Nuprl Lemma : lookup-list-map-remove_wf
∀[Key,Value:Type]. ∀[deqKey:EqDecider(Key)]. ∀[key:Key]. ∀[m:lookup-list-map-type(Key;Value)].
(lookup-list-map-remove(deqKey;key;m) ∈ lookup-list-map-type(Key;Value))
Proof
Definitions occuring in Statement :
lookup-list-map-remove: lookup-list-map-remove(deqKey;key;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 :
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-remove: lookup-list-map-remove(deqKey;key;m),
remove-alist: remove-alist(eq;L;x),
list_ind: list_ind,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
eqof: eqof(d),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
list: T List,
listp: A List+,
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-remove(deqKey;key;m) \mmember{} lookup-list-map-type(Key;Value))
Date html generated:
2016_05_17-PM-01_51_35
Last ObjectModification:
2016_01_17-AM-11_37_13
Theory : datatype-signatures
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