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:
2018_05_21-PM-01_05_57
Last ObjectModification:
2018_01_28-PM-02_02_05
Theory : num_thy_1
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