Nuprl Lemma : bag-member-size
∀[T:Type]. ∀[bs:bag(T)]. ∀[x:T]. 0 < #(bs) supposing x ↓∈ bs
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag-size: #(bs),
bag: bag(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
prop: ℙ,
squash: ↓T,
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
bag_wf,
nat_wf,
bag-size_wf,
member-less_than,
bag-member_wf,
bag-size-bag-member
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
dependent_pairFormation,
sqequalRule,
imageMemberEquality,
baseClosed,
isect_memberEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[bs:bag(T)]. \mforall{}[x:T]. 0 < \#(bs) supposing x \mdownarrow{}\mmember{} bs
Date html generated:
2016_05_15-PM-02_40_30
Last ObjectModification:
2016_01_16-AM-08_47_22
Theory : bags
Home
Index