Module: Mathlib.Condensed.Discrete.LocallyConstant

Goal state before:
pp: P : TopCat → Prop
inst✝⁴ : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), HasProp P (Subtype p)
S✝ : CompHausLike P
Y✝ : (CompHausLike P)ᵒᵖ ⥤ Type (max u w)
inst✝³ : HasProp P PUnit.{u + 1}
f✝ : LocallyConstant (↑S✝.toTop) (Y✝.obj (op (of P PUnit.{u + 1})))
T : CompHausLike P
g✝ : T ⟶ S✝
X✝ : TopCat
inst✝² : HasExplicitFiniteCoproducts P
inst✝¹ : HasExplicitPullbacks P
hs : ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y), EffectiveEpi f → Surjective ⇑(ConcreteCategory.hom f)
inst✝ : HasExplicitFiniteCoproducts P
X Y : Sheaf (coherentTopology (CompHausLike P)) (Type (max u w))
g : X ⟶ Y
this : Preregular (CompHausLike P)
S : (CompHausLike P)ᵒᵖ
f : LocallyConstant (↑(unop S).toTop) (X.obj.obj (op (of P PUnit.{u + 1})))
a : Fiber ⇑(map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f)
⊢ ∀
    (a_1 :
      Fiber
        ⇑(comap
            (TopCat.Hom.hom (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).hom)
            f)),
    (ConcreteCategory.hom
          (Y.obj.map
            (sigmaIncl
                (comap
                  (TopCat.Hom.hom
                    (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).hom)
                  f)
                a_1).op))
        (counitAppAppImage (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a) =
      (ConcreteCategory.hom
          (Y.obj.map
            (sigmaIncl
                (comap
                  (TopCat.Hom.hom
                    (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).hom)
                  f)
                a_1).op))
        ((ConcreteCategory.hom
            (Y.obj.map (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).op))
          ((ConcreteCategory.hom (g.hom.app S)) ((ConcreteCategory.hom (counitAppApp (unop S) X.obj)) f)))

Tactic:
intro b

Goal state after:
P : TopCat → Prop
inst✝⁴ : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), HasProp P (Subtype p)
S✝ : CompHausLike P
Y✝ : (CompHausLike P)ᵒᵖ ⥤ Type (max u w)
inst✝³ : HasProp P PUnit.{u + 1}
f✝ : LocallyConstant (↑S✝.toTop) (Y✝.obj (op (of P PUnit.{u + 1})))
T : CompHausLike P
g✝ : T ⟶ S✝
X✝ : TopCat
inst✝² : HasExplicitFiniteCoproducts P
inst✝¹ : HasExplicitPullbacks P
hs : ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y), EffectiveEpi f → Surjective ⇑(ConcreteCategory.hom f)
inst✝ : HasExplicitFiniteCoproducts P
X Y : Sheaf (coherentTopology (CompHausLike P)) (Type (max u w))
g : X ⟶ Y
this : Preregular (CompHausLike P)
S : (CompHausLike P)ᵒᵖ
f : LocallyConstant (↑(unop S).toTop) (X.obj.obj (op (of P PUnit.{u + 1})))
a : Fiber ⇑(map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f)
b :
  Fiber
    ⇑(comap (TopCat.Hom.hom (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).hom)
        f)
⊢ (ConcreteCategory.hom
        (Y.obj.map
          (sigmaIncl
              (comap
                (TopCat.Hom.hom
                  (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).hom)
                f)
              b).op))
      (counitAppAppImage (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a) =
    (ConcreteCategory.hom
        (Y.obj.map
          (sigmaIncl
              (comap
                (TopCat.Hom.hom
                  (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).hom)
                f)
              b).op))
      ((ConcreteCategory.hom
          (Y.obj.map (sigmaIncl (map (⇑(ConcreteCategory.hom (g.hom.app (op (of P PUnit.{u + 1}))))) f) a).op))
        ((ConcreteCategory.hom (g.hom.app S)) ((ConcreteCategory.hom (counitAppApp (unop S) X.obj)) f)))