Nuprl Lemma : lookup-list-map-inDom_wf
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key:Key]. ∀[m:lookup-list-map-type(Key;Value)].
  (lookup-list-map-inDom(deqKey;key;m) ∈ 𝔹)
Proof
Definitions occuring in Statement : 
lookup-list-map-inDom: lookup-list-map-inDom(deqKey;key;m)
, 
lookup-list-map-type: lookup-list-map-type(Key;Value)
, 
deq: EqDecider(T)
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
lookup-list-map-type: lookup-list-map-type(Key;Value)
, 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
not: ¬A
, 
top: Top
, 
and: P ∧ Q
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
or: P ∨ Q
, 
cons: [a / b]
, 
colength: colength(L)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
guard: {T}
, 
decidable: Dec(P)
, 
nil: []
, 
it: ⋅
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
sq_type: SQType(T)
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
lookup-list-map-inDom: lookup-list-map-inDom(deqKey;key;m)
, 
list_ind: list_ind, 
deq: EqDecider(T)
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[Key,Value:Type].  \mforall{}[deqKey:EqDecider(Key)].  \mforall{}[key:Key].  \mforall{}[m:lookup-list-map-type(Key;Value)].
    (lookup-list-map-inDom(deqKey;key;m)  \mmember{}  \mBbbB{})
Date html generated:
2016_05_17-PM-01_50_52
Last ObjectModification:
2016_01_17-AM-11_37_06
Theory : datatype-signatures
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