### Nuprl Lemma : member-list-to-set

`∀[T:Type]. ∀eq:EqDecider(T). ∀L:T List. ∀a:T.  ((a ∈ list-to-set(eq;L)) `⇐⇒` (a ∈ L))`

Proof

Definitions occuring in Statement :  list-to-set: `list-to-set(eq;L)` l_member: `(x ∈ l)` list: `T List` deq: `EqDecider(T)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `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-to-set-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{}L:T  List.  \mforall{}a:T.    ((a  \mmember{}  list-to-set(eq;L))  \mLeftarrow{}{}\mRightarrow{}  (a  \mmember{}  L))

Date html generated: 2016_05_14-PM-03_25_42
Last ObjectModification: 2015_12_26-PM-06_22_36

Theory : decidable!equality

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