Nuprl Lemma : self_divisor_mul
∀a:ℤ-o. ∀b:ℤ. (((a * b) | a) ⇒ (b ~ 1))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
divides: b | a,
int_nzero: ℤ-o,
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,
member: t ∈ T,
uall: ∀[x:A]. B[x],
int_nzero: ℤ-o,
prop: ℙ,
top: Top,
assoced: a ~ b,
and: P ∧ Q,
divides: b | a,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
divides_wf,
istype-int,
int_nzero_wf,
istype-void,
mul-commutes,
one-mul,
int_subtype_base,
mul_cancel_in_assoced
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
multiplyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :dependent_pairFormation_alt,
Error :equalityIsType4,
Error :inhabitedIsType,
applyEquality,
dependent_functionElimination,
natural_numberEquality,
independent_functionElimination
Latex:
\mforall{}a:\mBbbZ{}\msupminus{}\msupzero{}. \mforall{}b:\mBbbZ{}. (((a * b) | a) {}\mRightarrow{} (b \msim{} 1))
Date html generated:
2019_06_20-PM-02_22_57
Last ObjectModification:
2018_10_03-AM-00_12_37
Theory : num_thy_1
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