Nuprl Lemma : p-reduce-eqmod
∀p:ℕ+. ∀n:ℕ. ∀i:ℤ. (i mod(p^n) ≡ i mod p^n)
Proof
Definitions occuring in Statement :
p-reduce: i mod(p^n),
eqmod: a ≡ b mod m,
exp: i^n,
nat_plus: ℕ+,
nat: ℕ,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
p-reduce: i mod(p^n),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
mod-eqmod,
exp_wf_nat_plus,
nat_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
intEquality
Latex:
\mforall{}p:\mBbbN{}\msupplus{}. \mforall{}n:\mBbbN{}. \mforall{}i:\mBbbZ{}. (i mod(p\^{}n) \mequiv{} i mod p\^{}n)
Date html generated:
2018_05_21-PM-03_17_54
Last ObjectModification:
2018_05_19-AM-08_08_52
Theory : rings_1
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