Nuprl Lemma : mul_mon_of_rng_wf_c
∀[r:Rng]. (r↓xmn ∈ IMonoid)
Proof
Definitions occuring in Statement :
mul_mon_of_rng: r↓xmn,
rng: Rng,
imon: IMonoid,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
mul_mon_of_rng: r↓xmn,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
rng: Rng,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
mon: Mon,
imon: IMonoid
Lemmas referenced :
rng_wf,
rng_all_properties,
mk_mon,
rng_car_wf,
rng_eq_wf,
rng_le_wf,
rng_times_wf,
rng_one_wf,
subtype_rel_self,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
productElimination,
setElimination,
rename,
lambdaEquality,
independent_isectElimination,
applyEquality,
instantiate
Latex:
\mforall{}[r:Rng]. (r\mdownarrow{}xmn \mmember{} IMonoid)
Date html generated:
2016_05_15-PM-00_21_03
Last ObjectModification:
2015_12_27-AM-00_02_32
Theory : rings_1
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