Nuprl - Pf is member remove lemma 1 2 2

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At: is member remove lemma 1 2 2

1. T: Type
2. eq: {T=}
3. eq TT
4. x,y:T. eq(x,y) x = y
5. L: T List
6. x: T
7. u: T
8. v: T List
9. x(eq) v (M,N:T List. v = (M @ (x.N)) & remove(eq;x;v) = (M @ N))
10. eq(x,u) = false

x(eq) v (M,N:T List. u.v = (M @ (x.N)) & u.remove(eq;x;v) = (M @ N))

By: Analyze 0 THEN RenameVar `xx' -1 THEN Witness9 xx THEN Analyze -1 THEN Analyze -1

Generated subgoal:

1 9. eq(x,u) = false
10. xx: x(eq) v
11. M: T List
12. N: T List
13. v = (M @ (x.N)) & remove(eq;x;v) = (M @ N)
M,N:T List. u.v = (M @ (x.N)) & u.remove(eq;x;v) = (M @ N)

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