Nuprl Lemma : gcd_p_neg_arg_a
∀a,b,y:ℤ. (GCD(a;b;y) ⇒ GCD(-a;b;y))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
minus: -n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
gcd_p_wf,
istype-int,
gcd_p_sym,
gcd_p_neg_arg
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
minusEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}a,b,y:\mBbbZ{}. (GCD(a;b;y) {}\mRightarrow{} GCD(-a;b;y))
Date html generated:
2019_06_20-PM-02_21_41
Last ObjectModification:
2018_10_03-AM-00_12_13
Theory : num_thy_1
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