Module: Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks

Goal state before:
pp: case none
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
D : Type u₂
inst✝ : Category.{v₂, u₂} D
G : C ⥤ D
W X Y Z : C
h : X ⟶ Z
k : Y ⟶ Z
f : W ⟶ X
g : W ⟶ Y
comm : f ≫ h = g ≫ k
⊢ ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj (G.mapCocone (PushoutCocone.mk h k comm))).ι.app
        none ≫
      (Iso.refl
          ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj
              (G.mapCocone (PushoutCocone.mk h k comm))).pt).hom =
    (PushoutCocone.mk (G.map h) (G.map k) ⋯).ι.app none

pp: case some.left
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
D : Type u₂
inst✝ : Category.{v₂, u₂} D
G : C ⥤ D
W X Y Z : C
h : X ⟶ Z
k : Y ⟶ Z
f : W ⟶ X
g : W ⟶ Y
comm : f ≫ h = g ≫ k
⊢ ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj (G.mapCocone (PushoutCocone.mk h k comm))).ι.app
        (some WalkingPair.left) ≫
      (Iso.refl
          ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj
              (G.mapCocone (PushoutCocone.mk h k comm))).pt).hom =
    (PushoutCocone.mk (G.map h) (G.map k) ⋯).ι.app (some WalkingPair.left)

pp: case some.right
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
D : Type u₂
inst✝ : Category.{v₂, u₂} D
G : C ⥤ D
W X Y Z : C
h : X ⟶ Z
k : Y ⟶ Z
f : W ⟶ X
g : W ⟶ Y
comm : f ≫ h = g ≫ k
⊢ ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj (G.mapCocone (PushoutCocone.mk h k comm))).ι.app
        (some WalkingPair.right) ≫
      (Iso.refl
          ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj
              (G.mapCocone (PushoutCocone.mk h k comm))).pt).hom =
    (PushoutCocone.mk (G.map h) (G.map k) ⋯).ι.app (some WalkingPair.right)

Tactic:
<;>

Goal state after:
case none
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
D : Type u₂
inst✝ : Category.{v₂, u₂} D
G : C ⥤ D
W X Y Z : C
h : X ⟶ Z
k : Y ⟶ Z
f : W ⟶ X
g : W ⟶ Y
comm : f ≫ h = g ≫ k
⊢ ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj (G.mapCocone (PushoutCocone.mk h k comm))).ι.app
        none ≫
      (Iso.refl
          ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj
              (G.mapCocone (PushoutCocone.mk h k comm))).pt).hom =
    (PushoutCocone.mk (G.map h) (G.map k) ⋯).ι.app none

case some.left
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
D : Type u₂
inst✝ : Category.{v₂, u₂} D
G : C ⥤ D
W X Y Z : C
h : X ⟶ Z
k : Y ⟶ Z
f : W ⟶ X
g : W ⟶ Y
comm : f ≫ h = g ≫ k
⊢ ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj (G.mapCocone (PushoutCocone.mk h k comm))).ι.app
        (some WalkingPair.left) ≫
      (Iso.refl
          ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj
              (G.mapCocone (PushoutCocone.mk h k comm))).pt).hom =
    (PushoutCocone.mk (G.map h) (G.map k) ⋯).ι.app (some WalkingPair.left)

case some.right
C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
D : Type u₂
inst✝ : Category.{v₂, u₂} D
G : C ⥤ D
W X Y Z : C
h : X ⟶ Z
k : Y ⟶ Z
f : W ⟶ X
g : W ⟶ Y
comm : f ≫ h = g ≫ k
⊢ ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj (G.mapCocone (PushoutCocone.mk h k comm))).ι.app
        (some WalkingPair.right) ≫
      (Iso.refl
          ((Cocone.precompose (diagramIsoSpan (span f g ⋙ G)).symm.hom).obj
              (G.mapCocone (PushoutCocone.mk h k comm))).pt).hom =
    (PushoutCocone.mk (G.map h) (G.map k) ⋯).ι.app (some WalkingPair.right)