Nuprl - Pf list exists is member lemma 1 1 2 1 1 2 1 1 1 1

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At: list exists is member lemma 1 1 2 1 1 2 1 1 1 1

1. T: Type
2. eq: TT
3. (x,y:T. eq(x,y) x = y) & eq TT
4. P: TProp
5. L: T List
6. x: T
7. P(x)
8. u: T
9. v: T List
10. x(eq) v yv.P(y)
11. if eq(x,u) true else x(eq) v fi
12. eq(x,u) = false

x(eq) v

By: IfThenElseCases 11

Generated subgoals:

1 11. eq(x,u) = true
12. true
13. eq(x,u) = false
x(eq) v

2 11. eq(x,u) = false
12. x(eq) v
13. eq(x,u) = false
x(eq) v

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(35steps) PrintForm Definitions Lemmas list 3 jlc Sections Support(jlc) Doc