Nuprl Lemma : length-as-accum

[L:Top List]. (||L|| accumulate (with value and list item x): 1over list:  Lwith starting value: 0))


Proof




Definitions occuring in Statement :  length: ||as|| list_accum: list_accum list: List uall: [x:A]. B[x] top: Top add: m natural_number: $n sqequal: t
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A top: Top and: P ∧ Q prop: subtype_rel: A ⊆B guard: {T} or: P ∨ Q so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] cons: [a b] colength: colength(L) decidable: Dec(P) nil: [] it: so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b squash: T less_than': less_than'(a;b)
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list top_wf less_than_transitivity1 less_than_irreflexivity list_wf list-cases length_of_nil_lemma list_accum_nil_lemma zero-add product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int length_of_cons_lemma list_accum_cons_lemma add-associates add-commutes length_wf add-zero
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate cumulativity imageElimination isect_memberFormation

Latex:
\mforall{}[L:Top  List]
    (||L||  \msim{}  accumulate  (with  value  n  and  list  item  x):
                        n  +  1
                      over  list:
                          L
                      with  starting  value:
                        0))



Date html generated: 2018_05_21-PM-06_45_13
Last ObjectModification: 2017_07_26-PM-04_55_36

Theory : general


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