Nuprl Lemma : decidable__exists-single-valued-bag
∀[T:Type]. ∀b:bag(T). (single-valued-bag(b;T) ⇒ Dec(∃v:T. v ↓∈ b))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
not: ¬A,
false: False,
exists: ∃x:A. B[x],
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}[T:Type]. \mforall{}b:bag(T). (single-valued-bag(b;T) {}\mRightarrow{} Dec(\mexists{}v:T. v \mdownarrow{}\mmember{} b))
Date html generated:
2016_05_16-PM-01_46_00
Last ObjectModification:
2016_01_17-PM-07_47_04
Theory : event-ordering
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