Nuprl - Pf is member remove lemma 1 2

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

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. 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))

By: GenConcl (eq(x,u) = b) THEN BoolInd -2 THEN Rewrite (HigherC ifthenelse_evalC THENC TryC (HigherC assert_evalC)) 0

Generated subgoals:

1 10. eq(x,u) = true
True (M,N:T List. u.v = (M @ (x.N)) & v = (M @ N))

2 10. eq(x,u) = false
x(eq) v (M,N:T List. u.v = (M @ (x.N)) & u.remove(eq;x;v) = (M @ N))

About:

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

1	10. `eq(x,u) = true` `True (M,N:T List. u.v = (M @ (x.N)) & v = (M @ N))`
2	10. `eq(x,u) = false` `x(eq) v (M,N:T List. u.v = (M @ (x.N)) & u.remove(eq;x;v) = (M @ N))`