Nuprl Lemma : map-sig-isEmpty_wf
∀[Key,Value:Type]. ∀[m:map-sig{i:l}(Key;Value)]. (map-sig-isEmpty(m) ∈ map-sig-map(m) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
map-sig-isEmpty: map-sig-isEmpty(m),
map-sig-map: map-sig-map(m),
map-sig: map-sig{i:l}(Key;Value),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
map-sig-isEmpty: map-sig-isEmpty(m),
map-sig-map: map-sig-map(m),
map-sig: map-sig{i:l}(Key;Value),
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uimplies: b supposing a,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
band: p ∧b q,
not: ¬A,
cand: A c∧ B,
exposed-bfalse: exposed-bfalse
Latex:
\mforall{}[Key,Value:Type]. \mforall{}[m:map-sig\{i:l\}(Key;Value)]. (map-sig-isEmpty(m) \mmember{} map-sig-map(m) {}\mrightarrow{} \mBbbB{})
Date html generated:
2016_05_17-PM-01_47_29
Last ObjectModification:
2015_12_28-PM-08_51_31
Theory : datatype-signatures
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