Nuprl Lemma : l_member-bag-member
∀[T:Type]. ∀x:T. ∀L:T List. (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],
iff: P ⇐⇒ Q,
squash: ↓T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
rev_implies: P ⇐ Q,
bag-member: x ↓∈ bs,
exists: ∃x:A. B[x],
bag: bag(T),
quotient: x,y:A//B[x; y],
cand: A c∧ B,
guard: {T}
Lemmas referenced :
bag-member_wf,
list-subtype-bag,
squash_wf,
l_member_wf,
list_wf,
member-permutation,
member_wf,
permutation_wf,
equal_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
independent_pairFormation,
hypothesis,
sqequalHypSubstitution,
imageElimination,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
extract_by_obid,
isectElimination,
cumulativity,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
universeEquality,
pertypeElimination,
independent_functionElimination,
productEquality,
dependent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}L:T List. (x \mdownarrow{}\mmember{} L \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}(x \mmember{} L))
Date html generated:
2017_10_01-AM-08_53_44
Last ObjectModification:
2017_07_26-PM-04_35_27
Theory : bags
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