Zulip Chat Archive
Stream: general
Topic: rfl works but "by refl" doesn't
Kenny Lau (Dec 06 2020 at 06:39):
I have come across a most interesting example where rfl
works but by refl
doesn't:
import category_theory.opposites
universe u
lemma foo (β γ : Type u) (f : γ ⟶ β) (z : γ) : f.op.unop z = f z := rfl -- works
lemma bar (β γ : Type u) (f : γ ⟶ β) (z : γ) : f.op.unop z = f z := by refl -- fails!
lemma baz (β γ : Type u) (f : γ ⟶ β) (z : γ) : f.op.unop z = f z := by exact rfl -- works!
Kenny Lau (Dec 06 2020 at 07:06):
@Reid Barton @Bhavik Mehta
Mario Carneiro (Dec 06 2020 at 07:14):
apply rfl
also fails
Eric Wieser (Dec 06 2020 at 08:02):
irreducible
strikes again?
Eric Wieser (Dec 06 2020 at 08:02):
Oh never mind, those are long hom arrows
Reid Barton (Dec 06 2020 at 10:10):
opposite
is indeed irreducible
though
Last updated: Dec 20 2023 at 11:08 UTC