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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