Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive

Goal state before:
pp: case id
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g✝ : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g✝ = 𝟙 B
X✝ Z✝ : WalkingReflexivePair
g : X✝ ⟶ Z✝
⊢ (match X✝, Z✝, Hom.id X✝ ≫ g with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g✝
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g✝ ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match X✝, X✝, Hom.id X✝ with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g✝
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g✝ ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match X✝, Z✝, g with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g✝
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g✝ ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s

Tactic:
cases g

Goal state after:
case id.left
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g = 𝟙 B
⊢ (match one, zero, Hom.id one ≫ Hom.left with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match one, one, Hom.id one with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match one, zero, Hom.left with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s

case id.right
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g = 𝟙 B
⊢ (match one, zero, Hom.id one ≫ Hom.right with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match one, one, Hom.id one with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match one, zero, Hom.right with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s

case id.reflexion
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g = 𝟙 B
⊢ (match zero, one, Hom.id zero ≫ Hom.reflexion with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match zero, zero, Hom.id zero with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match zero, one, Hom.reflexion with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s

case id.leftCompReflexion
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g = 𝟙 B
⊢ (match one, one, Hom.id one ≫ Hom.leftCompReflexion with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match one, one, Hom.id one with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match one, one, Hom.leftCompReflexion with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s

case id.rightCompReflexion
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g = 𝟙 B
⊢ (match one, one, Hom.id one ≫ Hom.rightCompReflexion with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match one, one, Hom.id one with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match one, one, Hom.rightCompReflexion with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s

case id.id
C : Type u
inst✝ : Category.{v, u} C
A B : C
f g : A ⟶ B
s : B ⟶ A
sl : s ≫ f = 𝟙 B
sr : s ≫ g = 𝟙 B
X✝ : WalkingReflexivePair
⊢ (match X✝, X✝, Hom.id X✝ ≫ Hom.id X✝ with
    | x, .(x), Hom.id .(x) =>
      𝟙
        (match x with
        | zero => B
        | one => A)
    | .(one), .(zero), Hom.left => f
    | .(one), .(zero), Hom.right => g
    | .(zero), .(one), Hom.reflexion => s
    | .(one), .(one), Hom.rightCompReflexion => g ≫ s
    | .(one), .(one), Hom.leftCompReflexion => f ≫ s) =
    (match X✝, X✝, Hom.id X✝ with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s) ≫
      match X✝, X✝, Hom.id X✝ with
      | x, .(x), Hom.id .(x) =>
        𝟙
          (match x with
          | zero => B
          | one => A)
      | .(one), .(zero), Hom.left => f
      | .(one), .(zero), Hom.right => g
      | .(zero), .(one), Hom.reflexion => s
      | .(one), .(one), Hom.rightCompReflexion => g ≫ s
      | .(one), .(one), Hom.leftCompReflexion => f ≫ s