### Nuprl Lemma : member-list-diff

`∀[T:Type]. ∀eq:EqDecider(T). ∀as,bs:T List. ∀x:T.  ((x ∈ as-bs) `⇐⇒` (x ∈ as) ∧ (¬(x ∈ bs)))`

Proof

Definitions occuring in Statement :  list-diff: `as-bs` l_member: `(x ∈ l)` list: `T List` deq: `EqDecider(T)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` not: `¬A` and: `P ∧ Q` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` and: `P ∧ Q`
Lemmas referenced :  list-diff-property list_wf deq_wf
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaFormation dependent_functionElimination productElimination universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}eq:EqDecider(T).  \mforall{}as,bs:T  List.  \mforall{}x:T.    ((x  \mmember{}  as-bs)  \mLeftarrow{}{}\mRightarrow{}  (x  \mmember{}  as)  \mwedge{}  (\mneg{}(x  \mmember{}  bs)))

Date html generated: 2016_05_14-PM-03_29_52
Last ObjectModification: 2015_12_26-PM-06_02_51

Theory : decidable!equality

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