p (A : hsubtypes X) : prop (iseqclass X R.1 A) = propiseqclass X R.1 A
rem : Id (hsubtypes X) (setquotpr X R x.1).1 c.1 = <i> \(x : X) -> (rem' x) @ i -- inlined use of funext
where rem' (a : X) : Id hProp ((setquotpr X R x.1).1 a) (c.1 a) =
- uahp ((setquotpr X R x.1).1 a) (c.1 a) l2r r2l -- This is where uahp appears
+ uahp' ((setquotpr X R x.1).1 a) (c.1 a) l2r r2l -- This is where uahp appears
where
l2r (r : ((setquotpr X R x.1).1 a).1) : (c.1 a).1 = eqax1 X R.1 c.1 c.2 x.1 a r x.2
r2l : (c.1 a).1 -> ((setquotpr X R x.1).1 a).1 = eqax2 X R.1 c.1 c.2 x.1 a x.2
rem2 : Id (hsubtypes X) (setquotpr X R x).1 (setquotpr X R x').1 =
<i> \(x0 : X) -> rem x0 @ i
where
- rem (x0 : X) : Id hProp (R.1 x x0) (R.1 x' x0) = uahp (R.1 x x0) (R.1 x' x0) f g
+ rem (x0 : X) : Id hProp (R.1 x x0) (R.1 x' x0) = uahp' (R.1 x x0) (R.1 x' x0) f g
where
f (r0 : (R.1 x x0).1) : (R.1 x' x0).1 =
eqreltrans X R x' x x0 (eqrelsymm X R x x' a) r0