Nuprl Lemma : lookup-list-map-inDom_wf
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key:Key]. ∀[m:lookup-list-map-type(Key;Value)].
(lookup-list-map-inDom(deqKey;key;m) ∈ 𝔹)
Proof
Definitions occuring in Statement :
lookup-list-map-inDom: lookup-list-map-inDom(deqKey;key;m),
lookup-list-map-type: lookup-list-map-type(Key;Value),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list_wf,
list-cases,
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,
bor_wf,
lookup-list-map-type_wf,
deq_wf,
list_ind_nil_lemma,
bfalse_wf
\mforall{}[Key,Value:Type]. \mforall{}[deqKey:EqDecider(Key)]. \mforall{}[key:Key]. \mforall{}[m:lookup-list-map-type(Key;Value)].
(lookup-list-map-inDom(deqKey;key;m) \mmember{} \mBbbB{})
Date html generated:
2015_07_17-AM-08_23_49
Last ObjectModification:
2015_04_02-PM-05_44_44
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