Nuprl Lemma : bpa-equiv_wf
∀[p:ℕ+]. ∀[x,y:basic-padic(p)]. (bpa-equiv(p;x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
bpa-equiv: bpa-equiv(p;x;y),
basic-padic: basic-padic(p),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bpa-equiv: bpa-equiv(p;x;y),
basic-padic: basic-padic(p),
nat_plus: ℕ+
Lemmas referenced :
equal_wf,
p-adics_wf,
p-mul_wf,
p-int_wf,
exp_wf2,
basic-padic_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
hypothesisEquality,
extract_by_obid,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[x,y:basic-padic(p)]. (bpa-equiv(p;x;y) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-03_24_38
Last ObjectModification:
2018_05_19-AM-08_22_10
Theory : rings_1
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