fact: Fixpoint sperners_lemma_1d {n} : forall (f : Fin (n.+2) -> DHProp) (left_true : f fin_zero) (right_false : ~ f fin_last), {k : Fin n.+1 & f (fin_incl k) /\ ~ f (fsucc k)}.
imports: Basics Types HSet Spaces.Nat.Core Equiv.PathSplit