awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
id : ((Hom.id zero).comp Hom.reflexion).comp Hom.left = (Hom.id zero).comp (Hom.reflexion.comp Hom.left)
id₁ : ((Hom.id zero).comp Hom.reflexion).comp Hom.right = (Hom.id zero).comp (Hom.reflexion.comp Hom.right)
id₂ :
  ((Hom.id zero).comp Hom.reflexion).comp Hom.leftCompReflexion =
    (Hom.id zero).comp (Hom.reflexion.comp Hom.leftCompReflexion)
id₃ :
  ((Hom.id zero).comp Hom.reflexion).comp Hom.rightCompReflexion =
    (Hom.id zero).comp (Hom.reflexion.comp Hom.rightCompReflexion)
id₄ : ((Hom.id zero).comp Hom.reflexion).comp (Hom.id one) = (Hom.id zero).comp (Hom.reflexion.comp (Hom.id one))
⊢ ((Hom.id zero).comp Hom.reflexion).comp h = (Hom.id zero).comp (Hom.reflexion.comp h)

Tactic:
cases h
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
id : ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.left = (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.left)
id₁ :
  ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.right = (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.right)
id₂ :
  ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)
id₃ :
  ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
    (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)
id₄ :
  ((Hom.id one).comp Hom.leftCompReflexion).comp (Hom.id one) =
    (Hom.id one).comp (Hom.leftCompReflexion.comp (Hom.id one))
⊢ ((Hom.id one).comp Hom.leftCompReflexion).comp h = (Hom.id one).comp (Hom.leftCompReflexion.comp h)

Tactic:
cases h
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
id : ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.left = (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.left)
id₁ :
  ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.right = (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.right)
id₂ :
  ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
id₃ :
  ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)
id₄ :
  ((Hom.id one).comp Hom.rightCompReflexion).comp (Hom.id one) =
    (Hom.id one).comp (Hom.rightCompReflexion.comp (Hom.id one))
⊢ ((Hom.id one).comp Hom.rightCompReflexion).comp h = (Hom.id one).comp (Hom.rightCompReflexion.comp h)

Tactic:
cases h
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
W Z : WalkingReflexivePair
h : W.Hom Z
id : ((Hom.id one).comp (Hom.id one)).comp Hom.left = (Hom.id one).comp ((Hom.id one).comp Hom.left)
id₁ : ((Hom.id one).comp (Hom.id one)).comp Hom.right = (Hom.id one).comp ((Hom.id one).comp Hom.right)
id₂ : ((Hom.id zero).comp (Hom.id zero)).comp Hom.reflexion = (Hom.id zero).comp ((Hom.id zero).comp Hom.reflexion)
id₃ :
  ((Hom.id one).comp (Hom.id one)).comp Hom.leftCompReflexion =
    (Hom.id one).comp ((Hom.id one).comp Hom.leftCompReflexion)
id₄ :
  ((Hom.id one).comp (Hom.id one)).comp Hom.rightCompReflexion =
    (Hom.id one).comp ((Hom.id one).comp Hom.rightCompReflexion)
id₅ : ((Hom.id W).comp (Hom.id W)).comp (Hom.id W) = (Hom.id W).comp ((Hom.id W).comp (Hom.id W))
⊢ ((Hom.id W).comp (Hom.id W)).comp h = (Hom.id W).comp ((Hom.id W).comp h)

Tactic:
cases h
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp Hom.reflexion).comp Hom.left = Hom.left.comp (Hom.reflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp Hom.reflexion).comp Hom.right = Hom.left.comp (Hom.reflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp Hom.reflexion).comp Hom.leftCompReflexion = Hom.left.comp (Hom.reflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp Hom.reflexion).comp Hom.rightCompReflexion = Hom.left.comp (Hom.reflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp Hom.reflexion).comp (Hom.id one) = Hom.left.comp (Hom.reflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp (Hom.id zero)).comp Hom.reflexion = Hom.left.comp ((Hom.id zero).comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.left.comp (Hom.id zero)).comp (Hom.id zero) = Hom.left.comp ((Hom.id zero).comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp Hom.reflexion).comp Hom.left = Hom.right.comp (Hom.reflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp Hom.reflexion).comp Hom.right = Hom.right.comp (Hom.reflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp Hom.reflexion).comp Hom.leftCompReflexion = Hom.right.comp (Hom.reflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp Hom.reflexion).comp Hom.rightCompReflexion =
    Hom.right.comp (Hom.reflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp Hom.reflexion).comp (Hom.id one) = Hom.right.comp (Hom.reflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp (Hom.id zero)).comp Hom.reflexion = Hom.right.comp ((Hom.id zero).comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.right.comp (Hom.id zero)).comp (Hom.id zero) = Hom.right.comp ((Hom.id zero).comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.left).comp Hom.reflexion = Hom.reflexion.comp (Hom.left.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.left).comp (Hom.id zero) = Hom.reflexion.comp (Hom.left.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.right).comp Hom.reflexion = Hom.reflexion.comp (Hom.right.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.right).comp (Hom.id zero) = Hom.reflexion.comp (Hom.right.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.leftCompReflexion).comp Hom.left = Hom.reflexion.comp (Hom.leftCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.leftCompReflexion).comp Hom.right = Hom.reflexion.comp (Hom.leftCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    Hom.reflexion.comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
    Hom.reflexion.comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.leftCompReflexion).comp (Hom.id one) =
    Hom.reflexion.comp (Hom.leftCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.rightCompReflexion).comp Hom.left = Hom.reflexion.comp (Hom.rightCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.reflexion.comp (Hom.rightCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.reflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    Hom.reflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp Hom.rightCompReflexion).comp (Hom.id one) =
    Hom.reflexion.comp (Hom.rightCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp (Hom.id one)).comp Hom.left = Hom.reflexion.comp ((Hom.id one).comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp (Hom.id one)).comp Hom.right = Hom.reflexion.comp ((Hom.id one).comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.reflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
    Hom.reflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.reflexion.comp (Hom.id one)).comp (Hom.id one) = Hom.reflexion.comp ((Hom.id one).comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.left).comp Hom.reflexion = Hom.leftCompReflexion.comp (Hom.left.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.left).comp (Hom.id zero) = Hom.leftCompReflexion.comp (Hom.left.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.right).comp Hom.reflexion = Hom.leftCompReflexion.comp (Hom.right.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.right).comp (Hom.id zero) = Hom.leftCompReflexion.comp (Hom.right.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
    Hom.leftCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.leftCompReflexion).comp Hom.right =
    Hom.leftCompReflexion.comp (Hom.leftCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
    Hom.leftCompReflexion.comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.leftCompReflexion).comp (Hom.id one) =
    Hom.leftCompReflexion.comp (Hom.leftCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp (Hom.id one) =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
    Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp (Hom.id one) =
    Hom.leftCompReflexion.comp ((Hom.id one).comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.left).comp Hom.reflexion = Hom.rightCompReflexion.comp (Hom.left.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.left).comp (Hom.id zero) = Hom.rightCompReflexion.comp (Hom.left.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.right).comp Hom.reflexion =
    Hom.rightCompReflexion.comp (Hom.right.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.right).comp (Hom.id zero) =
    Hom.rightCompReflexion.comp (Hom.right.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp (Hom.id one) =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp (Hom.id one) =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
    Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp (Hom.id one) =
    Hom.rightCompReflexion.comp ((Hom.id one).comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.left).comp Hom.reflexion = (Hom.id one).comp (Hom.left.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.left).comp (Hom.id zero) = (Hom.id one).comp (Hom.left.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.right).comp Hom.reflexion = (Hom.id one).comp (Hom.right.comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.right).comp (Hom.id zero) = (Hom.id one).comp (Hom.right.comp (Hom.id zero))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id zero).comp Hom.reflexion).comp Hom.left = (Hom.id zero).comp (Hom.reflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id zero).comp Hom.reflexion).comp Hom.right = (Hom.id zero).comp (Hom.reflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id zero).comp Hom.reflexion).comp Hom.leftCompReflexion =
    (Hom.id zero).comp (Hom.reflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id zero).comp Hom.reflexion).comp Hom.rightCompReflexion =
    (Hom.id zero).comp (Hom.reflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id zero).comp Hom.reflexion).comp (Hom.id one) = (Hom.id zero).comp (Hom.reflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.left = (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.right = (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
    (Hom.id one).comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.leftCompReflexion).comp (Hom.id one) =
    (Hom.id one).comp (Hom.leftCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.left = (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.right = (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    (Hom.id one).comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp Hom.rightCompReflexion).comp (Hom.id one) =
    (Hom.id one).comp (Hom.rightCompReflexion.comp (Hom.id one))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp (Hom.id one)).comp Hom.left = (Hom.id one).comp ((Hom.id one).comp Hom.left)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp (Hom.id one)).comp Hom.right = (Hom.id one).comp ((Hom.id one).comp Hom.right)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id zero).comp (Hom.id zero)).comp Hom.reflexion = (Hom.id zero).comp ((Hom.id zero).comp Hom.reflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp (Hom.id one)).comp Hom.leftCompReflexion =
    (Hom.id one).comp ((Hom.id one).comp Hom.leftCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ ((Hom.id one).comp (Hom.id one)).comp Hom.rightCompReflexion =
    (Hom.id one).comp ((Hom.id one).comp Hom.rightCompReflexion)

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
W : WalkingReflexivePair
⊢ ((Hom.id W).comp (Hom.id W)).comp (Hom.id W) = (Hom.id W).comp ((Hom.id W).comp (Hom.id W))

Tactic:
rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
X : WalkingReflexivePair
⊢ id X = 𝟙 X

Tactic:
rfl

Premises used: rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ reflexion ≫ left = 𝟙 zero

Tactic:
rfl

Premises used: CategoryTheory.Limits.WalkingReflexivePair.Hom.comp, rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ reflexion ≫ right = 𝟙 zero

Tactic:
rfl

Premises used: CategoryTheory.Limits.WalkingReflexivePair.Hom.comp, rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ leftCompReflexion = left ≫ reflexion

Tactic:
rfl

Premises used: CategoryTheory.Limits.WalkingReflexivePair.Hom.comp, rfl
-- Module: Mathlib.CategoryTheory.Limits.Shapes.Reflexive
Goal:
⊢ rightCompReflexion = right ≫ reflexion

Tactic:
rfl

Premises used: CategoryTheory.Limits.WalkingReflexivePair.Hom.comp, rfl