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At: firstn lem1 1 2 2 1

1. T: Type
2. x:
3. 0 < x
4. as:T*. x-1 < ||as|| firstn(x-1+1;as) = (firstn(x-1;as) @ [as[(x-1)]])
5. as: T*
6. u: T
7. v: T*
8. x < ||v||+1

firstn(x+1;u.v) = (firstn(x;u.v) @ [(u.v)[x]])

By:
RecUnfold `firstn` 0
THEN
Reduce 0


Generated subgoal:

1 if 0 < x+1 u.firstn(x+1-1;v) else nil fi = (if 0 < x u.firstn(x-1;v) else nil fi @ [(u.v)[x]])


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intless_thanallimpliessubtractifthenelse