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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