Nuprl Lemma : add-nat-missing-prop
∀s:nat-missing-type(). ∀x,y:ℕ.
(↑member-nat-missing(x;add-nat-missing(y;s)) ⇐⇒ (x = y ∈ ℕ) ∨ (↑member-nat-missing(x;s)))
Proof
Definitions occuring in Statement :
add-nat-missing: add-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,
or: P ∨ Q,
equal: s = t ∈ T
Lemmas :
lt_int_wf,
iff_transitivity,
assert_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
bnot_wf,
in-missing_wf,
append_wf,
subtype_rel_list,
nat_wf,
from-upto_wf,
le_wf,
less_than_wf,
not_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_bnot,
assert-in-missing-nat-iff,
l_member_wf,
subtype_rel_sets,
decidable__le,
false_wf,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
zero-add,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
list_wf,
l-ordered_wf,
l_all_wf2,
or_wf,
equal_wf,
eq_int_wf,
equal-wf-base-T,
set_subtype_base,
int_subtype_base,
remove-combine_wf,
subtract_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
assert_of_lt_int,
eqff_to_assert,
assert_of_eq_int,
l-ordered-append,
l-ordered-from-upto-lt-nat,
from-upto-member-nat,
l_all_iff,
decidable__lt,
less-iff-le,
member_append,
not_over_or,
not_over_and,
le-add-cancel2,
decidable__equal_int,
not-equal-2,
l-ordered-remove-combine,
decidable__equal_nat,
remove-combine-implies-member2,
equal-wf-T-base,
less_than_transitivity1,
le_weakening,
less_than_transitivity2,
le_weakening2,
less_than_irreflexivity,
bool_cases_sqequal,
assert-bnot,
neg_assert_of_eq_int,
remove-combine-implies-member,
remove-combine-l-ordered-implies-member,
l_before_wf
\mforall{}s:nat-missing-type(). \mforall{}x,y:\mBbbN{}.
(\muparrow{}member-nat-missing(x;add-nat-missing(y;s)) \mLeftarrow{}{}\mRightarrow{} (x = y) \mvee{} (\muparrow{}member-nat-missing(x;s)))
Date html generated:
2015_07_17-AM-08_21_33
Last ObjectModification:
2015_04_02-PM-05_43_18
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