Nuprl Lemma : gcd_p_zero_rel
∀a,b:ℤ. (GCD(a;0;b) ⇒ ((a = b ∈ ℤ) ∨ (a = (-b) ∈ ℤ)))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
minus: -n,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
gcd_p: GCD(a;b;y),
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
cand: A c∧ B,
pm_equal: i = ± j
Lemmas referenced :
gcd_p_wf,
istype-int,
divides_reflexivity,
any_divs_zero,
divides_anti_sym
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
natural_numberEquality,
hypothesis,
Error :inhabitedIsType,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation
Latex:
\mforall{}a,b:\mBbbZ{}. (GCD(a;0;b) {}\mRightarrow{} ((a = b) \mvee{} (a = (-b))))
Date html generated:
2019_06_20-PM-02_21_33
Last ObjectModification:
2018_10_02-PM-11_35_12
Theory : num_thy_1
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