Nuprl Lemma : p-reduce_wf
∀[p:ℕ+]. ∀[n:ℕ]. ∀[i:ℤ]. (i mod(p^n) ∈ ℕp^n)
Proof
Definitions occuring in Statement :
p-reduce: i mod(p^n),
exp: i^n,
int_seg: {i..j-},
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-reduce: i mod(p^n),
subtype_rel: A ⊆r B,
nat_plus: ℕ+
Lemmas referenced :
modulus_wf_int_mod,
exp_wf_nat_plus,
int-subtype-int_mod,
exp_wf2,
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,
hypothesis,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbN{}]. \mforall{}[i:\mBbbZ{}]. (i mod(p\^{}n) \mmember{} \mBbbN{}p\^{}n)
Date html generated:
2018_05_21-PM-03_17_51
Last ObjectModification:
2018_05_19-AM-08_08_48
Theory : rings_1
Home
Index