Lemma about the coercion ℕ → WithBot ℕ.

An orphaned lemma about casting from ℕ to WithBot ℕ, exiled here to minimize imports to data.rat.order for porting purposes.

instance instWellFoundedRelationWithTopNat : WellFoundedRelation (WithTop ℕ)

Equations

• instWellFoundedRelationWithTopNat = { rel := fun x x_1 => x < x_1, wf := instWellFoundedRelationWithTopNat.proof_1 }

theorem Nat.cast_withTop (n : ℕ) : ↑n = ↑n

theorem Nat.cast_withBot (n : ℕ) : ↑n = ↑n