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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m' = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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:
<coq-core.plugins.ltac::subst@1>

Goals:
  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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)
  ============================
   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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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')
  ============================
   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

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m = Some x
  ============================
   (exists e : elt, find k m' = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m' = Some x
  ============================
   (exists e : elt, find k m = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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
  H4 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       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
  e' : elt
  H2 : find k m = Some e
  H3 : find k m' = Some e'
  ============================
   (eq_elt e e')

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m' = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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:
eapply ex_intro
Level 0: Backtrace:

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Failed to progress.

Goals:
  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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)
  ============================
   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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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')
  ============================
   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

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m = Some x
  ============================
   (exists e : elt, find k m' = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m' = Some x
  ============================
   (exists e : elt, find k m = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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
  H4 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       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
  e' : elt
  H2 : find k m = Some e
  H3 : find k m' = Some e'
  ============================
   (eq_elt e e')

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m' = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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:
specialize_dep_under_binders_by tac

Goals:
  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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)
  ============================
   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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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')
  ============================
   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

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m = Some x
  ============================
   (exists e : elt, find k m' = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m' = Some x
  ============================
   (exists e : elt, find k m = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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
  H4 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       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
  e' : elt
  H2 : find k m = Some e
  H3 : find k m' = Some e'
  ============================
   (eq_elt e e')

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m' = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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:
fun tac => specialize_gen_dep_under_binders_by false tac

Goals:
  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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)
  ============================
   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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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')
  ============================
   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

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m = Some x
  ============================
   (exists e : elt, find k m' = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m' = Some x
  ============================
   (exists e : elt, find k m = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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
  H4 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       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
  e' : elt
  H2 : find k m = Some e
  H3 : find k m' = Some e'
  ============================
   (eq_elt e e')

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m' = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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:
specialize_gen_dep_under_binders_by false tac

Goals:
  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 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
  H3 : 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
  k : key
  k0 : key
  e : elt
  H2 : E.eq k (k0, e).1
  H4 : 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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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)
  ============================
   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

  
  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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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 : key,
       (exists (e : elt) (y : key × elt),
          (E.eq k y.1 /\ e = y.2) /\ List.In y (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')
  ============================
   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

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m = Some x
  ============================
   (exists e : elt, find k m' = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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 : key,
       (exists e : elt, find k m' = Some e) ->
       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
  x : elt
  H2 : find k m' = Some x
  ============================
   (exists e : elt, find k m = Some e)

  
  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 : key,
       (exists e : elt, find k m = Some e) ->
       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
  H4 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       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
  e' : elt
  H2 : find k m = Some e
  H3 : find k m' = Some e'
  ============================
   (eq_elt e e')

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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

  
  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'
  H3 : forall (k : key) (e e' : elt),
       find k m = Some e -> find k m' = Some e' -> eq_elt e e'
  k : key
  x : elt
  H1 : find k m' = Some x
  H4 : forall k : key,
       (exists e : elt, find k m = Some e) ->
       exists e : elt, find k m' = Some e
  H5 : forall k : key,
       (exists e : elt, find k m' = Some e) ->
       exists e : elt, find k m = Some e
  ============================
   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:
fun all_ways tac =>
             repeat specialize_gen_dep_under_binders_by' all_ways tac