Nuprl Lemma : decidable__exists_bag-member
∀[T:Type]. ∀b:bag(T). Dec(↓∃x:T. x ↓∈ b)
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
not: ¬A,
rev_implies: P ⇐ Q,
false: False
Latex:
\mforall{}[T:Type]. \mforall{}b:bag(T). Dec(\mdownarrow{}\mexists{}x:T. x \mdownarrow{}\mmember{} b)
Date html generated:
2016_05_16-PM-01_38_56
Last ObjectModification:
2015_12_29-PM-02_08_16
Theory : event-ordering
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