Nuprl Lemma : rng_minus_zero
∀[r:Rng]. ((-r 0) = 0 ∈ |r|)
Proof
Definitions occuring in Statement :
rng: Rng
,
rng_minus: -r
,
rng_zero: 0
,
rng_car: |r|
,
uall: ∀[x:A]. B[x]
,
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_id: e
Lemmas referenced :
grp_inv_id,
add_grp_of_rng_wf_a,
grp_subtype_igrp,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule
Latex:
\mforall{}[r:Rng]. ((-r 0) = 0)
Date html generated:
2016_05_15-PM-00_21_17
Last ObjectModification:
2015_12_27-AM-00_02_19
Theory : rings_1
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