### Nuprl Lemma : no_repeats_reverse

`∀[T:Type]. ∀[L:T List].  uiff(no_repeats(T;rev(L));no_repeats(T;L))`

Proof

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

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    uiff(no\_repeats(T;rev(L));no\_repeats(T;L))

Date html generated: 2017_04_14-AM-08_40_54
Last ObjectModification: 2017_02_27-PM-03_32_24

Theory : list_0

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