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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