Nuprl Lemma : rng_plus_ac_1
∀[r:Rng]. ∀[a,b,c:|r|]. ((a +r (b +r c)) = (b +r (a +r c)) ∈ |r|)
Proof
Definitions occuring in Statement :
rng: Rng,
rng_plus: +r,
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,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
iabmonoid: IAbMonoid,
imon: IMonoid,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
rng: Rng
Lemmas referenced :
abmonoid_ac_1,
add_grp_of_rng_wf_b,
subtype_rel_sets,
grp_sig_wf,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
comm_wf,
set_wf,
rng_car_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
setEquality,
cumulativity,
setElimination,
rename,
lambdaEquality,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[r:Rng]. \mforall{}[a,b,c:|r|]. ((a +r (b +r c)) = (b +r (a +r c)))
Date html generated:
2016_05_15-PM-00_21_56
Last ObjectModification:
2015_12_27-AM-00_01_53
Theory : rings_1
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