Nuprl Lemma : sub-bags_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. (sub-bags(eq;bs) ∈ bag(bag(T))) supposing valueall-type(T)
Proof
Definitions occuring in Statement :
sub-bags: sub-bags(eq;bs),
bag: bag(T),
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sub-bags: sub-bags(eq;bs),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
bag-map_wf,
bag_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
bag-partitions_wf,
deq_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productEquality,
lambdaEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. (sub-bags(eq;bs) \mmember{} bag(bag(T))) supposing valueall-type(T)
Date html generated:
2016_05_15-PM-08_09_44
Last ObjectModification:
2015_12_27-PM-04_12_28
Theory : bags_2
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