Nuprl Lemma : bag-member-empty-weak
∀[T:Type]. ∀[x:T]. (x ↓∈ {} ⇐⇒ False)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
empty-bag: {},
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
false: False,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
bag-member: x ↓∈ bs,
squash: ↓T
Lemmas referenced :
false_wf,
empty-bag_wf,
bag-member_wf,
bag-member-empty
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_isectElimination,
hypothesis,
voidElimination,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. (x \mdownarrow{}\mmember{} \{\} \mLeftarrow{}{}\mRightarrow{} False)
Date html generated:
2016_05_15-PM-02_36_56
Last ObjectModification:
2016_01_16-AM-08_50_15
Theory : bags
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