- mid T m$ xs m$ mid f
-== mid T m$ ((mid id) m$ xs) m$ mid f, by 1
-== mid (○) m$ mid T m$ mid id m$ xs m$ mid f, by 3
-== mid ($id) m$ (mid (○) m$ mid T) m$ xs m$ mid f, by 4
-== mid (○) m$ mid ($id) m$ mid (○) m$ mid T m$ xs m$ mid f, by 3
-== mid ((○) ($id)) m$ mid (○) m$ mid T m$ xs m$ mid f, by 2
-== mid ((○) ($id) (○)) m$ mid T m$ xs m$ mid f, by 2
-== mid id m$ mid T m$ xs m$ mid f, by definitions of ○ and $
-== mid T m$ xs m$ mid f, by 1
-== mid ($f) m$ (mid T m$ xs), by 4
-== mid (○) m$ mid ($f) m$ mid T m$ xs, by 3
-== mid ((○) ($f)) m$ mid T m$ xs, by 2
-== mid ((○) ($f) T) m$ xs, by 2
-== mid f m$ xs, by definitions of ○ and $ and T == flip ($)
+ ⇧T ¢ xs ¢ ⇧f
+== ⇧T ¢ ((⇧id) ¢ xs) ¢ ⇧f, by 1
+== ⇧(○) ¢ ⇧T ¢ ⇧id ¢ xs ¢ ⇧f, by 3
+== ⇧($id) ¢ (⇧(○) ¢ ⇧T) ¢ xs ¢ ⇧f, by 4
+== ⇧(○) ¢ ⇧($id) ¢ ⇧(○) ¢ ⇧T ¢ xs ¢ ⇧f, by 3
+== ⇧((○) ($id)) ¢ ⇧(○) ¢ ⇧T ¢ xs ¢ ⇧f, by 2
+== ⇧((○) ($id) (○)) ¢ ⇧T ¢ xs ¢ ⇧f, by 2
+== ⇧id ¢ ⇧T ¢ xs ¢ ⇧f, by definitions of ○ and $
+== ⇧T ¢ xs ¢ ⇧f, by 1
+== ⇧($f) ¢ (⇧T ¢ xs), by 4
+== ⇧(○) ¢ ⇧($f) ¢ ⇧T ¢ xs, by 3
+== ⇧((○) ($f)) ¢ ⇧T ¢ xs, by 2
+== ⇧((○) ($f) T) ¢ xs, by 2
+== ⇧f ¢ xs, by definitions of ○ and $ and T == flip ($)