Nuprl Lemma : length_zip
∀[T1,T2:Type]. ∀[as:T1 List]. ∀[bs:T2 List]. ||zip(as;bs)|| = ||as|| ∈ ℤ supposing ||as|| = ||bs|| ∈ ℤ
Proof
Definitions occuring in Statement :
zip: zip(as;bs),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
zip: zip(as;bs),
list_ind: list_ind,
nil: [],
it: ⋅,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
squash: ↓T,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
equal_wf,
length_wf,
zip_wf,
equal-wf-base-T,
equal-wf-T-base,
nil_wf,
length_of_nil_lemma,
list_ind_nil_lemma,
equal-wf-base,
length_of_cons_lemma,
cons_wf,
list_ind_cons_lemma,
squash_wf,
true_wf,
add_functionality_wrt_eq,
decidable__equal_int,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
false_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
intEquality,
because_Cache,
productEquality,
independent_functionElimination,
baseClosed,
voidEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
addEquality,
natural_numberEquality,
axiomEquality,
applyEquality,
imageElimination,
independent_isectElimination,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
productElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
imageMemberEquality,
universeEquality
Latex:
\mforall{}[T1,T2:Type]. \mforall{}[as:T1 List]. \mforall{}[bs:T2 List]. ||zip(as;bs)|| = ||as|| supposing ||as|| = ||bs||
Date html generated:
2017_04_17-AM-08_55_08
Last ObjectModification:
2017_02_27-PM-05_10_44
Theory : list_1
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