Nuprl Lemma : gcd_elim
∀a,b:ℤ. ∃y:ℤ. (GCD(a;b;y) ∧ (gcd(a;b) = y ∈ ℤ))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
gcd: gcd(a;b),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
istype-int,
gcd_wf,
gcd_sat_pred,
gcd_p_wf,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :dependent_pairFormation_alt,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
independent_pairFormation,
because_Cache,
sqequalRule,
Error :productIsType,
Error :universeIsType,
isectElimination,
Error :equalityIsType4,
applyEquality
Latex:
\mforall{}a,b:\mBbbZ{}. \mexists{}y:\mBbbZ{}. (GCD(a;b;y) \mwedge{} (gcd(a;b) = y))
Date html generated:
2019_06_20-PM-02_21_57
Last ObjectModification:
2018_10_03-AM-00_12_19
Theory : num_thy_1
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