Nuprl Lemma : member-rev-append
∀[T:Type]. ∀x:T. ∀as,bs:T List. ((x ∈ rev(as) + bs) ⇐⇒ (x ∈ as) ∨ (x ∈ bs))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
rev-append: rev(as) + bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
reverse: rev(as),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
rev-append-property,
l_member_wf,
member_append,
reverse_wf,
member-reverse,
append_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :memTop,
hypothesis,
independent_pairFormation,
unionIsType,
universeIsType,
hypothesisEquality,
because_Cache,
productElimination,
independent_functionElimination,
dependent_functionElimination,
unionElimination,
inlFormation_alt,
inrFormation_alt,
promote_hyp,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}as,bs:T List. ((x \mmember{} rev(as) + bs) \mLeftarrow{}{}\mRightarrow{} (x \mmember{} as) \mvee{} (x \mmember{} bs))
Date html generated:
2020_05_19-PM-09_38_10
Last ObjectModification:
2020_01_25-AM-10_27_17
Theory : omega
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