Nuprl Lemma : bag-remove1_wf1
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[bs:T List]. (bag-remove1(eq;bs;x) ∈ T List?)
Proof
Definitions occuring in Statement :
bag-remove1: bag-remove1(eq;bs;a),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-remove1: bag-remove1(eq;bs;a)
Lemmas referenced :
bag_remove1_aux_wf,
nil_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[bs:T List]. (bag-remove1(eq;bs;x) \mmember{} T List?)
Date html generated:
2016_05_15-PM-08_03_49
Last ObjectModification:
2015_12_27-PM-04_14_59
Theory : bags_2
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