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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  E0 : find k m' = None
  H5 : True
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   True


DEBUG:Going to execute:
match goal with
           | |- context [ match ?X with
                          | _ => _
                          end ] => destruct X eqn:E
           | H:context [ match ?X with
                         | _ => _
                         end ] |- _ => destruct X eqn:E
           end

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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e0 : elt
  E : find k m = Some e0
  e1 : elt
  E0 : find k m' = Some e1
  H5 : eq_elt e0 e1
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   (eq_elt e0 e1)

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e0 : elt
  E : find k m = Some e0
  E0 : find k m' = None
  H5 : False
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   False

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  e0 : elt
  E0 : find k m' = Some e0
  H5 : False
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   False

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  E0 : find k m' = None
  H5 : True
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   True


DEBUG:Going to execute:
subst
Level 1: Backtrace:

No matching clauses for match.
Level 0: 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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e0 : elt
  E : find k m = Some e0
  e1 : elt
  E0 : find k m' = Some e1
  H5 : eq_elt e0 e1
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   (eq_elt e0 e1)

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e0 : elt
  E : find k m = Some e0
  E0 : find k m' = None
  H5 : False
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   False

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  e0 : elt
  E0 : find k m' = Some e0
  H5 : False
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   False

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  E0 : find k m' = None
  H5 : True
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   True


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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e0 : elt
  E : find k m = Some e0
  e1 : elt
  E0 : find k m' = Some e1
  H5 : eq_elt e0 e1
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   (eq_elt e0 e1)

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e0 : elt
  E : find k m = Some e0
  E0 : find k m' = None
  H5 : False
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   False

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  e0 : elt
  E0 : find k m' = Some e0
  H5 : False
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   False

  
  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'
  k : key
  H1 : forall k0 : key,
       E.eq k0 k ->
       match find k0 m with
       | Some x =>
           match find k0 m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k0 m' with
                 | Some _ => False
                 | None => True
                 end
       end
  H3 : forall (k k0 : key) (e : elt),
       E.eq k k0 ->
       List.In (k0, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  e : elt
  H2 : List.In (k, e) (elements m)
  H4 : forall (k : key) (e : elt),
       List.In (k, e) (elements m') ->
       match find k m with
       | Some x =>
           match find k m' with
           | Some y => eq_elt x y
           | None => False
           end
       | None => match find k m' with
                 | Some _ => False
                 | None => True
                 end
       end
  E : find k m = None
  E0 : find k m' = None
  H5 : True
  H6 : forall k : key, find k m' = find k m'
  H7 : forall k : key, find k m = find k m
  ============================
   True


DEBUG:Going to execute:
try congruence