Nuprl Lemma : l_member-permute
∀[T:Type]. ∀as,bs:T List. ∀x:T. ((x ∈ as @ bs) ⇐⇒ (x ∈ bs @ as))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
guard: {T},
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
l_member_wf,
or_wf,
member_append,
append_wf,
iff_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
hypothesis,
inrFormation,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
inlFormation,
because_Cache,
addLevel,
productElimination,
independent_functionElimination,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}as,bs:T List. \mforall{}x:T. ((x \mmember{} as @ bs) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} bs @ as))
Date html generated:
2019_10_15-AM-11_13_36
Last ObjectModification:
2018_08_25-PM-00_07_14
Theory : general
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