Nuprl Lemma : list_ind-as-fix

[L:Top List]. ∀[x,F:Top].
  (rec-case(L) of
   [] => x
   b::bs =>
    r.F[r;b;bs] fix((λR,L. if null(L) then else (R tl(L)) hd(L) tl(L) fi )) L)


Definitions occuring in Statement :  hd: hd(l) null: null(as) tl: tl(l) list_ind: list_ind list: List ifthenelse: if then else fi  uall: [x:A]. B[x] top: Top so_apply: x[s1;s2;s3] apply: a fix: fix(F) lambda: λx.A[x] sqequal: t
Definitions unfolded in proof :  so_apply: x[s1;s2;s3] uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] 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: so_lambda(x,y,z.t[x; y; z]) ifthenelse: if then else fi  btrue: tt cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] 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) bfalse: ff
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 top_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list_wf list-cases list_ind_nil_lemma null_nil_lemma reduce_tl_nil_lemma 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 list_ind_cons_lemma null_cons_lemma reduce_tl_cons_lemma reduce_hd_cons_lemma
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut thin lambdaFormation 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 applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate cumulativity imageElimination

\mforall{}[L:Top  List].  \mforall{}[x,F:Top].
    (rec-case(L)  of
      []  =>  x
      b::bs  =>
        r.F[r;b;bs]  \msim{}  fix((\mlambda{}R,L.  if  null(L)  then  x  else  F  (R  tl(L))  hd(L)  tl(L)  fi  ))  L)

Date html generated: 2017_10_01-AM-09_10_59
Last ObjectModification: 2017_07_26-PM-04_47_13

Theory : general

Home Index