Nuprl Lemma : gcd_p_wf
∀[a,b,y:ℤ]. (GCD(a;b;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
gcd_p: GCD(a;b;y),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
divides_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
because_Cache,
Error :universeIsType
Latex:
\mforall{}[a,b,y:\mBbbZ{}]. (GCD(a;b;y) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_21_20
Last ObjectModification:
2018_09_26-PM-05_49_04
Theory : num_thy_1
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