Module: Mathlib.Algebra.Category.Ring.Under.Property

Goal state before:
pp: Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop
hQi : RespectsIso fun {R S} [CommRing R] [CommRing S] ↦ Q
hQe : HasEqualizers fun {R S} [CommRing R] [CommRing S] ↦ Q
R : CommRingCat
A : Under R
x✝ : (toMorphismProperty fun {R S} [CommRing R] [CommRing S] ↦ Q).underObj.limitsOfShape WalkingParallelPair A
pres : LimitPresentation WalkingParallelPair A
hpres :
  ∀ (j : WalkingParallelPair), (toMorphismProperty fun {R S} [CommRing R] [CommRing S] ↦ Q).underObj (pres.diag.obj j)
e : A ≅
  R.mkUnder
    ↥((CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.left)).equalizer
        (CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.right))) :=
  (limit.isoLimitCone { cone := { pt := A, π := pres.π }, isLimit := pres.isLimit }).symm ≪≫
    HasLimit.isoOfNatIso (diagramIsoParallelPair pres.diag) ≪≫
      limit.isoLimitCone
        {
          cone :=
            CommRingCat.Under.equalizerFork (pres.diag.map WalkingParallelPairHom.left)
              (pres.diag.map WalkingParallelPairHom.right),
          isLimit :=
            CommRingCat.Under.equalizerForkIsLimit (pres.diag.map WalkingParallelPairHom.left)
              (pres.diag.map WalkingParallelPairHom.right) }
this : (toMorphismProperty fun {R S} [CommRing R] [CommRing S] ↦ Q).RespectsIso
⊢ toMorphismProperty (fun {R S} [CommRing R] [CommRing S] ↦ Q)
    ((R.mkUnder
          ↥((CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.left)).equalizer
              (CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.right)))).hom ≫
      Under.Hom.right e.inv)

Tactic:
(toMorphismProperty Q).cancel_right_of_respectsIso

Goal state after:
Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop
hQi : RespectsIso fun {R S} [CommRing R] [CommRing S] ↦ Q
hQe : HasEqualizers fun {R S} [CommRing R] [CommRing S] ↦ Q
R : CommRingCat
A : Under R
x✝ : (toMorphismProperty fun {R S} [CommRing R] [CommRing S] ↦ Q).underObj.limitsOfShape WalkingParallelPair A
pres : LimitPresentation WalkingParallelPair A
hpres :
  ∀ (j : WalkingParallelPair), (toMorphismProperty fun {R S} [CommRing R] [CommRing S] ↦ Q).underObj (pres.diag.obj j)
e : A ≅
  R.mkUnder
    ↥((CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.left)).equalizer
        (CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.right))) :=
  (limit.isoLimitCone { cone := { pt := A, π := pres.π }, isLimit := pres.isLimit }).symm ≪≫
    HasLimit.isoOfNatIso (diagramIsoParallelPair pres.diag) ≪≫
      limit.isoLimitCone
        {
          cone :=
            CommRingCat.Under.equalizerFork (pres.diag.map WalkingParallelPairHom.left)
              (pres.diag.map WalkingParallelPairHom.right),
          isLimit :=
            CommRingCat.Under.equalizerForkIsLimit (pres.diag.map WalkingParallelPairHom.left)
              (pres.diag.map WalkingParallelPairHom.right) }
this : (toMorphismProperty fun {R S} [CommRing R] [CommRing S] ↦ Q).RespectsIso
⊢ toMorphismProperty (fun {R S} [CommRing R] [CommRing S] ↦ Q)
    (R.mkUnder
        ↥((CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.left)).equalizer
            (CommRingCat.toAlgHom (pres.diag.map WalkingParallelPairHom.right)))).hom