Nuprl Lemma : p-sep_wf
∀[p:ℕ+]. ∀[x,y:p-adics(p)]. (p-sep(x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
p-sep: p-sep(x;y),
p-adics: p-adics(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,
p-sep: p-sep(x;y),
so_lambda: λ2x.t[x],
p-adics: p-adics(p),
subtype_rel: A ⊆r B,
int_seg: {i..j-},
nat_plus: ℕ+,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_plus_wf,
not_wf,
equal_wf,
int_seg_wf,
exp_wf2,
nat_plus_subtype_nat,
p-adics_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
intEquality,
applyEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[x,y:p-adics(p)]. (p-sep(x;y) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-03_23_09
Last ObjectModification:
2018_05_19-AM-08_21_25
Theory : rings_1
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