Nuprl Lemma : bag-only_wf2
∀[T:Type]. ∀[b:bag(T)]. only(b) ∈ T supposing single-valued-bag(b;T) ∧ 0 < #(b)
Proof
Definitions occuring in Statement :
single-valued-bag: single-valued-bag(b;T),
bag-only: only(bs),
bag-size: #(bs),
bag: bag(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
bag-only: only(bs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
and: P ∧ Q
Lemmas referenced :
and_wf,
single-valued-bag_wf,
less_than_wf,
bag-size_wf,
nat_wf,
bag_wf,
single-valued-bag-hd
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache,
universeEquality,
independent_isectElimination,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. only(b) \mmember{} T supposing single-valued-bag(b;T) \mwedge{} 0 < \#(b)
Date html generated:
2016_05_15-PM-02_49_07
Last ObjectModification:
2015_12_27-AM-09_35_13
Theory : bags
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