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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