mathlib-initiative/mathlib-tactics huggingface dataset:
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case tensorHom_def
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X₁✝ Y₁✝ X₂✝ Y₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ projectMapAux f✝¹ f✝ ⊗ₘ projectMapAux f✝¹ g✝ =
    projectMapAux f✝¹ f✝ ▷ projectObj f✝¹ X₂✝ ≫ projectObj f✝¹ Y₁✝ ◁ projectMapAux f✝¹ g✝

Tactic:
;

Goal state after:
case tensorHom_def
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X₁✝ Y₁✝ X₂✝ Y₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ projectMapAux f✝¹ f✝ ⊗ₘ projectMapAux f✝¹ g✝ =
    projectMapAux f✝¹ f✝ ▷ projectObj f✝¹ X₂✝ ≫ projectObj f✝¹ Y₁✝ ◁ projectMapAux f✝¹ g✝
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case comp_id
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ projectMapAux f✝¹ f✝ ≫ 𝟙 (projectObj f✝¹ Y✝) = projectMapAux f✝¹ f✝

Tactic:
;

Goal state after:
case comp_id
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ projectMapAux f✝¹ f✝ ≫ 𝟙 (projectObj f✝¹ Y✝) = projectMapAux f✝¹ f✝
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case id_comp
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ 𝟙 (projectObj f✝¹ X✝) ≫ projectMapAux f✝¹ f✝ = projectMapAux f✝¹ f✝

Tactic:
;

Goal state after:
case id_comp
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ 𝟙 (projectObj f✝¹ X✝) ≫ projectMapAux f✝¹ f✝ = projectMapAux f✝¹ f✝
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case assoc
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ U✝ V✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
h✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (projectMapAux f✝¹ f✝ ≫ projectMapAux f✝¹ g✝) ≫ projectMapAux f✝¹ h✝ =
    projectMapAux f✝¹ f✝ ≫ projectMapAux f✝¹ g✝ ≫ projectMapAux f✝¹ h✝

Tactic:
;

Goal state after:
case assoc
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝¹ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ U✝ V✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
h✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (projectMapAux f✝¹ f✝ ≫ projectMapAux f✝¹ g✝) ≫ projectMapAux f✝¹ h✝ =
    projectMapAux f✝¹ f✝ ≫ projectMapAux f✝¹ g✝ ≫ projectMapAux f✝¹ h✝
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case id_tensorHom_id
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ 𝟙 (projectObj f✝ X✝) ⊗ₘ 𝟙 (projectObj f✝ Y✝) = 𝟙 (projectObj f✝ (X✝.tensor Y✝))

Tactic:
;

Goal state after:
case id_tensorHom_id
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ 𝟙 (projectObj f✝ X✝) ⊗ₘ 𝟙 (projectObj f✝ Y✝) = 𝟙 (projectObj f✝ (X✝.tensor Y✝))
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case id_tensorHom_id
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ 𝟙 (projectObj f✝ X✝ ⊗ projectObj f✝ Y✝) = 𝟙 (projectObj f✝ (X✝.tensor Y✝))

Tactic:
;

Goal state after:
case id_tensorHom_id
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ 𝟙 (projectObj f✝ X✝ ⊗ projectObj f✝ Y✝) = 𝟙 (projectObj f✝ (X✝.tensor Y✝))
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case tensorHom_comp_tensorHom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X₁✝ Y₁✝ Z₁✝ X₂✝ Y₂✝ Z₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₁✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g₁✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (projectMapAux f✝ f₁✝ ⊗ₘ projectMapAux f✝ f₂✝) ≫ (projectMapAux f✝ g₁✝ ⊗ₘ projectMapAux f✝ g₂✝) =
    projectMapAux f✝ f₁✝ ≫ projectMapAux f✝ g₁✝ ⊗ₘ projectMapAux f✝ f₂✝ ≫ projectMapAux f✝ g₂✝

Tactic:
;

Goal state after:
case tensorHom_comp_tensorHom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X₁✝ Y₁✝ Z₁✝ X₂✝ Y₂✝ Z₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₁✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g₁✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (projectMapAux f✝ f₁✝ ⊗ₘ projectMapAux f✝ f₂✝) ≫ (projectMapAux f✝ g₁✝ ⊗ₘ projectMapAux f✝ g₂✝) =
    projectMapAux f✝ f₁✝ ≫ projectMapAux f✝ g₁✝ ⊗ₘ projectMapAux f✝ f₂✝ ≫ projectMapAux f✝ g₂✝
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case α_hom_inv
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ Z✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).hom ≫
      (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).inv =
    𝟙 (projectObj f✝ ((X✝.tensor Y✝).tensor Z✝))

Tactic:
;

Goal state after:
case α_hom_inv
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ Z✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).hom ≫
      (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).inv =
    𝟙 (projectObj f✝ ((X✝.tensor Y✝).tensor Z✝))
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case α_inv_hom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ Z✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).inv ≫
      (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).hom =
    𝟙 (projectObj f✝ (X✝.tensor (Y✝.tensor Z✝)))

Tactic:
;

Goal state after:
case α_inv_hom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ Y✝ Z✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).inv ≫
      (α_ (projectObj f✝ X✝) (projectObj f✝ Y✝) (projectObj f✝ Z✝)).hom =
    𝟙 (projectObj f✝ (X✝.tensor (Y✝.tensor Z✝)))
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case associator_naturality
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X₁✝ X₂✝ X₃✝ Y₁✝ Y₂✝ Y₃✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₁✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₃✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ ((projectMapAux f✝ f₁✝ ⊗ₘ projectMapAux f✝ f₂✝) ⊗ₘ projectMapAux f✝ f₃✝) ≫
      (α_ (projectObj f✝ Y₁✝) (projectObj f✝ Y₂✝) (projectObj f✝ Y₃✝)).hom =
    (α_ (projectObj f✝ X₁✝) (projectObj f✝ X₂✝) (projectObj f✝ X₃✝)).hom ≫
      (projectMapAux f✝ f₁✝ ⊗ₘ projectMapAux f✝ f₂✝ ⊗ₘ projectMapAux f✝ f₃✝)

Tactic:
;

Goal state after:
case associator_naturality
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X₁✝ X₂✝ X₃✝ Y₁✝ Y₂✝ Y₃✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₁✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₂✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f₃✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ ((projectMapAux f✝ f₁✝ ⊗ₘ projectMapAux f✝ f₂✝) ⊗ₘ projectMapAux f✝ f₃✝) ≫
      (α_ (projectObj f✝ Y₁✝) (projectObj f✝ Y₂✝) (projectObj f✝ Y₃✝)).hom =
    (α_ (projectObj f✝ X₁✝) (projectObj f✝ X₂✝) (projectObj f✝ X₃✝)).hom ≫
      (projectMapAux f✝ f₁✝ ⊗ₘ projectMapAux f✝ f₂✝ ⊗ₘ projectMapAux f✝ f₃✝)
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case ρ_hom_inv
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (ρ_ (projectObj f✝ X✝)).hom ≫ (ρ_ (projectObj f✝ X✝)).inv = 𝟙 (projectObj f✝ (X✝.tensor unit))

Tactic:
;

Goal state after:
case ρ_hom_inv
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (ρ_ (projectObj f✝ X✝)).hom ≫ (ρ_ (projectObj f✝ X✝)).inv = 𝟙 (projectObj f✝ (X✝.tensor unit))
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case ρ_inv_hom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (ρ_ (projectObj f✝ X✝)).inv ≫ (ρ_ (projectObj f✝ X✝)).hom = 𝟙 (projectObj f✝ X✝)

Tactic:
;

Goal state after:
case ρ_inv_hom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (ρ_ (projectObj f✝ X✝)).inv ≫ (ρ_ (projectObj f✝ X✝)).hom = 𝟙 (projectObj f✝ X✝)
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case l_hom_inv
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (λ_ (projectObj f✝ X✝)).hom ≫ (λ_ (projectObj f✝ X✝)).inv = 𝟙 (projectObj f✝ (unit.tensor X✝))

Tactic:
;

Goal state after:
case l_hom_inv
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (λ_ (projectObj f✝ X✝)).hom ≫ (λ_ (projectObj f✝ X✝)).inv = 𝟙 (projectObj f✝ (unit.tensor X✝))
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case l_inv_hom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (λ_ (projectObj f✝ X✝)).inv ≫ (λ_ (projectObj f✝ X✝)).hom = 𝟙 (projectObj f✝ X✝)

Tactic:
;

Goal state after:
case l_inv_hom
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f✝ : C → D
X Y : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f g : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
X✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ (λ_ (projectObj f✝ X✝)).inv ≫ (λ_ (projectObj f✝ X✝)).hom = 𝟙 (projectObj f✝ X✝)
Module: Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic

Goal state before:
pp: A : Type u₁
B : Type u₂
C : Type u₃
inst✝⁶ : Category.{v₁, u₁} A
inst✝⁵ : Category.{v₂, u₂} B
inst✝⁴ : Category.{v₃, u₃} C
F : A ⥤ B
G : C ⥤ B
A₁ : Type u₄
B₁ : Type u₅
C₁ : Type u₆
inst✝³ : Category.{v₄, u₄} A₁
inst✝² : Category.{v₅, u₅} B₁
inst✝¹ : Category.{v₆, u₆} C₁
F₁ : A₁ ⥤ B₁
G₁ : C₁ ⥤ B₁
X : Type u₇
inst✝ : Category.{v₇, u₇} X
X✝ : CatCospanTransform F G F₁ G₁
⊢ {
      app := fun S ↦
        { fst := { app := fun y ↦ (𝟙 X✝).left.app (S.fst.obj y), naturality := ⋯ },
          snd := { app := fun y ↦ (𝟙 X✝).right.app (S.snd.obj y), naturality := ⋯ }, w := ⋯ },
      naturality := ⋯ } =
    𝟙
      {
        obj := fun S ↦
          { fst := S.fst ⋙ X✝.left, snd := S.snd ⋙ X✝.right,
            iso :=
              S.fst.associator X✝.left F₁ ≪≫
                S.fst.isoWhiskerLeft (CatCommSq.iso F X✝.left X✝.base F₁).symm ≪≫
                  (S.fst.associator F X✝.base).symm ≪≫
                    isoWhiskerRight S.iso X✝.base ≪≫
                      S.snd.associator G X✝.base ≪≫
                        S.snd.isoWhiskerLeft (CatCommSq.iso G X✝.right X✝.base G₁) ≪≫
                          (S.snd.associator X✝.right G₁).symm },
        map := fun {x y} f ↦ { fst := whiskerRight f.fst X✝.left, snd := whiskerRight f.snd X✝.right, w := ⋯ },
        map_id := ⋯, map_comp := ⋯ }

Tactic:
;

Goal state after:
A : Type u₁
B : Type u₂
C : Type u₃
inst✝⁶ : Category.{v₁, u₁} A
inst✝⁵ : Category.{v₂, u₂} B
inst✝⁴ : Category.{v₃, u₃} C
F : A ⥤ B
G : C ⥤ B
A₁ : Type u₄
B₁ : Type u₅
C₁ : Type u₆
inst✝³ : Category.{v₄, u₄} A₁
inst✝² : Category.{v₅, u₅} B₁
inst✝¹ : Category.{v₆, u₆} C₁
F₁ : A₁ ⥤ B₁
G₁ : C₁ ⥤ B₁
X : Type u₇
inst✝ : Category.{v₇, u₇} X
X✝ : CatCospanTransform F G F₁ G₁
⊢ {
      app := fun S ↦
        { fst := { app := fun y ↦ (𝟙 X✝).left.app (S.fst.obj y), naturality := ⋯ },
          snd := { app := fun y ↦ (𝟙 X✝).right.app (S.snd.obj y), naturality := ⋯ }, w := ⋯ },
      naturality := ⋯ } =
    𝟙
      {
        obj := fun S ↦
          { fst := S.fst ⋙ X✝.left, snd := S.snd ⋙ X✝.right,
            iso :=
              S.fst.associator X✝.left F₁ ≪≫
                S.fst.isoWhiskerLeft (CatCommSq.iso F X✝.left X✝.base F₁).symm ≪≫
                  (S.fst.associator F X✝.base).symm ≪≫
                    isoWhiskerRight S.iso X✝.base ≪≫
                      S.snd.associator G X✝.base ≪≫
                        S.snd.isoWhiskerLeft (CatCommSq.iso G X✝.right X✝.base G₁) ≪≫
                          (S.snd.associator X✝.right G₁).symm },
        map := fun {x y} f ↦ { fst := whiskerRight f.fst X✝.left, snd := whiskerRight f.snd X✝.right, w := ⋯ },
        map_id := ⋯, map_comp := ⋯ }
Module: Mathlib.CategoryTheory.Monoidal.Free.Basic

Goal state before:
pp: case mk.mk
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f : C → D
X✝ Y✝ Z✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : X✝ ⟶ Y✝
a✝¹ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g✝ : Y✝ ⟶ Z✝
a✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ projectMap f X✝ Z✝ (Quot.mk (⇑(X✝.setoidHom Y✝)) a✝¹ ≫ Quot.mk (⇑(Y✝.setoidHom Z✝)) a✝) =
    projectMap f X✝ Y✝ (Quot.mk (⇑(X✝.setoidHom Y✝)) a✝¹) ≫ projectMap f Y✝ Z✝ (Quot.mk (⇑(Y✝.setoidHom Z✝)) a✝)

Tactic:
;

Goal state after:
case mk.mk
C : Type u
D : Type u'
inst✝¹ : Category.{v', u'} D
inst✝ : MonoidalCategory D
f : C → D
X✝ Y✝ Z✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
f✝ : X✝ ⟶ Y✝
a✝¹ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
g✝ : Y✝ ⟶ Z✝
a✝ : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
⊢ projectMap f X✝ Z✝ (Quot.mk (⇑(X✝.setoidHom Y✝)) a✝¹ ≫ Quot.mk (⇑(Y✝.setoidHom Z✝)) a✝) =
    projectMap f X✝ Y✝ (Quot.mk (⇑(X✝.setoidHom Y✝)) a✝¹) ≫ projectMap f Y✝ Z✝ (Quot.mk (⇑(Y✝.setoidHom Z✝)) a✝)