Nuprl Lemma : union-metric-space_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[X:T ⟶ MetricSpace]. (union-metric-space(T;eq;X) ∈ MetricSpace)
Proof
Definitions occuring in Statement :
union-metric-space: union-metric-space(T;eq;X),
metric-space: MetricSpace,
deq: EqDecider(T),
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,
union-metric-space: union-metric-space(T;eq;X),
all: ∀x:A. B[x],
implies: P ⇒ Q,
metric-space: MetricSpace,
pi1: fst(t),
metric: metric(X),
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
eqof: eqof(d),
pi2: snd(t),
subtype_rel: A ⊆r B,
bfalse: ff,
cand: A c∧ B,
prop: ℙ,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
le: A ≤ B,
less_than': less_than'(a;b),
label: ...$L... t,
squash: ↓T,
true: True,
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
stable: Stable{P}
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[X:T {}\mrightarrow{} MetricSpace]. (union-metric-space(T;eq;X) \mmember{} MetricSpace)
Date html generated:
2020_05_20-AM-11_39_36
Last ObjectModification:
2020_03_20-PM-01_13_09
Theory : reals
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