- delete_lemma
-
|- !f x. ~(part_fun_domain (update_fun f x undefined) x)
- delete_smaller
-
|- !f y.
FINITE {x | part_fun_domain f x} /\ part_fun_domain f y ==>
(CARD {x | part_fun_domain f x} =
SUC (CARD {x | part_fun_domain (update_fun f y undefined) x}))
- empty_part_fun_domain_EMPTY
-
|- {x | part_fun_domain empty_part_fun x} = {}
- EMPTY_part_fun_domain_imp_empty_part_fun
-
|- !f. ({x | part_fun_domain f x} = {}) ==> (f = empty_part_fun)
- gen_finfun_induction
-
|- !P.
(!f.
(!g.
CARD {x | part_fun_domain (finfun_apply g) x} <
CARD {x | part_fun_domain (finfun_apply f) x} ==>
P g) ==>
P f) ==>
(!f. P f)