awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp h)
have leftCompReflexion₁ : (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
  Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
leftCompReflexion₁ :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp h)
have leftCompReflexion₂ : (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
  Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
leftCompReflexion₁ :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
leftCompReflexion₂ :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp h)
have leftCompReflexion₃ : (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
  Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
leftCompReflexion₁ :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
leftCompReflexion₂ :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
leftCompReflexion₃ :
  (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)
⊢ (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp h)
have leftCompReflexion₄ : (Hom.leftCompReflexion.comp Hom.rightCompReflexion).comp (Hom.id one) =
  Hom.leftCompReflexion.comp (Hom.rightCompReflexion.comp (Hom.id one))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp h = Hom.leftCompReflexion.comp ((Hom.id one).comp h)
have leftCompReflexion : (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.left)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.left)
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp h = Hom.leftCompReflexion.comp ((Hom.id one).comp h)
have leftCompReflexion₁ : (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.right)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.left)
leftCompReflexion₁ :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.right)
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp h = Hom.leftCompReflexion.comp ((Hom.id one).comp h)
have leftCompReflexion₂ : (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
  Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.left)
leftCompReflexion₁ :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.right)
leftCompReflexion₂ :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp h = Hom.leftCompReflexion.comp ((Hom.id one).comp h)
have leftCompReflexion₃ : (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
  Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
leftCompReflexion :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.left)
leftCompReflexion₁ :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.right)
leftCompReflexion₂ :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)
leftCompReflexion₃ :
  (Hom.leftCompReflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
    Hom.leftCompReflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)
⊢ (Hom.leftCompReflexion.comp (Hom.id one)).comp h = Hom.leftCompReflexion.comp ((Hom.id one).comp h)
have leftCompReflexion₄ : (Hom.leftCompReflexion.comp (Hom.id one)).comp (Hom.id one) =
  Hom.leftCompReflexion.comp ((Hom.id one).comp (Hom.id one))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
⊢ (Hom.rightCompReflexion.comp Hom.left).comp h = Hom.rightCompReflexion.comp (Hom.left.comp h)
have rightCompReflexion : (Hom.rightCompReflexion.comp Hom.left).comp Hom.reflexion = Hom.rightCompReflexion.comp (Hom.left.comp Hom.reflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.left).comp Hom.reflexion = Hom.rightCompReflexion.comp (Hom.left.comp Hom.reflexion)
⊢ (Hom.rightCompReflexion.comp Hom.left).comp h = Hom.rightCompReflexion.comp (Hom.left.comp h)
have rightCompReflexion₁ : (Hom.rightCompReflexion.comp Hom.left).comp (Hom.id zero) = Hom.rightCompReflexion.comp (Hom.left.comp (Hom.id zero))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
⊢ (Hom.rightCompReflexion.comp Hom.right).comp h = Hom.rightCompReflexion.comp (Hom.right.comp h)
have rightCompReflexion : (Hom.rightCompReflexion.comp Hom.right).comp Hom.reflexion = Hom.rightCompReflexion.comp (Hom.right.comp Hom.reflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.right).comp Hom.reflexion =
    Hom.rightCompReflexion.comp (Hom.right.comp Hom.reflexion)
⊢ (Hom.rightCompReflexion.comp Hom.right).comp h = Hom.rightCompReflexion.comp (Hom.right.comp h)
have rightCompReflexion₁ : (Hom.rightCompReflexion.comp Hom.right).comp (Hom.id zero) = Hom.rightCompReflexion.comp (Hom.right.comp (Hom.id zero))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp h)
have rightCompReflexion : (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
  Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp h)
have rightCompReflexion₁ : (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.right =
  Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.right)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.right)
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp h)
have rightCompReflexion₂ : (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
  Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.right)
rightCompReflexion₂ :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp h)
have rightCompReflexion₃ : (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
  Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.right)
rightCompReflexion₂ :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.leftCompReflexion)
rightCompReflexion₃ :
  (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp Hom.rightCompReflexion =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp Hom.rightCompReflexion)
⊢ (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp h)
have rightCompReflexion₄ : (Hom.rightCompReflexion.comp Hom.leftCompReflexion).comp (Hom.id one) =
  Hom.rightCompReflexion.comp (Hom.leftCompReflexion.comp (Hom.id one))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp h)
have rightCompReflexion : (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
  Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp h)
have rightCompReflexion₁ : (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
  Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp h)
have rightCompReflexion₂ : (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
  Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
rightCompReflexion₂ :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp h)
have rightCompReflexion₃ : (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
  Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.left =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.right =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.right)
rightCompReflexion₂ :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.leftCompReflexion)
rightCompReflexion₃ :
  (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp Hom.rightCompReflexion =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp Hom.rightCompReflexion)
⊢ (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp h =
    Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp h)
have rightCompReflexion₄ : (Hom.rightCompReflexion.comp Hom.rightCompReflexion).comp (Hom.id one) =
  Hom.rightCompReflexion.comp (Hom.rightCompReflexion.comp (Hom.id one))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp h = Hom.rightCompReflexion.comp ((Hom.id one).comp h)
have rightCompReflexion : (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.left)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.left)
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp h = Hom.rightCompReflexion.comp ((Hom.id one).comp h)
have rightCompReflexion₁ : (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.right)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.right)
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp h = Hom.rightCompReflexion.comp ((Hom.id one).comp h)
have rightCompReflexion₂ : (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
  Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.right)
rightCompReflexion₂ :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp h = Hom.rightCompReflexion.comp ((Hom.id one).comp h)
have rightCompReflexion₃ : (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
  Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
rightCompReflexion :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.left = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.left)
rightCompReflexion₁ :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.right = Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.right)
rightCompReflexion₂ :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.leftCompReflexion =
    Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.leftCompReflexion)
rightCompReflexion₃ :
  (Hom.rightCompReflexion.comp (Hom.id one)).comp Hom.rightCompReflexion =
    Hom.rightCompReflexion.comp ((Hom.id one).comp Hom.rightCompReflexion)
⊢ (Hom.rightCompReflexion.comp (Hom.id one)).comp h = Hom.rightCompReflexion.comp ((Hom.id one).comp h)
have rightCompReflexion₄ : (Hom.rightCompReflexion.comp (Hom.id one)).comp (Hom.id one) =
  Hom.rightCompReflexion.comp ((Hom.id one).comp (Hom.id one))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
⊢ ((Hom.id one).comp Hom.left).comp h = (Hom.id one).comp (Hom.left.comp h)
have id : ((Hom.id one).comp Hom.left).comp Hom.reflexion = (Hom.id one).comp (Hom.left.comp Hom.reflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
id : ((Hom.id one).comp Hom.left).comp Hom.reflexion = (Hom.id one).comp (Hom.left.comp Hom.reflexion)
⊢ ((Hom.id one).comp Hom.left).comp h = (Hom.id one).comp (Hom.left.comp h)
have id₁ : ((Hom.id one).comp Hom.left).comp (Hom.id zero) = (Hom.id one).comp (Hom.left.comp (Hom.id zero))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
⊢ ((Hom.id one).comp Hom.right).comp h = (Hom.id one).comp (Hom.right.comp h)
have id : ((Hom.id one).comp Hom.right).comp Hom.reflexion = (Hom.id one).comp (Hom.right.comp Hom.reflexion)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : zero.Hom Z
id : ((Hom.id one).comp Hom.right).comp Hom.reflexion = (Hom.id one).comp (Hom.right.comp Hom.reflexion)
⊢ ((Hom.id one).comp Hom.right).comp h = (Hom.id one).comp (Hom.right.comp h)
have id₁ : ((Hom.id one).comp Hom.right).comp (Hom.id zero) = (Hom.id one).comp (Hom.right.comp (Hom.id zero))
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
Goal:
Z : WalkingReflexivePair
h : one.Hom Z
⊢ ((Hom.id zero).comp Hom.reflexion).comp h = (Hom.id zero).comp (Hom.reflexion.comp h)
have id : ((Hom.id zero).comp Hom.reflexion).comp Hom.left = (Hom.id zero).comp (Hom.reflexion.comp Hom.left)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
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)
⊢ ((Hom.id zero).comp Hom.reflexion).comp h = (Hom.id zero).comp (Hom.reflexion.comp h)
have id₁ : ((Hom.id zero).comp Hom.reflexion).comp Hom.right = (Hom.id zero).comp (Hom.reflexion.comp Hom.right)
Tactic: cases h
Cleared hypotheses: Z, h
-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Reflexive (goal)
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)
⊢ ((Hom.id zero).comp Hom.reflexion).comp h = (Hom.id zero).comp (Hom.reflexion.comp h)
have id₂ : ((Hom.id zero).comp Hom.reflexion).comp Hom.leftCompReflexion =
  (Hom.id zero).comp (Hom.reflexion.comp Hom.leftCompReflexion)
Tactic: cases h
Cleared hypotheses: Z, h