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

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At: not list all 2 implies exists not 1 2 1 1

1. T: Type
2. eq: {T}
3. P: T
4. L: T List
5. u: T
6. v: T List
7. xv.P(x) (x:{x:T| x(eq) v }. P(x))
8. (P(u) & xv.P(x))

x:{x:T| if eq(x,u) true else x(eq) v fi }. P(x)

By: Inst Thm* Dec(P) Dec(Q) ((P & Q) P Q) [P(u);xv.P(x)]

Generated subgoal:

1 9. (P(u) & xv.P(x)) P(u) xv.P(x)
x:{x:T| if eq(x,u) true else x(eq) v fi }. P(x)

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