Nuprl Lemma : exp-divides
∀x,y:ℤ.  ((x | y) 
⇒ (∀n:ℕ. (x^n | y^n)))
Proof
Definitions occuring in Statement : 
divides: b | a
, 
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
, 
divides: b | a
, 
exists: ∃x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
uimplies: b supposing a
, 
sq_type: SQType(T)
, 
guard: {T}
, 
true: True
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
exp_wf2, 
equal_wf, 
nat_wf, 
divides_wf, 
subtype_base_sq, 
int_subtype_base, 
squash_wf, 
true_wf, 
exp-of-mul, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
dependent_pairFormation, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
intEquality, 
multiplyEquality, 
instantiate, 
cumulativity, 
independent_isectElimination, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
equalityUniverse, 
levelHypothesis, 
natural_numberEquality, 
applyEquality, 
lambdaEquality, 
imageElimination, 
universeEquality, 
sqequalRule, 
imageMemberEquality, 
baseClosed
Latex:
\mforall{}x,y:\mBbbZ{}.    ((x  |  y)  {}\mRightarrow{}  (\mforall{}n:\mBbbN{}.  (x\^{}n  |  y\^{}n)))
Date html generated:
2017_04_17-AM-09_44_43
Last ObjectModification:
2017_02_27-PM-05_38_51
Theory : num_thy_1
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