Nuprl Lemma : sq_stable__coprime
∀i,j:ℤ. SqStable(CoPrime(i,j))
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
sq_stable: SqStable(P),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
coprime: CoPrime(a,b),
sq_stable: SqStable(P),
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T
Lemmas referenced :
decidable__divides_ext,
sq_stable_from_decidable,
all_wf,
squash_wf,
divides_wf,
and_wf,
one_divs_any
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
productElimination,
isectElimination,
intEquality,
natural_numberEquality,
lambdaEquality,
functionEquality,
imageElimination,
independent_functionElimination,
introduction,
imageMemberEquality,
baseClosed
Latex:
\mforall{}i,j:\mBbbZ{}. SqStable(CoPrime(i,j))
Date html generated:
2016_05_14-PM-04_19_39
Last ObjectModification:
2016_01_14-PM-11_40_21
Theory : num_thy_1
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