Nuprl Lemma : bag-drop_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. ∀[a:T]. (bag-drop(eq;bs;a) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-drop: bag-drop(eq;bs;a),
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-drop: bag-drop(eq;bs;a),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
bag-remove1_wf,
bag_wf,
unit_wf2,
equal_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
unionEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. \mforall{}[a:T]. (bag-drop(eq;bs;a) \mmember{} bag(T))
Date html generated:
2019_10_16-AM-11_31_16
Last ObjectModification:
2018_08_21-PM-01_59_14
Theory : bags_2
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