At:
l before-iff211211
1.
T: Type
2.
L: T List
3.
u: T
4.
v: T List
5.
x,y:T. x before y v (L1,L2,L3:T List. v = (L1 @ [x] @ L2 @ [y] @ L3))
6.
x: T
7.
y: T
8.
x before y v
9.
x before y v (L1,L2,L3:T List. v = (L1 @ [x] @ L2 @ [y] @ L3))
10.
L1: T List
11.
L2: T List
12.
L3: T List
13.
v = (L1 @ [x] @ L2 @ [y] @ L3)
[u / v] = ([u / L1] @ [x] @ L2 @ [y] @ L3)
By:
All Reduce
THEN
Analyze
Generated subgoals:
x,y:T. x before y 
v 
(
L1,L2,L3:T List. v = (L1 @ [x] @ L2 @ [y] @ L3))
(
[u / v] = ([u / L1] @ [x] @ L2 @ [y] @ L3)