Nuprl Lemma : gcd_assoc
∀a,b,c:ℤ. (gcd(gcd(a;b);c) ~ gcd(a;gcd(b;c)))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
gcd: gcd(a;b),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q,
assoced: a ~ b
Lemmas referenced :
istype-int,
gcd_p_wf,
gcd_sat_pred,
gcd_wf,
gcd_p_sym,
gcd_of_triple
Rules used in proof :
hypothesis,
extract_by_obid,
introduction,
cut,
hypothesisEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
equalityTransitivity,
Error :equalityIsType1,
isectElimination,
applyLambdaEquality,
hyp_replacement,
equalitySymmetry,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
because_Cache,
productElimination,
independent_pairFormation
Latex:
\mforall{}a,b,c:\mBbbZ{}. (gcd(gcd(a;b);c) \msim{} gcd(a;gcd(b;c)))
Date html generated:
2019_06_20-PM-02_22_33
Last ObjectModification:
2019_01_15-PM-03_19_15
Theory : num_thy_1
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