Nuprl - Pf not list all not iff list exists 1 2

1. T: Type
2. P: TProp
3. x:T. Dec(P(x))
4. L: T List
5. xL.P(x)

xL.(P(x))

By: ListInd 4

Generated subgoals:

1 xnil.P(x) xnil.(P(x))

2 5. u: T
6. v: T List
7. xv.P(x) xv.(P(x))
x(u.v).P(x) x(u.v).(P(x))

About:

1	`xnil.P(x) xnil.(P(x))`
2	5. `u:` `T` 6. `v:` `T List` 7. `xv.P(x) xv.(P(x))` `x(u.v).P(x) x(u.v).(P(x))`