Nuprl - Proof: select concat 2 1 2 1 1 1

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At: select concat 2 1 2 1 1 1

1. T : Type
2. (T List) List
3. u : T List
4. v : (T List) List
5.

||concat(v)||.
5.

||v||.
5. ||concat(firstn(m;v))||

n
5. & n-||concat(firstn(m;v))||<||v[m]||
5. & concat(v)[n] = v[m][(n-||concat(firstn(m;v))||)]
6. n :

||u @ concat(v)||
7.

n<||u||
8. m :

||v||
9. ||concat(firstn(m;v))||

n-||u||
10. n-||u||-||concat(firstn(m;v))||<||v[m]||
11. concat(v)[(n-||u||)] = v[m][(n-||u||-||concat(firstn(m;v))||)]

firstn(m+1;[u / v]) ~ [u / firstn(m;v)]

By:	RW (AddrC [1] (RecUnfoldC `firstn`)) 0 THEN Reduce 0 THEN SplitOnConclITE

Generated subgoals:

1 12. 0<m+1
[u / firstn(m+1-1;v)] ~ [u / firstn(m;v)]
1 step

2 12. m+10
nil ~ [u / firstn(m;v)]
Auto

About:

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1	12. 0<m+1 [u / firstn(m+1-1;v)] ~ [u / firstn(m;v)]	1 step
2	12. m+10 nil ~ [u / firstn(m;v)]	Auto