Nuprl Lemma : remove-nat-missing-prop
∀s:nat-missing-type(). ∀x,y:ℕ.
(↑member-nat-missing(x;remove-nat-missing(y;s)) ⇐⇒ (¬(x = y ∈ ℕ)) ∧ (↑member-nat-missing(x;s)))
Proof
Definitions occuring in Statement :
remove-nat-missing: remove-nat-missing(i;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,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
assert_of_null,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nat_wf,
equal-wf-T-base,
list_wf,
neg_assert_of_eq_int,
assert_of_lt_int,
less_than_wf,
nat-missing-type_wf,
le_antisymmetry_iff,
condition-implies-le,
subtract_wf,
add-associates,
minus-one-mul,
add-swap,
add_functionality_wrt_le,
add-commutes,
le-add-cancel-alt,
decidable__le,
false_wf,
not-le-2,
minus-add,
le-add-cancel2,
not_wf,
squash_wf,
true_wf,
l_member_wf,
iff_weakening_equal,
le_wf,
assert-member-nat-missing,
sq_stable__le,
minus-minus,
add-zero,
l-ordered-nil,
l_all_nil,
l-ordered_wf,
l_all_wf2,
assert_wf,
member-nat-missing_wf,
iff_wf,
value-type-has-value,
set-value-type,
int-value-type,
last_wf,
null_wf3,
subtype_rel_list,
top_wf,
sqequal-tt-to-assert,
sqequal-ff-to-assert,
all_wf,
select-last-in-nat-missing_wf,
subtype_rel_sets,
filter_wf5,
lt_int_wf,
l-ordered-filter,
l_all_iff,
member_filter_2,
set_wf,
nil_wf,
not_over_and,
decidable__l_member,
decidable__equal_nat,
le_transitivity,
and_wf,
decidable__equal_int,
not-equal-2,
le-add-cancel,
zero-le-nat,
le_weakening,
last_member,
select_wf,
non_neg_length,
length_wf_nat,
length_wf,
l-ordered-inst,
decidable__lt,
zero-add,
less-iff-le,
lelt_wf,
le_weakening2,
subtract-is-less,
int_seg_wf,
less_than_transitivity1,
less_than_irreflexivity,
member-insert-combine2,
or_wf,
exists_wf,
iseg_wf,
append_wf,
cons_wf,
int-minus-comparison-inc_wf,
comparison_wf,
length-append,
insert-combine_wf,
l-ordered-insert-combine,
less_than_transitivity2,
member-insert-combine,
l_exists_iff,
decidable__l_all-better-extract,
not-l_all-dec,
length-filter-pos,
le_int_wf,
assert_of_le_int,
tl_wf,
hd_wf,
not-ge-2,
list_decomp,
l-ordered-decomp,
l_before_wf,
bnot_wf,
cons_member,
hd_member,
list-cases,
null_nil_lemma,
length_of_nil_lemma,
product_subtype_list,
null_cons_lemma,
length_of_cons_lemma,
append_assoc,
list_ind_cons_lemma,
list_ind_nil_lemma,
l-ordered-decomp2,
member_filter,
iseg_member,
member_append
\mforall{}s:nat-missing-type(). \mforall{}x,y:\mBbbN{}.
(\muparrow{}member-nat-missing(x;remove-nat-missing(y;s)) \mLeftarrow{}{}\mRightarrow{} (\mneg{}(x = y)) \mwedge{} (\muparrow{}member-nat-missing(x;s)))
Date html generated:
2015_07_17-AM-08_21_56
Last ObjectModification:
2015_07_16-AM-10_52_14
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