Nuprl Lemma : map-snd-zip

[as,bs:Top List].  map(λp.(snd(p));zip(as;bs)) bs supposing ||as|| ||bs|| ∈ ℤ


Proof




Definitions occuring in Statement :  zip: zip(as;bs) length: ||as|| map: map(f;as) list: List uimplies: supposing a uall: [x:A]. B[x] top: Top pi2: snd(t) lambda: λx.A[x] int: sqequal: t equal: t ∈ T
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] and: P ∧ Q prop: or: P ∨ Q cons: [a b] colength: colength(L) nil: [] it: guard: {T} so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] le: A ≤ B decidable: Dec(P) subtype_rel: A ⊆B less_than': less_than'(a;b) less_than: a < b squash: T pi2: snd(t) uiff: uiff(P;Q)
Lemmas referenced :  nat_properties full-omega-unsat intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf istype-int 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 istype-less_than top_wf list-cases length_of_nil_lemma zip_nil_lemma map_nil_lemma product_subtype_list colength-cons-not-zero subtract-1-ge-0 subtype_base_sq intformeq_wf int_formula_prop_eq_lemma set_subtype_base int_subtype_base spread_cons_lemma length_of_cons_lemma le_weakening2 length_wf non_neg_length decidable__lt itermAdd_wf int_term_value_add_lemma istype-nat colength_wf_list decidable__le intformnot_wf int_formula_prop_not_lemma istype-le istype-void list_wf decidable__equal_int subtract_wf itermSubtract_wf int_term_value_subtract_lemma le_wf zip_cons_nil_lemma zip_cons_cons_lemma map_cons_lemma add-is-int-iff false_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut thin lambdaFormation_alt extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation_alt lambdaEquality_alt int_eqEquality dependent_functionElimination Error :memTop,  sqequalRule independent_pairFormation universeIsType voidElimination isect_memberEquality_alt axiomSqEquality isectIsTypeImplies inhabitedIsType functionIsTypeImplies unionElimination because_Cache equalityIstype baseClosed sqequalBase equalitySymmetry promote_hyp hypothesis_subsumption productElimination instantiate equalityTransitivity applyLambdaEquality addEquality applyEquality dependent_set_memberEquality_alt imageElimination baseApply closedConclusion intEquality pointwiseFunctionality

Latex:
\mforall{}[as,bs:Top  List].    map(\mlambda{}p.(snd(p));zip(as;bs))  \msim{}  bs  supposing  ||as||  =  ||bs||



Date html generated: 2020_05_19-PM-09_50_14
Last ObjectModification: 2020_02_27-PM-04_05_09

Theory : list_1


Home Index