Nuprl Lemma : int-decr-map-find_wf
∀[Value:Type]. ∀[k:ℤ]. ∀[m:int-decr-map-type(Value)].
(int-decr-map-find(k;m) ∈ {v:Value| (¬↑null(m)) ∧ (<k, v> ∈ m)} + (↓(∀p∈m.¬(k = (fst(p)) ∈ ℤ))))
Proof
Definitions occuring in Statement :
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
null: null(as),
assert: ↑b,
uall: ∀[x:A]. B[x],
pi1: fst(t),
not: ¬A,
squash: ↓T,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
pair: <a, b>,
product: x:A × B[x],
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
l-ordered_wf,
gt_wf,
equal-wf-T-base,
colength_wf_list,
list_wf,
list-cases,
null_nil_lemma,
l_all_nil,
l-ordered-nil-true,
nil_wf,
true_wf,
equal-wf-base,
not_wf,
l_member_wf,
squash_wf,
l_all_wf2,
equal-wf-base-T,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
null_cons_lemma,
find-combine-cons,
l-ordered-cons,
cons_wf,
all_wf,
member_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
int-decr-map-type_wf,
value-type-has-value,
int-value-type,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
cons_member,
lt_int_wf,
assert_of_lt_int,
l_all_cons,
l_all_iff
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[m:int-decr-map-type(Value)].
(int-decr-map-find(k;m) \mmember{} \{v:Value| (\mneg{}\muparrow{}null(m)) \mwedge{} (<k, v> \mmember{} m)\} + (\mdownarrow{}(\mforall{}p\mmember{}m.\mneg{}(k = (fst(p))))))
Date html generated:
2015_07_17-AM-08_22_49
Last ObjectModification:
2015_04_02-PM-05_43_55
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