Nuprl Lemma : lookup-list-map-remove-prop
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key2:Key]. ∀[m:lookup-list-map-type(Key;Value)]. ∀[key1:Key].
(lookup-list-map-find(deqKey;key1;lookup-list-map-remove(deqKey;key2;m))
= if deqKey key1 key2 then inr ⋅ else lookup-list-map-find(deqKey;key1;m) fi
∈ (Value?))
Proof
Definitions occuring in Statement :
lookup-list-map-remove: lookup-list-map-remove(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),
ifthenelse: if b then t else f fi ,
it: ⋅,
uall: ∀[x:A]. B[x],
unit: Unit,
apply: f a,
inr: inr 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-remove_wf,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
it_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
list_wf,
nil_wf,
subtype_rel_list,
lookup-list-map-type_wf,
deq_wf,
list_ind_cons_lemma,
apply_alist_cons_lemma,
eqof_wf
\mforall{}[Key,Value:Type]. \mforall{}[deqKey:EqDecider(Key)]. \mforall{}[key2:Key]. \mforall{}[m:lookup-list-map-type(Key;Value)].
\mforall{}[key1:Key].
(lookup-list-map-find(deqKey;key1;lookup-list-map-remove(deqKey;key2;m))
= if deqKey key1 key2 then inr \mcdot{} else lookup-list-map-find(deqKey;key1;m) fi )
Date html generated:
2015_07_17-AM-08_24_12
Last ObjectModification:
2015_04_02-PM-05_45_09
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