Nuprl Lemma : isEmpty-nat-missing-prop
∀s:nat-missing-type(). (↑isEmpty-nat-missing(s) ⇐⇒ ∀x:ℕ. (¬↑member-nat-missing(x;s)))
Proof
Definitions occuring in Statement :
isEmpty-nat-missing: isEmpty-nat-missing(s),
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,
not: ¬A
Lemmas :
iff_transitivity,
assert_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
null_wf3,
subtype_rel_list,
nat_wf,
top_wf,
less_than_wf,
equal-wf-T-base,
list_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_null,
less_than_transitivity1,
less_than_irreflexivity,
le_wf,
not_wf,
l_member_wf,
assert-member-nat-missing,
member-nat-missing_wf,
isEmpty-nat-missing_wf,
sq_stable__assert,
all_wf,
nat-missing-type_wf,
decidable__lt,
not_over_and,
decidable__le,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero,
add-associates,
add-commutes,
le-add-cancel,
l_all_iff,
decidable__assert,
member_exists,
less_than_transitivity2,
le_weakening2
\mforall{}s:nat-missing-type(). (\muparrow{}isEmpty-nat-missing(s) \mLeftarrow{}{}\mRightarrow{} \mforall{}x:\mBbbN{}. (\mneg{}\muparrow{}member-nat-missing(x;s)))
Date html generated:
2015_07_17-AM-08_21_27
Last ObjectModification:
2015_04_02-PM-05_43_13
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