Nuprl Lemma : unzip-as-accum

∀[as:(Top × Top) List]
  (unzip(as) ~ accumulate (with value p and list item a):
                let p1,p2 = p 
                in let a1,a2 = a 
                   in <p1 @ [a1], p2 @ [a2]>
               over list:
                 as
               with starting value:
                <[], []>))


Proof



Definitions occuring in Statement :  unzip: unzip(as),  append: as @ bs,  list_accum: list_accum,  cons: [a / b],  nil: [],  list: T List,  uall: ∀[x:A]. B[x],  top: Top,  spread: spread def,  pair: <a, b>,  product: x:A × B[x],  sqequal: s ~ t
Definitions unfolded in proof :  unzip: unzip(as),  all: ∀x:A. B[x],  uall: ∀[x:A]. B[x],  member: t ∈ T,  nat: ℕ,  implies: P ⇒ Q,  false: False,  ge: i ≥ j ,  uimplies: b supposing a,  satisfiable_int_formula: satisfiable_int_formula(fmla),  exists: ∃x:A. B[x],  not: ¬A,  top: Top,  and: P ∧ Q,  prop: ℙ,  subtype_rel: A ⊆r B,  guard: {T},  or: P ∨ Q,  so_lambda: λ2x y.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),  pi1: fst(t),  pi2: snd(t),  append: as @ bs,  so_lambda: so_lambda(x,y,z.t[x; y; z]),  so_apply: x[s1;s2;s3]
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,  list_wf,  top_wf,  equal-wf-T-base,  nat_wf,  colength_wf_list,  less_than_transitivity1,  less_than_irreflexivity,  list-cases,  map_nil_lemma,  list_accum_nil_lemma,  append_nil_sq,  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,  map_cons_lemma,  list_accum_cons_lemma,  append_wf,  cons_wf,  nil_wf,  append_assoc_sq,  list_ind_cons_lemma,  list_ind_nil_lemma
Rules used in proof :  cut,  sqequalSubstitution,  sqequalRule,  sqequalReflexivity,  sqequalTransitivity,  computationStep,  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,  independent_pairFormation,  computeAll,  independent_functionElimination,  sqequalAxiom,  productEquality,  applyEquality,  because_Cache,  unionElimination,  promote_hyp,  hypothesis_subsumption,  productElimination,  equalityTransitivity,  equalitySymmetry,  applyLambdaEquality,  dependent_set_memberEquality,  addEquality,  baseClosed,  instantiate,  cumulativity,  imageElimination,  isect_memberFormation
Latex:
\mforall{}[as:(Top  \mtimes{}  Top)  List]
    (unzip(as)  \msim{}  accumulate  (with  value  p  and  list  item  a):
                                let  p1,p2  =  p 
                                in  let  a1,a2  =  a 
                                      in  <p1  @  [a1],  p2  @  [a2]>
                              over  list:
                                  as
                              with  starting  value:
                                <[],  []>))


Date html generated: 2018_05_21-PM-06_52_43
Last ObjectModification: 2017_07_26-PM-04_58_28

Theory : general


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