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At: equal appends

T:Type, a,c,b,d:T List. (a @ b) = (c @ d) (e:T List. a = (c @ e) & d = (e @ b) c = (a @ e) & b = (e @ d))

By:
InductionOnList
THEN
Reduce 0


Generated subgoals:

11. T: Type
2. a: T List
c,b,d:T List. b = (c @ d) (e:T List. nil = (c @ e) & d = (e @ b) c = e & b = (e @ d))
1 step
 
21. T: Type
2. a: T List
3. u: T
4. v: T List
5. c,b,d:T List. (v @ b) = (c @ d) (e:T List. v = (c @ e) & d = (e @ b) c = (v @ e) & b = (e @ d))
c,b,d:T List. [u / (v @ b)] = (c @ d) (e:T List. [u / v] = (c @ e) & d = (e @ b) c = [u / (v @ e)] & b = (e @ d))
3 steps

About:
listconsniluniverseequalimpliesandorallexists

(5steps total) PrintForm Definitions graph 1 1 Sections Graphs Doc