Nuprl Lemma : rng_minus_over_plus
∀[r:Rng]. ∀[a,b:|r|]. ((-r (a +r b)) = ((-r b) +r (-r a)) ∈ |r|)
Proof
Definitions occuring in Statement :
rng: Rng,
rng_minus: -r,
rng_plus: +r,
rng_car: |r|,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
grp_inv: ~,
pi2: snd(t),
grp_op: *,
rng: Rng
Lemmas referenced :
grp_inv_thru_op,
add_grp_of_rng_wf_a,
grp_subtype_igrp,
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,
isect_memberEquality,
axiomEquality,
setElimination,
rename
Latex:
\mforall{}[r:Rng]. \mforall{}[a,b:|r|]. ((-r (a +r b)) = ((-r b) +r (-r a)))
Date html generated:
2016_05_15-PM-00_21_14
Last ObjectModification:
2015_12_27-AM-00_02_25
Theory : rings_1
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