Nuprl Lemma : mkpadic_wf

∀[p:ℕ+]. ∀[n:ℕ]. ∀[a:p-adics(p)].  ((a/p^n) ∈ padic(p))


Proof




Definitions occuring in Statement :  mkpadic: (a/p^n),  padic: padic(p),  p-adics: p-adics(p),  nat_plus: ℕ+,  nat: ℕ,  uall: ∀[x:A]. B[x],  member: t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  mkpadic: (a/p^n),  basic-padic: basic-padic(p),  nat_plus: ℕ+
Lemmas referenced :  bpa-norm_wf_padic,  p-adics_wf,  nat_wf,  nat_plus_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation,  introduction,  cut,  sqequalRule,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  independent_pairEquality,  hypothesis,  axiomEquality,  equalityTransitivity,  equalitySymmetry,  setElimination,  rename,  isect_memberEquality,  because_Cache

Latex:
\mforall{}[p:\mBbbN{}\msupplus{}].  \mforall{}[n:\mBbbN{}].  \mforall{}[a:p-adics(p)].    ((a/p\^{}n)  \mmember{}  padic(p))



Date html generated: 2018_05_21-PM-03_26_28
Last ObjectModification: 2018_05_19-AM-08_23_34

Theory : rings_1


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