Goal:
  
  elt : Type
  eq_elt : elt -> elt -> Prop
  m : t elt
  m' : t elt
  H : forall x y : key, E.eq x y -> find x m = find y m
  H0 : forall x y : key, E.eq x y -> find x m' = find y m'
  H1 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m) ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  k : key
  e : elt
  H2 : List.In (k, e) (elements m')
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H5 : forall (k : key) (e : elt),
       List.In (k, e) (elements m) ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  ============================
   match find k m with
   | Some x =>
       match find k m' with
       | Some y => eq_elt x y
       | None => False
       end
   | None => match find k m' with
             | Some _ => False
             | None => True
             end
   end


DEBUG:Going to execute:
tryif
            (let H := FindHyp.find_hyp T in
             fail 2 "Already a hypothesis" H "of type" T) then 
            fail else pose proof defn 
DEBUG LTAC Evaluated term: (fun (k : key) (e : elt) => H1 k k e (E.eq_refl k))
DEBUG LTAC Evaluated term: (forall (k : key) (e : elt),
                            List.In (k, e) (elements m) ->
                            match find k m with
                            | Some x =>
                                match find k m' with
                                | Some y => eq_elt x y
                                | None => False
                                end
                            | None =>
                                match find k m' with
                                | Some _ => False
                                | None => True
                                end
                            end)