- lift_CASES
-
|- !l. (?x. l = lift x) \/ (l = undefined)
- lift_INDUCTION
-
|- !P. (!x. P (lift x)) /\ P undefined ==> (!l. P l)
- lift_ONE_ONE
-
|- !x x'. (lift x = lift x') = x = x'
- lift_constructors_distinct
-
|- !x. ~(lift x = undefined)
- lift_Axiom
-
|- !f e. ?!fn. (!x. fn (lift x) = f x) /\ (fn undefined = e)
- undef_not_lift
-
|- !x. ~(undefined = lift x)
- undefined_not_exists_THM
-
|- !y. (y = undefined) = ~(?x. y = lift x)
- exists_not_undefined_THM
-
|- !y. (?x. y = lift x) = ~(y = undefined)
- is_defined_lemma
-
|- (!x. is_defined (lift x)) /\ ~(is_defined undefined)
- is_defined_is_not_undefined
-
|- !x. is_defined x = ~(x = undefined)
- lift_lower_THM
-
|- !y. (lift (lower y) = y) = is_defined y
- lower_ONE_ONE
-
|- !x y. is_defined x /\ is_defined y ==> ((lower x = lower y) = x = y)