Nuprl - Proof: l member decomp2 2 2 2

(11steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc

1. T: Type
2. x,y:T. Dec(x = y)
3. s: T List
4. u: T
5. v: T List
6. z:T. (z v) (s1,s2:T List. v = (s1 @ [z / s2]) & (z s1))
7. z: T
8. (z [u / v])
9. z = u
10. s1,s2:T List. v = (s1 @ [z / s2]) & (z s1)

s1,s2:T List. [u / v] = (s1 @ [z / s2]) & (z s1)

By: ExRepD THEN InstConcl [[u / s1];s2] THEN Reduce 0

Generated subgoals:

1 10. s1: T List
11. s2: T List
12. v = (s1 @ [z / s2])
13. (z s1)
[u / v] = [u / (s1 @ [z / s2])] 1 step

2 10. s1: T List
11. s2: T List
12. v = (s1 @ [z / s2])
13. (z s1)
(z [u / s1]) 1 step

About:

(11steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc

1	10. `s1:` `T List` 11. `s2:` `T List` 12. `v = (s1 @ [z / s2])` 13. `(z s1)` `[u / v] = [u / (s1 @ [z / s2])]`	1 step

2	10. `s1:` `T List` 11. `s2:` `T List` 12. `v = (s1 @ [z / s2])` 13. `(z s1)` `(z [u / s1])`	1 step