### Nuprl Lemma : member-reverse

`∀[T:Type]. ∀L:T List. ∀x:T.  ((x ∈ rev(L)) `⇐⇒` (x ∈ L))`

Proof

Definitions occuring in Statement :  l_member: `(x ∈ l)` reverse: `rev(as)` 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` l_member: `(x ∈ l)` exists: `∃x:A. B[x]` cand: `A c∧ B` member: `t ∈ T` prop: `ℙ` rev_implies: `P `` Q` squash: `↓T` nat: `ℕ` int_seg: `{i..j-}` lelt: `i ≤ j < k` le: `A ≤ B` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` top: `Top` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_stable: `SqStable(P)` subtract: `n - m` uiff: `uiff(P;Q)` nat_plus: `ℕ+` less_than: `a < b` less_than': `less_than'(a;b)` not: `¬A` false: `False` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` sq_type: `SQType(T)`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation independent_pairFormation sqequalHypSubstitution productElimination thin cut introduction extract_by_obid isectElimination cumulativity hypothesisEquality hypothesis universeEquality applyEquality lambdaEquality imageElimination equalityTransitivity equalitySymmetry because_Cache setElimination rename dependent_set_memberEquality natural_numberEquality sqequalRule imageMemberEquality baseClosed independent_isectElimination independent_functionElimination isect_memberEquality voidElimination voidEquality dependent_pairFormation sqequalIntensionalEquality intEquality dependent_functionElimination promote_hyp productEquality addLevel addEquality multiplyEquality levelHypothesis minusEquality unionElimination instantiate

Latex:
\mforall{}[T:Type].  \mforall{}L:T  List.  \mforall{}x:T.    ((x  \mmember{}  rev(L))  \mLeftarrow{}{}\mRightarrow{}  (x  \mmember{}  L))

Date html generated: 2017_04_14-AM-08_40_40
Last ObjectModification: 2017_02_27-PM-03_31_13

Theory : list_0

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