Nuprl Lemma : p-digits_wf
∀[p:ℕ+]. ∀[a:p-adics(p)]. (p-digits(p;a) ∈ ℕ+ ⟶ ℕp)
Proof
Definitions occuring in Statement :
p-digits: p-digits(p;a),
p-adics: p-adics(p),
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-digits: p-digits(p;a),
nat_plus: ℕ+
Lemmas referenced :
p-digit_wf,
nat_plus_wf,
p-adics_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[a:p-adics(p)]. (p-digits(p;a) \mmember{} \mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbN{}p)
Date html generated:
2018_05_21-PM-03_21_33
Last ObjectModification:
2018_05_19-AM-08_18_35
Theory : rings_1
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