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At: l before-iff

T:Type, L:T List, x,y:T. x before y L (L1,L2,L3:T List. L = (L1 @ [x] @ L2 @ [y] @ L3))

By: InductionOnList

Generated subgoals:

11. T: Type
2. L: T List
x,y:T. x before y nil (L1,L2,L3:T List. nil = (L1 @ [x] @ L2 @ [y] @ L3))
1 step
 
21. 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))
x,y:T. x before y [u / v] (L1,L2,L3:T List. [u / v] = (L1 @ [x] @ L2 @ [y] @ L3))
12 steps

About:
listconsconsniluniverseequalallexists

(14steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc