Nuprl Lemma : zip_unzip
∀[T1,T2:Type]. ∀[as:(T1 × T2) List]. (zip(fst(unzip(as));snd(unzip(as))) = as ∈ ((T1 × T2) List))
Proof
Definitions occuring in Statement :
unzip: unzip(as),
zip: zip(as;bs),
list: T List,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
unzip: unzip(as),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
pi1: fst(t),
pi2: snd(t),
top: Top,
squash: ↓T,
true: True
Lemmas referenced :
list_induction,
equal_wf,
list_wf,
zip_wf,
map_wf,
pi1_wf,
pi2_wf,
map_nil_lemma,
zip_nil_lemma,
nil_wf,
map_cons_lemma,
zip_cons_cons_lemma,
cons_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
productEquality,
cumulativity,
hypothesisEquality,
lambdaEquality,
hypothesis,
independent_pairEquality,
productElimination,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
rename,
axiomEquality,
universeEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[T1,T2:Type]. \mforall{}[as:(T1 \mtimes{} T2) List]. (zip(fst(unzip(as));snd(unzip(as))) = as)
Date html generated:
2017_04_17-AM-08_55_36
Last ObjectModification:
2017_02_27-PM-05_10_23
Theory : list_1
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