Nuprl Lemma : p-units_wf
∀[p:ℤ]. (p-units(p) ∈ Type)
Proof
Definitions occuring in Statement :
p-units: p-units(p),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-units: p-units(p),
p-adics: p-adics(p),
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
nat: ℕ,
le: A ≤ B,
false: False,
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
p-adics_wf,
not_wf,
equal-wf-T-base,
less_than_wf,
int_seg_wf,
exp_wf2,
false_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
applyEquality,
setElimination,
rename,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
lambdaEquality,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:\mBbbZ{}]. (p-units(p) \mmember{} Type)
Date html generated:
2018_05_21-PM-03_20_18
Last ObjectModification:
2018_05_19-AM-08_11_29
Theory : rings_1
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