Nuprl Lemma : mul-assoced-one
∀x,y:ℤ. (((x * y) ~ 1)
⇒ (x ~ 1))
Proof
Definitions occuring in Statement :
assoced: a ~ b
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
multiply: n * m
,
natural_number: $n
,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
assoced: a ~ b
,
and: P ∧ Q
,
cand: A c∧ B
,
member: t ∈ T
,
prop: ℙ
,
uall: ∀[x:A]. B[x]
,
divides: b | a
,
exists: ∃x:A. B[x]
,
guard: {T}
Lemmas referenced :
one_divs_any,
assoced_wf,
equal_wf,
divides_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
isectElimination,
multiplyEquality,
natural_numberEquality,
intEquality,
dependent_pairFormation,
independent_functionElimination
Latex:
\mforall{}x,y:\mBbbZ{}. (((x * y) \msim{} 1) {}\mRightarrow{} (x \msim{} 1))
Date html generated:
2016_05_15-PM-04_45_54
Last ObjectModification:
2015_12_27-PM-02_37_34
Theory : general
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