RingHom.StableUnderComposition.respectsIso

theorem RingHom.StableUnderComposition.respectsIso : ∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}, RingHom.StableUnderComposition P → (∀ {R S : Type u} [inst : CommRing R] [inst_1 : CommRing S] (e : R ≃+* S), P e.toRingHom) → RingHom.RespectsIso P

The theorem `RingHom.StableUnderComposition.respectsIso` states that for any property `P` of ring homomorphisms, if `P` is stable under composition (i.e., the composition of two ring homomorphisms that satisfy `P` also satisfies `P`), and if `P` holds for any isomorphism (viewed as a ring homomorphism), then `P` respects isomorphisms. This means that if `P` holds for a ring homomorphism `f`, it will still hold when `f` is pre- or post-composed with an isomorphism.

More concisely: If a property `P` of ring homomorphisms is stable under composition and holds for isomorphisms, then `P` respects isomorphisms.