Nuprl - Proof: l member decomp2

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

T:Type. (x,y:T. Dec(x = y)) (s:T List, z:T. (z s) (s1,s2:T List. s = (s1 @ [z / s2]) & (z s1)))

By: InductionOnList

Generated subgoals:

1 1. T: Type
2. x,y:T. Dec(x = y)
3. s: T List
4. z: T
5. (z nil)
s1,s2:T List. nil = (s1 @ [z / s2]) & (z s1) 1 step

2 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])
s1,s2:T List. [u / v] = (s1 @ [z / s2]) & (z s1) 9 steps

About:

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

1	1. `T:` `Type` 2. `x,y:T. Dec(x = y)` 3. `s:` `T List` 4. `z:` `T` 5. `(z nil)` `s1,s2:T List. nil = (s1 @ [z / s2]) & (z s1)`	1 step

2	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])` `s1,s2:T List. [u / v] = (s1 @ [z / s2]) & (z s1)`	9 steps