[Elab.info] command @ ⟨13, 0⟩-⟨15, 6⟩
  Nat : Type @ ⟨13, 11⟩-⟨13, 14⟩
    Nat : Type @ ⟨13, 11⟩-⟨13, 14⟩
  x : Nat @ ⟨13, 7⟩-⟨13, 8⟩
  Nat × Nat : Type @ ⟨13, 18⟩-⟨13, 27⟩
    Macro expansion
    Nat × Nat
    ===>
    Prod✝ Nat Nat
      Prod : Type → Type → Type @ ⟨13, 18⟩†-⟨13, 22⟩†
      Nat : Type @ ⟨13, 18⟩-⟨13, 21⟩
        Nat : Type @ ⟨13, 18⟩-⟨13, 21⟩
      Nat : Type @ ⟨13, 24⟩-⟨13, 27⟩
        Nat : Type @ ⟨13, 24⟩-⟨13, 27⟩
  let y : Nat × Nat := (x, x);
  id y : Nat × Nat @ ⟨14, 2⟩-⟨15, 6⟩
    Nat × Nat : Type @ ⟨14, 6⟩-⟨14, 7⟩
    (x, x) : Nat × Nat @ ⟨14, 11⟩-⟨14, 17⟩
      Macro expansion
      ⟨x, x⟩
      ===>
      Prod.mk✝ x x
        (x, x) : Nat × Nat @ ⟨14, 11⟩†-⟨14, 16⟩
          Prod.mk : {α β : Type} → α → β → α × β @ ⟨14, 11⟩†-⟨17, 8⟩†
          x : Nat @ ⟨14, 12⟩-⟨14, 13⟩
            x : Nat @ ⟨14, 12⟩-⟨14, 13⟩
          x : Nat @ ⟨14, 15⟩-⟨14, 16⟩
            x : Nat @ ⟨14, 15⟩-⟨14, 16⟩
    y : Nat × Nat @ ⟨14, 6⟩-⟨14, 7⟩
    id y : Nat × Nat @ ⟨15, 2⟩-⟨15, 6⟩
      id : {α : Type} → α → α @ ⟨15, 2⟩-⟨15, 4⟩
      y : Nat × Nat @ ⟨15, 5⟩-⟨15, 6⟩
        y : Nat × Nat @ ⟨15, 5⟩-⟨15, 6⟩
[Elab.info] command @ ⟨17, 0⟩-⟨19, 8⟩
  ∀ (x y : Nat), Bool → x + 0 = x : Prop @ ⟨17, 8⟩-⟨17, 44⟩
    Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
      Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
    x : Nat @ ⟨17, 9⟩-⟨17, 10⟩
    Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
      Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
    y : Nat @ ⟨17, 11⟩-⟨17, 12⟩
    Bool → x + 0 = x : Prop @ ⟨17, 22⟩-⟨17, 44⟩
      Bool : Type @ ⟨17, 27⟩-⟨17, 31⟩
        Bool : Type @ ⟨17, 27⟩-⟨17, 31⟩
      b : Bool @ ⟨17, 23⟩-⟨17, 24⟩
      x + 0 = x : Prop @ ⟨17, 35⟩-⟨17, 44⟩
        Macro expansion
        x + 0 = x
        ===>
        binrel% Eq✝ (x + 0)x
          x + 0 : Nat @ ⟨17, 35⟩-⟨17, 40⟩
            Macro expansion
            x + 0
            ===>
            HAdd.hAdd✝ x 0
              HAdd.hAdd : {α β γ : Type} → [self : HAdd α β γ] → α → β → γ @ ⟨17, 35⟩†-⟨17, 44⟩†
              x : Nat @ ⟨17, 35⟩-⟨17, 36⟩
                x : Nat @ ⟨17, 35⟩-⟨17, 36⟩
              0 : Nat @ ⟨17, 39⟩-⟨17, 40⟩
          x : Nat @ ⟨17, 43⟩-⟨17, 44⟩
            x : Nat @ ⟨17, 43⟩-⟨17, 44⟩
  fun (x y : Nat) (b : Bool) =>
    ofEqTrue
      (Eq.trans (congrFun (congrArg Eq (Nat.add_zero x)) x)
        (eqSelf x)) : ∀ (x y : Nat), Bool → x + 0 = x @ ⟨18, 2⟩-⟨19, 8⟩
    Nat : Type @ ⟨18, 6⟩-⟨18, 7⟩
    x : Nat @ ⟨18, 6⟩-⟨18, 7⟩
    Nat : Type @ ⟨18, 8⟩-⟨18, 9⟩
    y : Nat @ ⟨18, 8⟩-⟨18, 9⟩
    Bool : Type @ ⟨18, 10⟩-⟨18, 11⟩
    b : Bool @ ⟨18, 10⟩-⟨18, 11⟩
    Tactic @ ⟨19, 4⟩-⟨19, 8⟩
    before 
    x y : Nat
    b : Bool
    ⊢ x + 0 = x
    after no goals
      Tactic @ ⟨19, 4⟩-⟨19, 8⟩
      before 
      x y : Nat
      b : Bool
      ⊢ x + 0 = x
      after no goals
        Tactic @ ⟨19, 4⟩-⟨19, 8⟩
        before 
        x y : Nat
        b : Bool
        ⊢ x + 0 = x
        after no goals
[Elab.info] command @ ⟨21, 0⟩-⟨25, 10⟩
  Nat → Nat → Bool → Nat : Type @ ⟨21, 9⟩-⟨21, 39⟩
    Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
      Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
    x : Nat @ ⟨21, 10⟩-⟨21, 11⟩
    Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
      Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
    y : Nat @ ⟨21, 12⟩-⟨21, 13⟩
    Bool → Nat : Type @ ⟨21, 23⟩-⟨21, 39⟩
      Bool : Type @ ⟨21, 28⟩-⟨21, 32⟩
        Bool : Type @ ⟨21, 28⟩-⟨21, 32⟩
      b : Bool @ ⟨21, 24⟩-⟨21, 25⟩
      Nat : Type @ ⟨21, 36⟩-⟨21, 39⟩
        Nat : Type @ ⟨21, 36⟩-⟨21, 39⟩
  fun (x y : Nat) (b : Bool) =>
    let x : Nat × Nat := (x + y, x - y);
    match x with 
    | (z, w) =>
      let z1 : Nat := z + w;
      z + z1 : Nat → Nat → Bool → Nat @ ⟨22, 2⟩-⟨25, 10⟩
    Nat : Type @ ⟨22, 6⟩-⟨22, 7⟩
    x : Nat @ ⟨22, 6⟩-⟨22, 7⟩
    Nat : Type @ ⟨22, 8⟩-⟨22, 9⟩
    y : Nat @ ⟨22, 8⟩-⟨22, 9⟩
    Bool : Type @ ⟨22, 10⟩-⟨22, 11⟩
    b : Bool @ ⟨22, 10⟩-⟨22, 11⟩
    let x : Nat × Nat := (x + y, x - y);
    match x with 
    | (z, w) =>
      let z1 : Nat := z + w;
      z + z1 : Nat @ ⟨23, 4⟩-⟨25, 10⟩
      Macro expansion
      let (z, w) := (x + y, x - y)
      let z1 := z + w 
      z + z1
      ===>
      let x✝ : _ := (x + y, x - y);
      match x✝ with 
      | (z, w) =>
        let z1 := z + w 
        z + z1
        let x : Nat × Nat := (x + y, x - y);
        match x with 
        | (z, w) =>
          let z1 : Nat := z + w;
          z + z1 : Nat @ ⟨23, 4⟩†-⟨25, 10⟩
          Nat × Nat : Type @ ⟨23, 4⟩-⟨23, 5⟩
          (x + y, x - y) : Nat × Nat @ ⟨23, 18⟩-⟨23, 32⟩
            Macro expansion
            (x + y, x - y)
            ===>
            Prod.mk✝ (x + y) (x - y)
              (x + y, x - y) : Nat × Nat @ ⟨23, 18⟩†-⟨23, 31⟩
                Prod.mk : {α β : Type} → α → β → α × β @ ⟨23, 18⟩†-⟨23, 25⟩†
                x + y : Nat @ ⟨23, 19⟩-⟨23, 24⟩
                  Macro expansion
                  x + y
                  ===>
                  HAdd.hAdd✝ x y
                    HAdd.hAdd : {α β γ : Type} → [self : HAdd α β γ] → α → β → γ @ ⟨23, 19⟩†-⟨23, 28⟩†
                    x : Nat @ ⟨23, 19⟩-⟨23, 20⟩
                      x : Nat @ ⟨23, 19⟩-⟨23, 20⟩
                    y : Nat @ ⟨23, 23⟩-⟨23, 24⟩
                      y : Nat @ ⟨23, 23⟩-⟨23, 24⟩
                x - y : Nat @ ⟨23, 26⟩-⟨23, 31⟩
                  Macro expansion
                  x - y
                  ===>
                  HSub.hSub✝ x y
                    HSub.hSub : {α β γ : Type} → [self : HSub α β γ] → α → β → γ @ ⟨23, 26⟩†-⟨24, 2⟩†
                    x : Nat @ ⟨23, 26⟩-⟨23, 27⟩
                      x : Nat @ ⟨23, 26⟩-⟨23, 27⟩
                    y : Nat @ ⟨23, 30⟩-⟨23, 31⟩
                      y : Nat @ ⟨23, 30⟩-⟨23, 31⟩
          x✝ : Nat × Nat @ ⟨23, 4⟩†-⟨25, 10⟩†
          match x✝ with 
          | (z, w) =>
            let z1 : Nat := z + w;
            z + z1 : Nat @ ⟨23, 4⟩†-⟨25, 10⟩
            [.] `z : none
            [.] `w : none
            (z, w) : Nat × Nat @ ⟨23, 8⟩-⟨23, 14⟩
              Macro expansion
              (z, w)
              ===>
              Prod.mk✝ z w
                (z, w) : Nat × Nat @ ⟨23, 8⟩†-⟨23, 13⟩
                  Prod.mk : {α β : Type} → α → β → α × β @ ⟨23, 8⟩†-⟨23, 15⟩†
                  z : Nat @ ⟨23, 9⟩-⟨23, 10⟩
                    z : Nat @ ⟨23, 9⟩-⟨23, 10⟩
                  w : Nat @ ⟨23, 12⟩-⟨23, 13⟩
                    w : Nat @ ⟨23, 12⟩-⟨23, 13⟩
            let z1 : Nat := z + w;
            z + z1 : Nat @ ⟨24, 4⟩-⟨25, 10⟩
              Nat : Type @ ⟨24, 8⟩-⟨24, 9⟩
              z + w : Nat @ ⟨24, 14⟩-⟨24, 19⟩
                Macro expansion
                z + w
                ===>
                HAdd.hAdd✝ z w
                  HAdd.hAdd : {α β γ : Type} → [self : HAdd α β γ] → α → β → γ @ ⟨24, 14⟩†-⟨25, 3⟩†
                  z : Nat @ ⟨24, 14⟩-⟨24, 15⟩
                    z : Nat @ ⟨24, 14⟩-⟨24, 15⟩
                  w : Nat @ ⟨24, 18⟩-⟨24, 19⟩
                    w : Nat @ ⟨24, 18⟩-⟨24, 19⟩
              z1 : Nat @ ⟨24, 8⟩-⟨24, 10⟩
              z + z1 : Nat @ ⟨25, 4⟩-⟨25, 10⟩
                Macro expansion
                z + z1
                ===>
                HAdd.hAdd✝ z z1
                  HAdd.hAdd : {α β γ : Type} → [self : HAdd α β γ] → α → β → γ @ ⟨25, 4⟩†-⟨27, 1⟩†
                  z : Nat @ ⟨25, 4⟩-⟨25, 5⟩
                    z : Nat @ ⟨25, 4⟩-⟨25, 5⟩
                  z1 : Nat @ ⟨25, 8⟩-⟨25, 10⟩
                    z1 : Nat @ ⟨25, 8⟩-⟨25, 10⟩
[Elab.info] command @ ⟨27, 0⟩-⟨28, 17⟩
  Nat × Array (Array Nat) : Type @ ⟨27, 12⟩-⟨27, 35⟩
    Macro expansion
    Nat × Array (Array Nat)
    ===>
    Prod✝ Nat (Array (Array Nat))
      Prod : Type → Type → Type @ ⟨27, 12⟩†-⟨27, 16⟩†
      Nat : Type @ ⟨27, 12⟩-⟨27, 15⟩
        Nat : Type @ ⟨27, 12⟩-⟨27, 15⟩
      Array (Array Nat) : Type @ ⟨27, 18⟩-⟨27, 35⟩
        Array : Type → Type @ ⟨27, 18⟩-⟨27, 23⟩
        Array Nat : Type @ ⟨27, 24⟩-⟨27, 35⟩
          Array Nat : Type @ ⟨27, 25⟩-⟨27, 34⟩
            Array : Type → Type @ ⟨27, 25⟩-⟨27, 30⟩
            Nat : Type @ ⟨27, 31⟩-⟨27, 34⟩
              Nat : Type @ ⟨27, 31⟩-⟨27, 34⟩
  s : Nat × Array (Array Nat) @ ⟨27, 8⟩-⟨27, 9⟩
  Array Nat : Type @ ⟨27, 39⟩-⟨27, 48⟩
    Array : Type → Type @ ⟨27, 39⟩-⟨27, 44⟩
    Nat : Type @ ⟨27, 45⟩-⟨27, 48⟩
      Nat : Type @ ⟨27, 45⟩-⟨27, 48⟩
  Array.push (Array.getOp s.snd 1) s.fst : Array Nat @ ⟨28, 2⟩-⟨28, 17⟩
    s : Nat × Array (Array Nat) @ ⟨28, 2⟩-⟨28, 3⟩
    Prod.snd : {α β : Type} → α × β → β @ ⟨28, 4⟩-⟨28, 5⟩
    Array.getOp : {α : Type} → [inst : Inhabited α] → Array α → Nat → α @ ⟨28, 5⟩-⟨28, 6⟩
    1 : Nat @ ⟨28, 6⟩-⟨28, 7⟩
    [.] Array.getOp s.snd 1 : Array Nat @ ⟨28, 2⟩-⟨28, 13⟩
    Array.push : {α : Type} → Array α → α → Array α @ ⟨28, 9⟩-⟨28, 13⟩
    s.fst : Nat @ ⟨28, 14⟩-⟨28, 17⟩
      s : Nat × Array (Array Nat) @ ⟨28, 14⟩-⟨28, 15⟩
      Prod.fst : {α β : Type} → α × β → α @ ⟨28, 16⟩-⟨28, 17⟩
[Elab.info] command @ ⟨30, 0⟩-⟨31, 20⟩
  B : Type @ ⟨30, 14⟩-⟨30, 15⟩
    B : Type @ ⟨30, 14⟩-⟨30, 15⟩
  arg : B @ ⟨30, 8⟩-⟨30, 11⟩
  Nat : Type @ ⟨30, 19⟩-⟨30, 22⟩
    Nat : Type @ ⟨30, 19⟩-⟨30, 22⟩
  A.val arg.pair.fst 0 : Nat @ ⟨31, 2⟩-⟨31, 20⟩
    arg : B @ ⟨31, 2⟩-⟨31, 5⟩
    [.] arg : B @ ⟨31, 2⟩-⟨31, 18⟩
    B.pair : B → A × A @ ⟨31, 6⟩-⟨31, 10⟩
    [.] arg.pair : A × A @ ⟨31, 2⟩-⟨31, 18⟩
    Prod.fst : {α β : Type} → α × β → α @ ⟨31, 11⟩-⟨31, 14⟩
    [.] arg.pair.fst : A @ ⟨31, 2⟩-⟨31, 18⟩
    A.val : A → Nat → Nat @ ⟨31, 15⟩-⟨31, 18⟩
    0 : Nat @ ⟨31, 19⟩-⟨31, 20⟩
[Elab.info] command @ ⟨33, 0⟩-⟨35, 1⟩
  Nat : Type @ ⟨33, 12⟩-⟨33, 15⟩
    Nat : Type @ ⟨33, 12⟩-⟨33, 15⟩
  x : Nat @ ⟨33, 8⟩-⟨33, 9⟩
  B : Type @ ⟨33, 19⟩-⟨33, 20⟩
    B : Type @ ⟨33, 19⟩-⟨33, 20⟩
  { pair := ({ val := id }, { val := id }) } : B @ ⟨33, 24⟩-⟨35, 1⟩
    ({ val := id }, { val := id }) : A × A @ ⟨34, 10⟩-⟨34, 40⟩
      Macro expansion
      ({ val := id }, { val := id })
      ===>
      Prod.mk✝ { val := id } { val := id }
        ({ val := id }, { val := id }) : A × A @ ⟨34, 10⟩†-⟨34, 39⟩
          Prod.mk : {α β : Type} → α → β → α × β @ ⟨34, 10⟩†-⟨34, 17⟩†
          { val := id } : A @ ⟨34, 11⟩-⟨34, 24⟩
            id : Nat → Nat @ ⟨34, 20⟩-⟨34, 22⟩
              id : {α : Type} → α → α @ ⟨34, 20⟩-⟨34, 22⟩
            val : Nat → Nat := id @ ⟨34, 13⟩-⟨34, 16⟩
          { val := id } : A @ ⟨34, 26⟩-⟨34, 39⟩
            id : Nat → Nat @ ⟨34, 35⟩-⟨34, 37⟩
              id : {α : Type} → α → α @ ⟨34, 35⟩-⟨34, 37⟩
            val : Nat → Nat := id @ ⟨34, 28⟩-⟨34, 31⟩
    pair : A × A := ({ val := id }, { val := id }) @ ⟨34, 2⟩-⟨34, 6⟩
def id.{u} : {α : Sort u} → α → α :=
fun {α : Sort u} (a : α) => a
[Elab.info] command @ ⟨37, 0⟩-⟨37, 9⟩
  id : {α : Sort u} → α → α @ ⟨37, 7⟩-⟨37, 9⟩