Nuprl Lemma : better-gcd_wf
∀[x,y:ℤ]. (better-gcd(x;y) ∈ ℤ)
Proof
Definitions occuring in Statement :
better-gcd: better-gcd(a;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
better-gcd-gcd,
gcd_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y:\mBbbZ{}]. (better-gcd(x;y) \mmember{} \mBbbZ{})
Date html generated:
2016_05_13-PM-03_37_05
Last ObjectModification:
2015_12_26-AM-09_41_53
Theory : arithmetic
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