Nuprl Lemma : gcd_p_sym
∀a,b,y:ℤ. (GCD(a;b;y) ⇒ GCD(b;a;y))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
divides_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
independent_pairFormation,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
Error :productIsType,
Error :universeIsType,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType,
Error :functionIsType
Latex:
\mforall{}a,b,y:\mBbbZ{}. (GCD(a;b;y) {}\mRightarrow{} GCD(b;a;y))
Date html generated:
2019_06_20-PM-02_21_35
Last ObjectModification:
2018_10_02-PM-11_35_09
Theory : num_thy_1
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