comparison, c = c0 -> q' = c0 -> q'' = c0
  ============================
   (q' = c -> q'' = c)


DEBUG:Going to execute:
apply Hqs