Nuprl Lemma : coprime-exp
∀a,b:ℤ. (CoPrime(a,b) ⇒ (∀n,m:ℕ. CoPrime(a^m,b^n)))
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
exp: i^n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
coprime-exp1,
exp_wf2,
coprime_symmetry,
nat_wf,
coprime_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache,
intEquality
Latex:
\mforall{}a,b:\mBbbZ{}. (CoPrime(a,b) {}\mRightarrow{} (\mforall{}n,m:\mBbbN{}. CoPrime(a\^{}m,b\^{}n)))
Date html generated:
2016_05_15-PM-04_50_06
Last ObjectModification:
2015_12_27-PM-02_35_02
Theory : general
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