Nuprl Lemma : mk-lookup-list-map_wf
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. (mk-lookup-list-map(Key;Value;deqKey) ∈ map-sig{i:l}(Key;Value))
Proof
Definitions occuring in Statement :
mk-lookup-list-map: mk-lookup-list-map(Key;Value;deqKey),
map-sig: map-sig{i:l}(Key;Value),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
mk-lookup-list-map: mk-lookup-list-map(Key;Value;deqKey),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
lookup-list-map-type: lookup-list-map-type(Key;Value),
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
valueall-type: valueall-type(T),
has-value: (a)↓,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
lookup-list-map-eqKey: lookup-list-map-eqKey(keyDeq),
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
band: p ∧b q,
exposed-bfalse: exposed-bfalse
Latex:
\mforall{}[Key,Value:Type]. \mforall{}[deqKey:EqDecider(Key)].
(mk-lookup-list-map(Key;Value;deqKey) \mmember{} map-sig\{i:l\}(Key;Value))
Date html generated:
2016_05_17-PM-01_51_49
Last ObjectModification:
2015_12_28-PM-08_51_13
Theory : datatype-signatures
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