Nuprl Lemma : assert-in-missing-nat-iff
∀i:ℕ. ∀missing:{l:ℕ List| l-ordered(ℕ;x,y.x < y;l)} . (↑in-missing(i;missing) ⇐⇒ (i ∈ missing))
Proof
Definitions occuring in Statement :
in-missing: in-missing(i;missing),
l_member: (x ∈ l),
list: T List,
nat: ℕ,
assert: ↑b,
less_than: a < b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
l-ordered: l-ordered(T;x,y.R[x; y];L)
Lemmas :
assert-in-missing-nat,
assert_wf,
in-missing_wf,
subtype_rel_list,
nat_wf,
sq_stable__assert,
list_induction,
l_member_wf,
false_wf,
true_wf,
l-ordered-nil-true,
less_than_wf,
nil_member,
nil_wf,
l-ordered_wf,
reduce_cons_lemma,
iff_transitivity,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
bor_wf,
eq_int_wf,
le_wf,
or_wf,
equal_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_bor,
assert_of_eq_int,
sq_stable__le,
le_weakening,
decidable__equal_int,
not-equal-2,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-commutes,
le-add-cancel,
add-swap,
equal-wf-base,
int_subtype_base,
le_weakening2,
all_wf,
l-ordered-cons,
cons_member,
cons_wf,
set_wf,
list_wf
\mforall{}i:\mBbbN{}. \mforall{}missing:\{l:\mBbbN{} List| l-ordered(\mBbbN{};x,y.x < y;l)\} . (\muparrow{}in-missing(i;missing) \mLeftarrow{}{}\mRightarrow{} (i \mmember{} missing))
Date html generated:
2015_07_17-AM-08_21_21
Last ObjectModification:
2015_04_02-PM-05_43_04
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