Nuprl Lemma : zip_wf

[T1,T2:Type]. ∀[as:T1 List]. ∀[bs:T2 List].  (zip(as;bs) ∈ (T1 × T2) List)


Proof




Definitions occuring in Statement :  zip: zip(as;bs) list: List uall: [x:A]. B[x] member: t ∈ T product: 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 ≥  uimplies: supposing a not: ¬A satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] top: Top and: P ∧ Q prop: guard: {T} or: P ∨ Q zip: zip(as;bs) list_ind: list_ind nil: [] it: cons: [a b] le: A ≤ B less_than': less_than'(a;b) colength: colength(L) so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b squash: T so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] decidable: Dec(P) subtype_rel: A ⊆B so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3]
Lemmas referenced :  nat_properties full-omega-unsat intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf istype-int int_formula_prop_and_lemma istype-void 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 intformeq_wf int_formula_prop_eq_lemma list-cases nil_wf list_wf product_subtype_list colength-cons-not-zero colength_wf_list istype-false le_wf subtract-1-ge-0 subtype_base_sq set_subtype_base int_subtype_base spread_cons_lemma decidable__equal_int subtract_wf intformnot_wf itermSubtract_wf itermAdd_wf int_formula_prop_not_lemma int_term_value_subtract_lemma int_term_value_add_lemma decidable__le list_ind_cons_lemma list_ind_nil_lemma cons_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut thin Error :lambdaFormation_alt,  extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination Error :dependent_pairFormation_alt,  Error :lambdaEquality_alt,  int_eqEquality dependent_functionElimination Error :isect_memberEquality_alt,  voidElimination independent_pairFormation Error :universeIsType,  axiomEquality equalityTransitivity equalitySymmetry applyLambdaEquality Error :functionIsTypeImplies,  Error :inhabitedIsType,  unionElimination productEquality promote_hyp hypothesis_subsumption productElimination Error :equalityIsType1,  because_Cache Error :dependent_set_memberEquality_alt,  instantiate imageElimination Error :equalityIsType4,  baseApply closedConclusion baseClosed applyEquality intEquality independent_pairEquality universeEquality

Latex:
\mforall{}[T1,T2:Type].  \mforall{}[as:T1  List].  \mforall{}[bs:T2  List].    (zip(as;bs)  \mmember{}  (T1  \mtimes{}  T2)  List)



Date html generated: 2019_06_20-PM-01_47_12
Last ObjectModification: 2018_10_06-PM-06_09_35

Theory : list_1


Home Index