### Nuprl Lemma : zip_length

`∀[T1,T2:Type]. ∀[as:T1 List]. ∀[bs:T2 List].  ((||zip(as;bs)|| ≤ ||as||) ∧ (||zip(as;bs)|| ≤ ||bs||))`

Proof

Definitions occuring in Statement :  zip: `zip(as;bs)` length: `||as||` list: `T List` uall: `∀[x:A]. B[x]` le: `A ≤ B` and: `P ∧ Q` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` prop: `ℙ` and: `P ∧ Q` so_apply: `x[s]` implies: `P `` Q` all: `∀x:A. B[x]` le: `A ≤ B` not: `¬A` false: `False` zip: `zip(as;bs)` so_lambda: `so_lambda(x,y,z.t[x; y; z])` top: `Top` so_apply: `x[s1;s2;s3]` cand: `A c∧ B` less_than': `less_than'(a;b)` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` nat: `ℕ` guard: `{T}` uiff: `uiff(P;Q)`
Lemmas referenced :  list_induction uall_wf list_wf le_wf length_wf zip_wf less_than'_wf list_ind_nil_lemma length_of_nil_lemma false_wf non_neg_length decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf cons_wf list_ind_cons_lemma length_of_cons_lemma add_nat_wf length_wf_nat nat_wf nat_properties add-is-int-iff itermAdd_wf intformeq_wf int_term_value_add_lemma int_formula_prop_eq_lemma equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality cumulativity hypothesis productEquality independent_functionElimination lambdaFormation rename because_Cache dependent_functionElimination isect_memberEquality productElimination independent_pairEquality axiomEquality equalityTransitivity equalitySymmetry universeEquality voidElimination voidEquality independent_pairFormation natural_numberEquality unionElimination independent_isectElimination dependent_pairFormation int_eqEquality intEquality computeAll dependent_set_memberEquality applyLambdaEquality setElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed addEquality

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

Date html generated: 2017_04_17-AM-08_54_36
Last ObjectModification: 2017_02_27-PM-05_11_08

Theory : list_1

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