isos'
ls' = mapWithKey (\gamma isoG ->
- pathComp i (b `face` gamma) (v `face` gamma)
+ pathComp i (b `face` gamma) (vi0 `face` gamma)
(isoFun isoG `app` (us' ! gamma)) (vs `face` gamma))
isos'
else fst (uls'' ! gamma))
isosI1
--- assumes u and u' : A are solutions of us + (i0 -> u(i0))
--- The output is an L-path in A(i1) between u(i1) and u'(i1)
+-- Assumes u' : A is a solution of us + (i0 -> u0)
+-- The output is an L-path in A(i1) between comp i u0 us and u'(i1)
pathComp :: Name -> Val -> Val -> Val -> System Val -> Val
-pathComp i a u u' us = VPath j $ comp i a (u `face` (i ~> 0)) us'
- where j = fresh (Atom i,a,us,u,u')
- us' = insertsSystem [(j ~> 0, u), (j ~> 1, u')] us
+pathComp i a u0 u' us = VPath j $ comp i a u0 us'
+ where j = fresh (Atom i,a,us,u0,u')
+ us' = insertsSystem [(j ~> 1, u')] us
-- Grad Lemma, takes an iso f, a system us and a value v, s.t. f us =
-- border v. Outputs (u,p) s.t. border u = us and a path p between v