Nuprl Lemma : lookup-list-map-empty-prop
∀[Key:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key:Key]. (¬↑lookup-list-map-inDom(deqKey;key;lookup-list-map-empty()))
Proof
Definitions occuring in Statement :
lookup-list-map-empty: lookup-list-map-empty(),
lookup-list-map-inDom: lookup-list-map-inDom(deqKey;key;m),
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
lookup-list-map-empty: lookup-list-map-empty(),
lookup-list-map-inDom: lookup-list-map-inDom(deqKey;key;m),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Latex:
\mforall{}[Key:Type]. \mforall{}[deqKey:EqDecider(Key)]. \mforall{}[key:Key].
(\mneg{}\muparrow{}lookup-list-map-inDom(deqKey;key;lookup-list-map-empty()))
Date html generated:
2016_05_17-PM-01_51_02
Last ObjectModification:
2015_12_28-PM-08_50_11
Theory : datatype-signatures
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