Nuprl Lemma : bag-restrict_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[b:bag(T)]. ((b|x) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-restrict: (b|x),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-restrict: (b|x),
so_lambda: λ2x.t[x],
deq: EqDecider(T),
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
bag-filter_wf,
subtype_rel_bag,
assert_wf,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
setElimination,
rename,
hypothesis,
because_Cache,
setEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[b:bag(T)]. ((b|x) \mmember{} bag(T))
Date html generated:
2016_05_15-PM-08_10_14
Last ObjectModification:
2015_12_27-PM-04_12_13
Theory : bags_2
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