### Nuprl Lemma : select_wf

`∀[A:Type]. ∀[l:A List]. ∀[n:ℤ].  (l[n] ∈ A) supposing (n < ||l|| and (0 ≤ n))`

Proof

Definitions occuring in Statement :  select: `L[n]` length: `||as||` list: `T List` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` member: `t ∈ T` natural_number: `\$n` int: `ℤ` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` subtype_rel: `A ⊆r B` or: `P ∨ Q` le: `A ≤ B` and: `P ∧ Q` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` top: `Top` so_apply: `x[s1;s2]` squash: `↓T` sq_stable: `SqStable(P)` uiff: `uiff(P;Q)` not: `¬A` less_than': `less_than'(a;b)` true: `True` decidable: `Dec(P)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtract: `n - m` nil: `[]` it: `⋅` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` select: `L[n]` bool: `𝔹` unit: `Unit` btrue: `tt` bfalse: `ff` exists: `∃x:A. B[x]` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` has-value: `(a)↓` nat_plus: `ℕ+`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity intEquality applyEquality because_Cache unionElimination productElimination voidEquality promote_hyp hypothesis_subsumption applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality instantiate equalityElimination lessCases sqequalAxiom dependent_pairFormation callbyvalueReduce sqequalIntensionalEquality universeEquality multiplyEquality

Latex:
\mforall{}[A:Type].  \mforall{}[l:A  List].  \mforall{}[n:\mBbbZ{}].    (l[n]  \mmember{}  A)  supposing  (n  <  ||l||  and  (0  \mleq{}  n))

Date html generated: 2017_04_14-AM-08_36_30
Last ObjectModification: 2017_02_27-PM-03_28_36

Theory : list_0

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