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'
  ============================
   ((forall x : key × elt,
     List.In x (elements m) ->
     let
     '(k, _) := x in
      match find k m with
      | Some x0 =>
          match find k m' with
          | Some y0 => eq_elt x0 y0
          | None => False
          end
      | None => match find k m' with
                | Some _ => False
                | None => True
                end
      end) /\
    (forall x : key × elt,
     List.In x (elements m') ->
     let
     '(k, _) := x in
      match find k m with
      | Some x0 =>
          match find k m' with
          | Some y0 => eq_elt x0 y0
          | None => False
          end
      | None => match find k m' with
                | Some _ => False
                | None => True
                end
      end) <->
    (forall k : key,
     (exists e : elt, find k m = Some e) <->
     (exists e : elt, find k m' = Some e)) /\
    (forall (k : key) (e e' : elt),
     find k m = Some e -> find k m' = Some e' -> eq_elt e e'))


DEBUG:Going to execute:
<coq-core.plugins.ltac::transitivity@0>
DEBUG LTAC Evaluated term: (let eq_opt_elt :=
                              fun x y : option elt =>
                              match x with
                              | Some x0 =>
                                  match y with
                                  | Some y0 => eq_elt x0 y0
                                  | None => False
                                  end
                              | None =>
                                  match y with
                                  | Some _ => False
                                  | None => True
                                  end
                              end in
                            (forall k : key,
                             In k m -> eq_opt_elt (find k m) (find k m')) /\
                            (forall k : key,
                             In k m' -> eq_opt_elt (find k m) (find k m')))
DEBUG LTAC Evaluated term: (let eq_opt_elt :=
                              fun x y : option elt =>
                              match x with
                              | Some x0 =>
                                  match y with
                                  | Some y0 => eq_elt x0 y0
                                  | None => False
                                  end
                              | None =>
                                  match y with
                                  | Some _ => False
                                  | None => True
                                  end
                              end in
                            (forall k : key,
                             In k m -> eq_opt_elt (find k m) (find k m')) /\
                            (forall k : key,
                             In k m' -> eq_opt_elt (find k m) (find k m')))