Nuprl Lemma : assert-bag-null-sq
∀bs:bag(Top). ((↑bag-null(bs)) ⇒ (bs ~ {}))
Proof
Definitions occuring in Statement :
bag-null: bag-null(bs),
empty-bag: {},
bag: bag(T),
assert: ↑b,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
assert-bag-null,
top_wf,
equal-empty-bag,
assert_wf,
bag-null_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
productElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}bs:bag(Top). ((\muparrow{}bag-null(bs)) {}\mRightarrow{} (bs \msim{} \{\}))
Date html generated:
2016_05_15-PM-02_25_16
Last ObjectModification:
2015_12_27-AM-09_53_04
Theory : bags
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