Nuprl Lemma : lookup-list-map-add-prop
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key2:Key]. ∀[val:Value]. ∀[m:lookup-list-map-type(Key;Value)].
∀[key1:Key].
(lookup-list-map-find(deqKey;key1;lookup-list-map-add(deqKey;key2;val;m))
= if (deqKey key1 key2) ∧b (¬blookup-list-map-inDom(deqKey;key2;m))
then inl val
else lookup-list-map-find(deqKey;key1;m)
fi
∈ (Value?))
Proof
Definitions occuring in Statement :
lookup-list-map-add: lookup-list-map-add(deqKey;key;val;m),
lookup-list-map-inDom: lookup-list-map-inDom(deqKey;key;m),
lookup-list-map-find: lookup-list-map-find(deqKey;key;m),
lookup-list-map-type: lookup-list-map-type(Key;Value),
deq: EqDecider(T),
band: p ∧b q,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
unit: Unit,
apply: f a,
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Lemmas :
list_induction,
equal_wf,
unit_wf2,
lookup-list-map-find_wf,
lookup-list-map-add_wf,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
bnot_wf,
lookup-list-map-inDom_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
eqff_to_assert,
assert-bnot,
iff_transitivity,
assert_wf,
eqof_wf,
not_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_bnot,
list_wf,
lookup-list-map-type_wf,
deq_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
it_wf,
apply_alist_cons_lemma,
apply-alist_wf
\mforall{}[Key,Value:Type]. \mforall{}[deqKey:EqDecider(Key)]. \mforall{}[key2:Key]. \mforall{}[val:Value].
\mforall{}[m:lookup-list-map-type(Key;Value)]. \mforall{}[key1:Key].
(lookup-list-map-find(deqKey;key1;lookup-list-map-add(deqKey;key2;val;m))
= if (deqKey key1 key2) \mwedge{}\msubb{} (\mneg{}\msubb{}lookup-list-map-inDom(deqKey;key2;m))
then inl val
else lookup-list-map-find(deqKey;key1;m)
fi )
Date html generated:
2015_07_17-AM-08_24_07
Last ObjectModification:
2015_04_02-PM-05_45_04
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