Nuprl Lemma : unzip-zip
∀[as,bs:Top List]. unzip(zip(as;bs)) ~ <as, bs> 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],
top: Top,
pair: <a, b>,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
unzip: unzip(as),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
map-fst-zip,
map-snd-zip,
istype-int,
length_wf_nat,
top_wf,
set_subtype_base,
le_wf,
int_subtype_base,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
axiomSqEquality,
equalityIstype,
applyEquality,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
sqequalBase,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType
Latex:
\mforall{}[as,bs:Top List]. unzip(zip(as;bs)) \msim{} <as, bs> supposing ||as|| = ||bs||
Date html generated:
2020_05_19-PM-09_50_26
Last ObjectModification:
2020_02_27-PM-04_06_06
Theory : list_1
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