### Nuprl Lemma : reject_wf

`∀[A:Type]. ∀[l:A List]. ∀[n:ℤ].  (l\[n] ∈ A List)`

Proof

Definitions occuring in Statement :  reject: `as\[i]` list: `T List` uall: `∀[x:A]. B[x]` member: `t ∈ T` int: `ℤ` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` reject: `as\[i]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` so_lambda: `so_lambda(x,y,z.t[x; y; z])` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` so_apply: `x[s1;s2;s3]` nat: `ℕ` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` ge: `i ≥ j ` le_int: `i ≤z j` lt_int: `i <z j`
Lemmas referenced :  decidable__lt list_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int tl_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf list_ind_wf nil_wf cons_wf not-le-2 condition-implies-le minus-add minus-zero add-zero add-commutes zero-add less-iff-le add_functionality_wrt_le add-associates le-add-cancel2 nat_wf decidable__le false_wf not-lt-2 minus-one-mul minus-one-mul-top le-add-cancel nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf not_wf subtract_wf not-ge-2 minus-minus add-swap decidable__int_equal int_subtype_base not-equal-2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality natural_numberEquality hypothesis unionElimination sqequalRule axiomEquality equalityTransitivity equalitySymmetry intEquality isect_memberEquality isectElimination because_Cache cumulativity universeEquality lambdaFormation equalityElimination productElimination independent_isectElimination dependent_pairFormation promote_hyp instantiate independent_functionElimination voidElimination lambdaEquality addEquality applyEquality voidEquality minusEquality hypothesis_subsumption setElimination rename dependent_set_memberEquality independent_pairFormation intWeakElimination

Latex:
\mforall{}[A:Type].  \mforall{}[l:A  List].  \mforall{}[n:\mBbbZ{}].    (l\mbackslash{}[n]  \mmember{}  A  List)

Date html generated: 2017_04_14-AM-08_34_29
Last ObjectModification: 2017_02_27-PM-03_22_16

Theory : list_0

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