Nuprl Lemma : list-member-bag-member
∀[T:Type]. ∀L:T List. ∀x:T. ((x ∈ L) ⇒ x ↓∈ L)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bag-member: x ↓∈ bs,
exists: ∃x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
squash: ↓T
Lemmas referenced :
list-subtype-bag,
equal_wf,
bag_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
dependent_pairFormation,
hypothesisEquality,
independent_pairFormation,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
lambdaEquality,
hypothesis,
sqequalRule,
productEquality,
cumulativity,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
imageElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x:T. ((x \mmember{} L) {}\mRightarrow{} x \mdownarrow{}\mmember{} L)
Date html generated:
2017_10_01-AM-08_54_43
Last ObjectModification:
2017_07_26-PM-04_36_28
Theory : bags
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