Nuprl Lemma : unzip_zip
∀[T1,T2:Type]. ∀[as:T1 List]. ∀[bs:T2 List].
unzip(zip(as;bs)) = <as, bs> ∈ (T1 List × (T2 List)) supposing ||as|| = ||bs|| ∈ ℤ
Proof
Definitions occuring in Statement :
unzip: unzip(as),
zip: zip(as;bs),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
unzip-zip,
subtype_rel_list,
top_wf,
istype-int,
length_wf_nat,
set_subtype_base,
le_wf,
int_subtype_base,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
independent_isectElimination,
lambdaEquality_alt,
Error :memTop,
universeIsType,
independent_pairEquality,
equalityIstype,
intEquality,
natural_numberEquality,
sqequalBase,
equalitySymmetry,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T1,T2:Type]. \mforall{}[as:T1 List]. \mforall{}[bs:T2 List]. unzip(zip(as;bs)) = <as, bs> supposing ||as|| = ||bs||
Date html generated:
2020_05_19-PM-09_50_38
Last ObjectModification:
2020_02_27-PM-04_07_28
Theory : list_1
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