Nuprl Lemma : lookup-list-map-add_wf
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key:Key]. ∀[val:Value]. ∀[m:lookup-list-map-type(Key;Value)].
(lookup-list-map-add(deqKey;key;val;m) ∈ lookup-list-map-type(Key;Value))
Proof
Definitions occuring in Statement :
lookup-list-map-add: lookup-list-map-add(deqKey;key;val;m),
lookup-list-map-type: lookup-list-map-type(Key;Value),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lookup-list-map-add: lookup-list-map-add(deqKey;key;val;m),
lookup-list-map-type: lookup-list-map-type(Key;Value),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Latex:
\mforall{}[Key,Value:Type]. \mforall{}[deqKey:EqDecider(Key)]. \mforall{}[key:Key]. \mforall{}[val:Value].
\mforall{}[m:lookup-list-map-type(Key;Value)].
(lookup-list-map-add(deqKey;key;val;m) \mmember{} lookup-list-map-type(Key;Value))
Date html generated:
2016_05_17-PM-01_51_25
Last ObjectModification:
2015_12_28-PM-08_50_19
Theory : datatype-signatures
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