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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   ?T0


DEBUG:Going to execute:
type of H

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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (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) (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) (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) (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) (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) (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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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 pair
DEBUG LTAC Evaluated term: elt
DEBUG LTAC Evaluated term: Type
Level 3: type of H
 has value 
Type

Level 3: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 2: evaluation
raised the exception
Backtrace:

No matching clauses for match.

Level 2: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 1: evaluation
raised the exception
Backtrace:

No matching clauses for match.

Level 0: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No matching clauses for match.
Level 6: interpretation of term ltac:((let H := fresh in
                                       pose  H  :=
                                        ltac:((let v := tac ltac:(()) in
                                               refine
                                               v)); exact H))
raised the exception
Backtrace:

No matching clauses for match.

Level 6: evaluation of term
raised the exception
Backtrace:

No matching clauses for match.

Level 6: Backtrace:

No matching clauses for match.
Level 5: Backtrace:

No matching clauses for match.
Level 5: evaluation
raised the exception
Backtrace:

No matching clauses for match.

Level 5: Backtrace:

No matching clauses for match.
Level 5: Backtrace:

No matching clauses for match.
Level 4: Backtrace:

No matching clauses for match.
Level 4: evaluation
raised the exception
Backtrace:

No matching clauses for match.

Level 4: Backtrace:

No matching clauses for match.
Level 3: Backtrace:

No matching clauses for match.
Level 3: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No matching clauses for match.

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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (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) (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) (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) (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) (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) (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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (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) (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) (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) (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) (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) (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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (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) (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) (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) (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) (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) (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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (p : key × elt),
       E.eq k p.1 ->
       List.In p (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) (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) (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) (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) (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) (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) (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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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) (e : elt),
       find k m = Some e -> exists e0 : elt, find k m' = Some e0
  H5 : forall (k : key) (e : elt),
       find k m' = Some e -> exists e0 : elt, find k m = Some e0
  ============================
   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