Goal:
  
  ============================
   (forall (A : Type) (v : A) (l : tree A) (o : option A) 
      (r : tree A) (p : positive),
    set p v (Node l o r) =
    match p with
    | xI q => Node l o (set q v r)
    | xO q => Node (set q v l) o r
    | xH => Node l (Some v) r
    end)


DEBUG:Going to execute:
destruct l, o, r, p

Goals:
    A : Type  v : A  a : A  p : positive
  ============================
   (set (xI p) v (Node Empty (Some a) Empty) =
    Node Empty (Some a) (set p v Empty))

    A : Type  v : A  a : A  p : positive
  ============================
   (set (xO p) v (Node Empty (Some a) Empty) =
    Node (set p v Empty) (Some a) Empty)

    A : Type  v : A  a : A
  ============================
   (set xH v (Node Empty (Some a) Empty) = Node Empty (Some v) Empty)

    A : Type  v : A  a : A  t0 : tree' A  p : positive
  ============================
   (set (xI p) v (Node Empty (Some a) (Nodes t0)) =
    Node Empty (Some a) (set p v (Nodes t0)))

    A : Type  v : A  a : A  t0 : tree' A  p : positive
  ============================
   (set (xO p) v (Node Empty (Some a) (Nodes t0)) =
    Node (set p v Empty) (Some a) (Nodes t0))

    A : Type  v : A  a : A  t0 : tree' A
  ============================
   (set xH v (Node Empty (Some a) (Nodes t0)) =
    Node Empty (Some v) (Nodes t0))

    A : Type  v : A  p : positive
  ============================
   (set (xI p) v (Node Empty None Empty) = Node Empty None (set p v Empty))

    A : Type  v : A  p : positive
  ============================
   (set (xO p) v (Node Empty None Empty) = Node (set p v Empty) None Empty)

    A : Type  v : A
  ============================
   (set xH v (Node Empty None Empty) = Node Empty (Some v) Empty)

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xI p) v (Node Empty None (Nodes t0)) =
    Node Empty None (set p v (Nodes t0)))

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xO p) v (Node Empty None (Nodes t0)) =
    Node (set p v Empty) None (Nodes t0))

    A : Type  v : A  t0 : tree' A
  ============================
   (set xH v (Node Empty None (Nodes t0)) = Node Empty (Some v) (Nodes t0))

    A : Type  v : A  t0 : tree' A  a : A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) (Some a) Empty) =
    Node (Nodes t0) (Some a) (set p v Empty))

    A : Type  v : A  t0 : tree' A  a : A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) (Some a) Empty) =
    Node (set p v (Nodes t0)) (Some a) Empty)

    A : Type  v : A  t0 : tree' A  a : A
  ============================
   (set xH v (Node (Nodes t0) (Some a) Empty) =
    Node (Nodes t0) (Some v) Empty)

    A : Type  v : A  t0 : tree' A  a : A  t1 : tree' A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) (Some a) (Nodes t1)) =
    Node (Nodes t0) (Some a) (set p v (Nodes t1)))

    A : Type  v : A  t0 : tree' A  a : A  t1 : tree' A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) (Some a) (Nodes t1)) =
    Node (set p v (Nodes t0)) (Some a) (Nodes t1))

    A : Type  v : A  t0 : tree' A  a : A  t1 : tree' A
  ============================
   (set xH v (Node (Nodes t0) (Some a) (Nodes t1)) =
    Node (Nodes t0) (Some v) (Nodes t1))

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) None Empty) =
    Node (Nodes t0) None (set p v Empty))

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) None Empty) =
    Node (set p v (Nodes t0)) None Empty)

    A : Type  v : A  t0 : tree' A
  ============================
   (set xH v (Node (Nodes t0) None Empty) = Node (Nodes t0) (Some v) Empty)

    A : Type  v : A  t0 : tree' A  t1 : tree' A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) None (Nodes t1)) =
    Node (Nodes t0) None (set p v (Nodes t1)))

    A : Type  v : A  t0 : tree' A  t1 : tree' A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) None (Nodes t1)) =
    Node (set p v (Nodes t0)) None (Nodes t1))

    A : Type  v : A  t0 : tree' A  t1 : tree' A
  ============================
   (set xH v (Node (Nodes t0) None (Nodes t1)) =
    Node (Nodes t0) (Some v) (Nodes t1))


DEBUG:Going to execute:
reflexivity

Goals:
    A : Type  v : A  a : A  p : positive
  ============================
   (set (xI p) v (Node Empty (Some a) Empty) =
    Node Empty (Some a) (set p v Empty))

    A : Type  v : A  a : A  p : positive
  ============================
   (set (xO p) v (Node Empty (Some a) Empty) =
    Node (set p v Empty) (Some a) Empty)

    A : Type  v : A  a : A
  ============================
   (set xH v (Node Empty (Some a) Empty) = Node Empty (Some v) Empty)

    A : Type  v : A  a : A  t0 : tree' A  p : positive
  ============================
   (set (xI p) v (Node Empty (Some a) (Nodes t0)) =
    Node Empty (Some a) (set p v (Nodes t0)))

    A : Type  v : A  a : A  t0 : tree' A  p : positive
  ============================
   (set (xO p) v (Node Empty (Some a) (Nodes t0)) =
    Node (set p v Empty) (Some a) (Nodes t0))

    A : Type  v : A  a : A  t0 : tree' A
  ============================
   (set xH v (Node Empty (Some a) (Nodes t0)) =
    Node Empty (Some v) (Nodes t0))

    A : Type  v : A  p : positive
  ============================
   (set (xI p) v (Node Empty None Empty) = Node Empty None (set p v Empty))

    A : Type  v : A  p : positive
  ============================
   (set (xO p) v (Node Empty None Empty) = Node (set p v Empty) None Empty)

    A : Type  v : A
  ============================
   (set xH v (Node Empty None Empty) = Node Empty (Some v) Empty)

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xI p) v (Node Empty None (Nodes t0)) =
    Node Empty None (set p v (Nodes t0)))

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xO p) v (Node Empty None (Nodes t0)) =
    Node (set p v Empty) None (Nodes t0))

    A : Type  v : A  t0 : tree' A
  ============================
   (set xH v (Node Empty None (Nodes t0)) = Node Empty (Some v) (Nodes t0))

    A : Type  v : A  t0 : tree' A  a : A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) (Some a) Empty) =
    Node (Nodes t0) (Some a) (set p v Empty))

    A : Type  v : A  t0 : tree' A  a : A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) (Some a) Empty) =
    Node (set p v (Nodes t0)) (Some a) Empty)

    A : Type  v : A  t0 : tree' A  a : A
  ============================
   (set xH v (Node (Nodes t0) (Some a) Empty) =
    Node (Nodes t0) (Some v) Empty)

    A : Type  v : A  t0 : tree' A  a : A  t1 : tree' A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) (Some a) (Nodes t1)) =
    Node (Nodes t0) (Some a) (set p v (Nodes t1)))

    A : Type  v : A  t0 : tree' A  a : A  t1 : tree' A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) (Some a) (Nodes t1)) =
    Node (set p v (Nodes t0)) (Some a) (Nodes t1))

    A : Type  v : A  t0 : tree' A  a : A  t1 : tree' A
  ============================
   (set xH v (Node (Nodes t0) (Some a) (Nodes t1)) =
    Node (Nodes t0) (Some v) (Nodes t1))

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) None Empty) =
    Node (Nodes t0) None (set p v Empty))

    A : Type  v : A  t0 : tree' A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) None Empty) =
    Node (set p v (Nodes t0)) None Empty)

    A : Type  v : A  t0 : tree' A
  ============================
   (set xH v (Node (Nodes t0) None Empty) = Node (Nodes t0) (Some v) Empty)

    A : Type  v : A  t0 : tree' A  t1 : tree' A  p : positive
  ============================
   (set (xI p) v (Node (Nodes t0) None (Nodes t1)) =
    Node (Nodes t0) None (set p v (Nodes t1)))

    A : Type  v : A  t0 : tree' A  t1 : tree' A  p : positive
  ============================
   (set (xO p) v (Node (Nodes t0) None (Nodes t1)) =
    Node (set p v (Nodes t0)) None (Nodes t1))

    A : Type  v : A  t0 : tree' A  t1 : tree' A
  ============================
   (set xH v (Node (Nodes t0) None (Nodes t1)) =
    Node (Nodes t0) (Some v) (Nodes t1))


DEBUG:Going to execute:
fun => <coq-core.plugins.ltac::reflexivity@0>