more test cases, problem in Tree.newt

newt/Tree.newt

@@ -0,0 +1,70 @@
+module Tree
+
+-- https://youtu.be/v2yXrOkzt5w?t=3013
+
+data Nat : U where
+  Z : Nat
+  S : Nat -> Nat
+
+data Unit : U where
+  MkUnit : Unit
+
+data Void : U where
+
+infixl 4 _+_
+
+data _+_ : U -> U -> U where
+  inl : {A B : U} -> A -> A + B
+  inr : {A B : U} -> B -> A + B
+
+infix 4 _<=_
+
+_<=_ : Nat -> Nat -> U
+Z <= y = Unit
+S x <= Z = Void
+S x <= S y = x <= y
+
+cmp : (x y : Nat) -> (x <= y) + (y <= x)
+cmp Z y = inl MkUnit
+cmp (S z) Z = inr MkUnit
+cmp (S x) (S y) = cmp x y
+
+-- 53:21
+
+data Bnd : U where
+  Bot : Bnd
+  N : Nat -> Bnd
+  Top : Bnd
+
+infix 4 _<<=_
+
+_<<=_ : Bnd -> Bnd -> U
+Bot <<= _ = Unit
+N x <<= N y = x <= y
+_ <<= Top = Unit
+_ <<= _ = Void
+
+data Intv : Bnd -> Bnd -> U where
+  MkInt : {l u : Bnd} (x : Nat) (lx : l <<= N x) (xu : N x <<= u) -> Intv l u
+
+data T23 : Bnd -> Bnd -> Nat -> U where
+  leaf : {l u : Bnd} {h : Nat} (lu : l <<= u) -> T23 l u Z
+  node2 : {l u : Bnd} {h : Nat} (x : _)
+    (tlx : T23 l (N x) h) (txu : T23 (N x) u h) ->
+    T23 l u (S h)
+  node3 : {l u : Bnd} {h : Nat} (x y : _)
+    (tlx : T23 l (N x) h) (txy : T23 (N x) (N y) h) (tyu : T23 (N y) u h) ->
+    T23 l u (S h)
+
+-- -- 56:
+
+infixl 5 _*_
+infixl 1 _,_
+data Sg : (A : U) -> (A -> U) -> U where
+  _,_ : {A : U} {B : A -> U} -> (a : A) -> B a -> Sg A B
+
+data _*_ : (A B : U) -> U where
+   Foo : {A B : U} -> A -> B -> A * B
+
+TooBig : Bnd -> Bnd -> Nat -> U
+TooBig l u h = Sg Nat (\ x => T23 l (N x) h * T23 (N x) u h)