(13steps) PrintForm Definitions Lemmas list 3 jlc Sections Support(jlc) Doc

At: is member remove lemma 1
1. T: Type
2. eq: {T=}
3. eq TT
4. x,y:T. eq(x,y) x = y
5. L: T List
6. x: T
7. x(eq) L

M,N:T List. L = (M @ (x.N)) & remove(eq;x;L) = (M @ N)
By:
ListInd 5
THEN
Rewrite (HigherC is_member_unrollC THENC TryC (HigherC assert_evalC) THENC HigherC remove_unrollC) 0
Generated subgoals:

1 False (M,N:T List. nil = (M @ (x.N)) & nil = (M @ N))
27. u: T
8. v: T List
9. x(eq) v (M,N:T List. v = (M @ (x.N)) & remove(eq;x;v) = (M @ N))
if eq(x,u) true else x(eq) v fi (M,N:T List. u.v = (M @ (x.N)) & if eq(x,u) v else u.remove(eq;x;v) fi = (M @ N))

About:
listconsnilboolbtrueifthenelseassertapplyfunction
universeequalmemberimpliesandfalseallexists

(13steps) PrintForm Definitions Lemmas list 3 jlc Sections Support(jlc) Doc