Nuprl Lemma : divides_functionality_wrt_assoced
∀a,a',b,b':ℤ. ((a ~ a') ⇒ (b ~ b') ⇒ (a | b ⇐⇒ a' | b'))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
divides: b | a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
assoced: a ~ b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
member: t ∈ T,
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
divides_transitivity,
divides_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
Error :universeIsType,
isectElimination,
Error :productIsType,
Error :inhabitedIsType
Latex:
\mforall{}a,a',b,b':\mBbbZ{}. ((a \msim{} a') {}\mRightarrow{} (b \msim{} b') {}\mRightarrow{} (a | b \mLeftarrow{}{}\mRightarrow{} a' | b'))
Date html generated:
2019_06_20-PM-02_20_52
Last ObjectModification:
2018_10_03-AM-00_35_50
Theory : num_thy_1
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