- INL
-
|- !x. ISL x ==> (INL (OUTL x) = x)
- INR
-
|- !x. ISR x ==> (INR (OUTR x) = x)
- INR_INL_11
-
|- (!y x. (INL x = INL y) = (x = y)) /\ !y x. (INR x = INR y) = (x = y)
- INR_neq_INL
-
|- !v1 v2. ~(INR v2 = INL v1)
- ISL_OR_ISR
-
|- !x. ISL x \/ ISR x
- sum_Axiom
-
|- !f g. ?h. (!x. h (INL x) = f x) /\ !y. h (INR y) = g y
- sum_case_cong
-
|- !g' g f' f M' M.
(M = M') /\ (!x. (M' = INL x) ==> (f x = f' x)) /\
(!y. (M' = INR y) ==> (g y = g' y)) ==>
(sum_case f g M = sum_case f' g' M')
- sum_CASES
-
|- !s. (?x. s = INL x) \/ ?x. s = INR x
- sum_distinct
-
|- !x y. ~(INL x = INR y)
- sum_INDUCT
-
|- !P. (!x. P (INL x)) /\ (!x. P (INR x)) ==> !s. P s