-- Grad Lemma, takes a line eq in U, 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
-- and f u, where f is transNegLine eq
-gradLemmaU :: Val -> Val -> System Val -> Val -> (Val, Val)
-gradLemmaU b eq us v = (u, VPath i theta)
- where i:j:_ = freshs (b,eq,us,v)
- ej = eq @@ j
- a = eq @@ One
- ws = mapWithKey (\alpha uAlpha ->
- transFillNeg j (ej `face` alpha) uAlpha) us
- u = comp j ej v ws
- w = fill j ej v ws
- xs = insertSystem (i ~> 0) w $
- insertSystem (i ~> 1) (transFillNeg j ej u) $ ws
- theta = compNeg j ej u xs
+-- gradLemmaU :: Val -> Val -> System Val -> Val -> (Val, Val)
+-- gradLemmaU b eq us v = (u, VPath i theta)
+-- where i:j:_ = freshs (b,eq,us,v)
+-- ej = eq @@ j
+-- a = eq @@ One
+-- ws = mapWithKey (\alpha uAlpha ->
+-- transFillNeg j (ej `face` alpha) uAlpha) us
+-- u = comp j ej v ws
+-- w = fill j ej v ws
+-- xs = insertSystem (i ~> 0) w $
+-- insertSystem (i ~> 1) (transFillNeg j ej u) $ ws
+-- theta = compNeg j ej u xs