@prefix log: <http://www.w3.org/2000/10/swap/log.n3#>.
@prefix : <#>.

{:x :in {:x :list :b}} a log:Truth; log:forAll :b, :x.
{{:x :in :b} log:implies {:x :in {:a :list :b}}} a log:Truth; log:forAll :a, :b, :x.

{{:nil :list {:z :list :nil}} :append :z} a log:Truth; log:forAll :z.
{{{:b :list {:z :list :nil}} :append :c} log:implies
  {{{:a :list :b} :list {:z :list :nil}} :append {:a :list :c}}} a log:Truth; log:forAll :a, :b, :c, :z.