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At: is intersection implies exists element 1 2 1
1. T: Type
2. eq: {T=}
3. L: T List
4. M: T List
5. u: T
6. v: T List
7. v(eq)M (x:{x:T| x(eq) v }. x(eq) M)
8. u(eq) M

x:{x:T| if eq(x,u) true else x(eq) v fi }. x(eq) M
By: Witness u
Generated subgoal:

1 u {x:T| if eq(x,u) true else x(eq) v fi }

About:
listbtrueifthenelseassert
setapplyuniversememberimplies
exists

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