Nuprl Lemma : unzip_wf
∀[T1,T2:Type]. ∀[as:(T1 × T2) List]. (unzip(as) ∈ T1 List × (T2 List))
Proof
Definitions occuring in Statement :
unzip: unzip(as),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
unzip: unzip(as),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
map_wf,
pi1_wf,
pi2_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
independent_pairEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
isect_memberEquality,
because_Cache,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[T1,T2:Type]. \mforall{}[as:(T1 \mtimes{} T2) List]. (unzip(as) \mmember{} T1 List \mtimes{} (T2 List))
Date html generated:
2019_06_20-PM-01_47_22
Last ObjectModification:
2018_09_26-PM-02_51_08
Theory : list_1
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