Nuprl Lemma : mul_mon_of_rng_wf_b
∀[r:CRng]. (r↓xmn ∈ AbMon)
Proof
Definitions occuring in Statement :
mul_mon_of_rng: r↓xmn,
crng: CRng,
abmonoid: AbMon,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
mul_mon_of_rng: r↓xmn,
crng: CRng,
rng: Rng,
uimplies: b supposing a
Lemmas referenced :
crng_all_properties,
crng_wf,
mk_abmonoid,
rng_car_wf,
rng_eq_wf,
rng_le_wf,
rng_times_wf,
rng_one_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
lambdaEquality,
independent_isectElimination
Latex:
\mforall{}[r:CRng]. (r\mdownarrow{}xmn \mmember{} AbMon)
Date html generated:
2016_05_15-PM-00_21_07
Last ObjectModification:
2015_12_27-AM-00_02_29
Theory : rings_1
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