Goal:
  
  A : Type
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xH <> xH -> get xH (set xH x m1) = get xH m1
  IHm2 : xH <> xH -> get xH (set xH x m2) = get xH m2
  H0 : xH <> xH
  ============================
   (Some x = o)


DEBUG:Going to execute:
apply IHi
Level 0: Backtrace:

The variable IHi was not found in the current environment.

Goals:
  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  H : xI i <> xI j
  ============================
   (i <> j)

  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xI i <> xI j -> get (xI i) (set (xI j) x m1) = get (xI i) m1
  IHm2 : xI i <> xI j -> get (xI i) (set (xI j) x m2) = get (xI i) m2
  H0 : xI i <> xI j
  ============================
   (i <> j)

  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  H : xO i <> xO j
  ============================
   (i <> j)

  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xO i <> xO j -> get (xO i) (set (xO j) x m1) = get (xO i) m1
  IHm2 : xO i <> xO j -> get (xO i) (set (xO j) x m2) = get (xO i) m2
  H0 : xO i <> xO j
  ============================
   (i <> j)

    A : Type  x : A  H : xH <> xH
  ============================
   (Some x = get xH Empty)

  
  A : Type
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xH <> xH -> get xH (set xH x m1) = get xH m1
  IHm2 : xH <> xH -> get xH (set xH x m2) = get xH m2
  H0 : xH <> xH
  ============================
   (Some x = o)


DEBUG:Going to execute:
congruence
Level 0: Backtrace:

The variable IHi was not found in the current environment.

Goals:
  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  H : xI i <> xI j
  ============================
   (i <> j)

  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xI i <> xI j -> get (xI i) (set (xI j) x m1) = get (xI i) m1
  IHm2 : xI i <> xI j -> get (xI i) (set (xI j) x m2) = get (xI i) m2
  H0 : xI i <> xI j
  ============================
   (i <> j)

  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  H : xO i <> xO j
  ============================
   (i <> j)

  
  A : Type
  i : positive
  IHi : forall (j : positive) (x : A) (m : tree A),
        i <> j -> get i (set j x m) = get i m
  j : positive
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xO i <> xO j -> get (xO i) (set (xO j) x m1) = get (xO i) m1
  IHm2 : xO i <> xO j -> get (xO i) (set (xO j) x m2) = get (xO i) m2
  H0 : xO i <> xO j
  ============================
   (i <> j)

    A : Type  x : A  H : xH <> xH
  ============================
   (Some x = get xH Empty)

  
  A : Type
  x : A
  m1 : tree A
  o : option A
  m2 : tree A
  H : not_trivially_empty m1 o m2
  IHm1 : xH <> xH -> get xH (set xH x m1) = get xH m1
  IHm2 : xH <> xH -> get xH (set xH x m2) = get xH m2
  H0 : xH <> xH
  ============================
   (Some x = o)


DEBUG:Going to execute:
<coq-core.plugins.cc::cc@0> $1