Nuprl Lemma : q-rng-nexp_wf
∀[r:ℚ]. ∀[n:ℕ]. (q-rng-nexp(r;n) ∈ ℚ)
Proof
Definitions occuring in Statement :
q-rng-nexp: q-rng-nexp(r;n),
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q-rng-nexp: q-rng-nexp(r;n),
subtype_rel: A ⊆r B,
crng: CRng,
qrng: <ℚ+*>,
rng_car: |r|,
pi1: fst(t),
rng: Rng
Lemmas referenced :
rng_nexp_wf,
qrng_wf,
crng_wf,
rng_car_wf,
nat_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r:\mBbbQ{}]. \mforall{}[n:\mBbbN{}]. (q-rng-nexp(r;n) \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-11_06_26
Last ObjectModification:
2015_12_27-PM-07_44_56
Theory : rationals
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