Nuprl Lemma : gcd_is_divisor_1
∀a,b:ℤ. (gcd(a;b) | a)
Proof
Definitions occuring in Statement :
divides: b | a,
gcd: gcd(a;b),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
gcd_p: GCD(a;b;y),
and: P ∧ Q
Lemmas referenced :
istype-int,
gcd_wf,
gcd_sat_pred,
gcd_p_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
isectElimination,
Error :equalityIsType1,
equalityTransitivity,
independent_functionElimination,
productElimination
Latex:
\mforall{}a,b:\mBbbZ{}. (gcd(a;b) | a)
Date html generated:
2019_06_20-PM-02_22_04
Last ObjectModification:
2018_10_03-AM-00_12_14
Theory : num_thy_1
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