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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