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

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

By: Analyze -1 THEN Thin -1 THEN FwdThru -1 [-2]

Generated subgoal:

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

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