proposition: Lemma bool_map_equiv_not_idmap (f : { f : Bool <~> Bool & ~(forall x, f x = x) }) : forall b, ~(f.1 b = b).
proof: Proof. intro b. intro H''. apply f.2. intro b'. pose proof (eval_bool_isequiv f.1). destruct b', b, (f.1 true), (f.1 false); simpl in *; match goal with | _ => assumption | _ => reflexivity | [ H : true = false |- _ ] => exact (match true_ne_false H with end) | [ H : false = true |- _ ] => exact (match false_ne_true H with end) end. Qed.
imports: HoTT(Basics Types HProp HSet Projective TruncType Truncations Modalities.Notnot Modalities.Open Modalities.Closed BoundedSearch Equiv.BiInv Spaces.Nat Spaces.Torus.TorusEquivCircles Metatheory.Core Metatheory.FunextVarieties)