Nuprl Lemma : null-bag-empty
∀T:Type. ∀x:bag(T). (↑bag-null(x) ⇐⇒ x = {} ∈ bag(T))
Proof
Definitions occuring in Statement :
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs),
empty-bag: {},
bag: bag(T)
Definitions unfolded in proof :
all: ∀x:A. B[x],
bag-null: bag-null(bs),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B
Latex:
\mforall{}T:Type. \mforall{}x:bag(T). (\muparrow{}bag-null(x) \mLeftarrow{}{}\mRightarrow{} x = \{\})
Date html generated:
2016_05_17-AM-11_09_48
Last ObjectModification:
2015_12_29-PM-05_16_03
Theory : process-model
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