### Nuprl Lemma : select_append_back

`∀[T:Type]. ∀[as,bs:T List]. ∀[i:{||as||..||as|| + ||bs||-}].  (as @ bs[i] = bs[i - ||as||] ∈ T)`

Proof

Definitions occuring in Statement :  select: `L[n]` length: `||as||` append: `as @ bs` list: `T List` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` subtract: `n - m` add: `n + m` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` uimplies: `b supposing a` all: `∀x:A. B[x]` implies: `P `` Q` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]` prop: `ℙ` top: `Top` lelt: `i ≤ j < k` and: `P ∧ Q` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` le: `A ≤ B` ge: `i ≥ j ` subtract: `n - m` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` uiff: `uiff(P;Q)` false: `False` not: `¬A` decidable: `Dec(P)` or: `P ∨ Q` cand: `A c∧ B` sq_stable: `SqStable(P)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` guard: `{T}`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis addEquality because_Cache universeEquality isect_memberFormation sqequalRule isect_memberEquality axiomEquality lambdaEquality setElimination rename independent_isectElimination lambdaFormation dependent_pairFormation sqequalIntensionalEquality applyEquality intEquality natural_numberEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination productElimination promote_hyp voidElimination voidEquality multiplyEquality minusEquality dependent_set_memberEquality independent_pairFormation imageMemberEquality baseClosed unionElimination imageElimination productEquality baseApply closedConclusion

Latex:
\mforall{}[T:Type].  \mforall{}[as,bs:T  List].  \mforall{}[i:\{||as||..||as||  +  ||bs||\msupminus{}\}].    (as  @  bs[i]  =  bs[i  -  ||as||])

Date html generated: 2017_04_14-AM-08_38_00
Last ObjectModification: 2017_02_27-PM-03_30_08

Theory : list_0

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