Nuprl Lemma : bag-member-iff-sq-list-member
∀[T:Type]. ∀L:T List. ∀x:T. uiff(x ↓∈ L;↓(x ∈ L))
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
l_member: (x ∈ l),
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
squash: ↓T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
bag-member: x ↓∈ bs,
sq_stable: SqStable(P),
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
sq_stable__bag-member,
list_wf,
l_member_wf,
squash_wf,
list-subtype-bag,
bag-member_wf,
list-member-bag-member,
bag-member-sq-list-member
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
independent_pairFormation,
introduction,
independent_isectElimination,
imageElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
applyEquality,
because_Cache,
lambdaEquality,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x:T. uiff(x \mdownarrow{}\mmember{} L;\mdownarrow{}(x \mmember{} L))
Date html generated:
2016_05_15-PM-02_39_56
Last ObjectModification:
2016_01_16-AM-08_47_42
Theory : bags
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