At:
list exists exists1221111
1.
T: Type
2.
eq: {T=}
3.
eq TT
4.
x,y:T. eq(x,y) x = y
5.
P: TType
6.
L: T List
7.
u: T
8.
v: T List
9.
xv.P(x) (x:{x:T| x(eq) v }. P(x))
10.
xv.P(x) (x:{x:T| x(eq) v }. P(x))
11.
x: T
12.
if eq(x,u) true else x(eq) v fi
13.
P(x)
Dec(x = u)
By:
Witness4 x
THEN
With u (Analyze -1)
Generated subgoal:
4. P: TType 5. L: T List 6. u: T 7. v: T List 8. xv.P(x) (x:{x:T| x(eq) v }. P(x)) 9. xv.P(x) (x:{x:T| x(eq) v }. P(x)) 10. x: T 11. if eq(x,u) true else x(eq) v fi 12. P(x) 13. eq(x,u) x = u Dec(x = u)