### Nuprl Lemma : select_append_front

`∀[T:Type]. ∀[as,bs:T List]. ∀[i:ℕ||as||].  (as @ bs[i] = as[i] ∈ 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]` natural_number: `\$n` 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` sq_stable: `SqStable(P)` implies: `P `` Q` lelt: `i ≤ j < k` and: `P ∧ Q` squash: `↓T` top: `Top` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]` prop: `ℙ` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` false: `False` guard: `{T}` le: `A ≤ B` ge: `i ≥ j ` subtract: `n - m` uiff: `uiff(P;Q)` nat_plus: `ℕ+` less_than: `a < b` less_than': `less_than'(a;b)` true: `True` not: `¬A` decidable: `Dec(P)` or: `P ∨ Q` sq_type: `SQType(T)` cons: `[a / b]` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  int_seg_wf length_wf list_wf list_induction all_wf equal_wf select_wf append_wf sq_stable__le length-append non_neg_length length_wf_nat nat_wf set_subtype_base le_wf int_subtype_base length_of_nil_lemma list_ind_nil_lemma stuck-spread base_wf less_than_transitivity1 less_than_irreflexivity length_of_cons_lemma list_ind_cons_lemma add_functionality_wrt_le subtract_wf le_reflexive minus-one-mul zero-add one-mul add-mul-special add-associates two-mul add-commutes mul-distributes-right zero-mul not-lt-2 minus-one-mul-top add-swap omega-shadow less_than_wf mul-distributes minus-add mul-commutes mul-associates mul-swap add-zero less-iff-le le-add-cancel-alt int_seg_properties nat_properties decidable__lt decidable__int_equal subtype_base_sq false_wf not-equal-2 le-add-cancel condition-implies-le minus-zero squash_wf true_wf length_append subtype_rel_list top_wf iff_weakening_equal not-equal-implies-less subtype_rel_self not-le-2 decidable__le le-add-cancel2 minus-minus lelt_wf select_cons_tl
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality cumulativity hypothesisEquality hypothesis because_Cache universeEquality isect_memberFormation sqequalRule isect_memberEquality axiomEquality lambdaEquality setElimination rename independent_isectElimination independent_functionElimination productElimination imageMemberEquality baseClosed imageElimination voidElimination voidEquality lambdaFormation dependent_pairFormation sqequalIntensionalEquality applyEquality intEquality equalityTransitivity equalitySymmetry dependent_functionElimination promote_hyp addEquality multiplyEquality minusEquality dependent_set_memberEquality independent_pairFormation unionElimination instantiate

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

Date html generated: 2017_04_14-AM-08_38_21
Last ObjectModification: 2017_02_27-PM-03_29_42

Theory : list_0

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