Nuprl Lemma : union-nat-missing-prop
∀s1,s2:nat-missing-type(). ∀x:ℕ.
(↑member-nat-missing(x;union-nat-missing(s1;s2)) ⇐⇒ (↑member-nat-missing(x;s1)) ∨ (↑member-nat-missing(x;s2)))
Proof
Definitions occuring in Statement :
union-nat-missing: union-nat-missing(s1;s2),
member-nat-missing: member-nat-missing(i;s),
nat-missing-type: nat-missing-type(),
nat: ℕ,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q
Lemmas :
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
nat_wf,
nat-missing-type_wf,
or_wf,
not_wf,
l_member_wf,
list_wf,
l-ordered_wf,
less_than_wf,
l_all_wf2,
assert-member-nat-missing,
assert_wf,
member-nat-missing_wf,
iff_wf,
union-nat-missing-pos-prop,
subtype_rel_sets,
union-nat-missing-pos_wf,
sq_stable__le,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel
\mforall{}s1,s2:nat-missing-type(). \mforall{}x:\mBbbN{}.
(\muparrow{}member-nat-missing(x;union-nat-missing(s1;s2))
\mLeftarrow{}{}\mRightarrow{} (\muparrow{}member-nat-missing(x;s1)) \mvee{} (\muparrow{}member-nat-missing(x;s2)))
Date html generated:
2015_07_17-AM-08_21_40
Last ObjectModification:
2015_04_02-PM-05_43_23
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