Nuprl Lemma : map-index_aux_wf

[A,B:Type]. ∀[L:A List]. ∀[x:ℤ]. ∀[f:{x..x ||L||-} ⟶ A ⟶ B].  (map-index_aux(f;L) x ∈ List)


Proof




Definitions occuring in Statement :  map-index_aux: map-index_aux(f;L) length: ||as|| list: List int_seg: {i..j-} uall: [x:A]. B[x] member: t ∈ T apply: a function: x:A ⟶ B[x] add: m int: 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 ≥  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 map-index_aux: map-index_aux(f;L) so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3] 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) int_seg: {i..j-} lelt: i ≤ j < k le: 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 int_seg_wf length_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases length_of_nil_lemma list_ind_nil_lemma nil_wf 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_ind_cons_lemma cons_wf non_neg_length decidable__lt lelt_wf subtype_rel_dep_function int_seg_subtype subtype_rel_self 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 dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry functionEquality addEquality cumulativity applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination applyLambdaEquality dependent_set_memberEquality baseClosed instantiate imageElimination functionExtensionality universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[L:A  List].  \mforall{}[x:\mBbbZ{}].  \mforall{}[f:\{x..x  +  ||L||\msupminus{}\}  {}\mrightarrow{}  A  {}\mrightarrow{}  B].    (map-index\_aux(f;L)  x  \mmember{}  B  List)



Date html generated: 2017_04_17-AM-08_53_33
Last ObjectModification: 2017_02_27-PM-05_11_36

Theory : list_1


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