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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