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At: equal appends case1

T:Type, x1,z,x2,x3:T List. ||x1||||z|| (x1 @ x2) = (z @ x3) (z':T List. z = (x1 @ z') & x2 = (z' @ x3))

By:
InductionOnList
THEN
Reduce 0


Generated subgoals:

11. T: Type
2. x1: T List
z,x2,x3:T List. 0||z|| x2 = (z @ x3) (z':T List. z = z' & x2 = (z' @ x3))
1 step
 
21. T: Type
2. x1: T List
3. u: T
4. v: T List
5. z,x2,x3:T List. ||v||||z|| (v @ x2) = (z @ x3) (z':T List. z = (v @ z') & x2 = (z' @ x3))
z,x2,x3:T List. ||v||+1||z|| [u / (v @ x2)] = (z @ x3) (z':T List. z = [u / (v @ z')] & x2 = (z' @ x3))
6 steps

About:
listconsnatural_numberadduniverse
equalimpliesandall
exists

(8steps total) PrintForm Definitions graph 1 1 Sections Graphs Doc