Nuprl Lemma : list_accum_wf

[T,T':Type]. ∀[l:T List]. ∀[y:T']. ∀[f:T' ⟶ T ⟶ T'].
  (accumulate (with value and list item a):
   over list:
   with starting value:
    y) ∈ T')


Definitions occuring in Statement :  list_accum: list_accum list: List uall: [x:A]. B[x] so_apply: x[s1;s2] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] nat: implies:  Q false: False ge: i ≥  guard: {T} uimplies: supposing a prop: subtype_rel: A ⊆B or: P ∨ Q list_accum: list_accum nil: [] it: cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] top: Top so_apply: x[s1;s2] squash: T sq_stable: SqStable(P) uiff: uiff(P;Q) and: P ∧ Q le: A ≤ B not: ¬A less_than': less_than'(a;b) true: True decidable: Dec(P) iff: ⇐⇒ Q rev_implies:  Q subtract: m so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b
Lemmas referenced :  nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list int_subtype_base list-cases product_subtype_list spread_cons_lemma sq_stable__le le_antisymmetry_iff add_functionality_wrt_le add-associates add-zero zero-add le-add-cancel decidable__le false_wf not-le-2 condition-implies-le minus-add minus-one-mul minus-one-mul-top add-commutes le_wf equal_wf subtract_wf not-ge-2 less-iff-le minus-minus add-swap subtype_base_sq set_subtype_base list_wf
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 axiomEquality equalityTransitivity equalitySymmetry applyEquality because_Cache unionElimination callbyvalueReduce sqleReflexivity promote_hyp hypothesis_subsumption productElimination isect_memberEquality voidEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate cumulativity functionEquality universeEquality

\mforall{}[T,T':Type].  \mforall{}[l:T  List].  \mforall{}[y:T'].  \mforall{}[f:T'  {}\mrightarrow{}  T  {}\mrightarrow{}  T'].
    (accumulate  (with  value  x  and  list  item  a):
      over  list:
      with  starting  value:
        y)  \mmember{}  T')

Date html generated: 2018_05_21-PM-00_18_36
Last ObjectModification: 2018_05_19-AM-06_58_45

Theory : list_0

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