Nuprl Lemma : crng_times_comm
∀[r:CRng]. ∀[a,b:|r|]. ((a * b) = (b * a) ∈ |r|)
Proof
Definitions occuring in Statement :
crng: CRng,
rng_times: *,
rng_car: |r|,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
mul_mon_of_rng: r↓xmn,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
crng: CRng,
rng: Rng
Lemmas referenced :
abmonoid_comm,
mul_mon_of_rng_wf_b,
abmonoid_subtype_iabmonoid,
rng_car_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
setElimination,
rename
Latex:
\mforall{}[r:CRng]. \mforall{}[a,b:|r|]. ((a * b) = (b * a))
Date html generated:
2016_05_15-PM-00_21_33
Last ObjectModification:
2015_12_27-AM-00_02_10
Theory : rings_1
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