Nuprl Lemma : gcd_p_neg_arg_2
∀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],
iff: P ⇐⇒ Q,
minus: -n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
gcd_p_wf,
istype-int,
gcd_p_neg_arg,
squash_wf,
true_wf,
minus_minus_cancel,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
independent_pairFormation,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
minusEquality,
Error :inhabitedIsType,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination
Latex:
\mforall{}a,b,y:\mBbbZ{}. (GCD(a;b;y) \mLeftarrow{}{}\mRightarrow{} GCD(a;-b;y))
Date html generated:
2019_06_20-PM-02_21_43
Last ObjectModification:
2018_10_03-AM-00_12_09
Theory : num_thy_1
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