(L R : Type) (s : InSort S L R) (xL : L -> No) (xR : R -> No) (xcut : forall (l : L) (r : R), xL l < xR r) (L' R' : Type) (s' : InSort S L' R') (yL : L' -> No) (yR : R' -> No) (ycut : forall (l : L') (r : R'), yL l < yR r) : le' {{xL | xR // xcut}} {{yL | yR // ycut}} = ((forall l, lt' (xL l) {{ yL | yR // ycut }}) * (forall r', lt' {{ xL | xR // xcut }} (yR r'))) (** For some reason, Coq has a really hard time checking the version of this that asserts an equality in [HProp].
Require Import HoTT.Basics HoTT.Types. Require Import TruncType HSet. Require Import HoTT.Truncations.Core.