Nuprl Lemma : exp_assoced
∀n:ℕ+. ∀x,y:ℤ. (x^n ~ y^n ⇐⇒ x ~ y)
Proof
Definitions occuring in Statement :
assoced: a ~ b,
exp: i^n,
nat_plus: ℕ+,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
assoced: a ~ b,
exists: ∃x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
assoced_wf,
exp_wf2,
nat_plus_subtype_nat,
nat_plus_wf,
exp-divides-exp2,
divides_wf,
assoced_functionality_wrt_assoced,
exp_functionality_wrt_assoced,
assoced_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
intEquality,
productElimination,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
independent_isectElimination
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}x,y:\mBbbZ{}. (x\^{}n \msim{} y\^{}n \mLeftarrow{}{}\mRightarrow{} x \msim{} y)
Date html generated:
2018_05_21-PM-01_11_05
Last ObjectModification:
2018_01_28-PM-02_04_05
Theory : num_thy_1
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