### Nuprl Lemma : quot_ring_car_elim_b

`∀r:CRng. ∀a:Ideal(r){i}. ∀d:detach_fun(|r|;a).`
`  ((∀w:|r|. SqStable(a w)) `` (∀u,v:|r|.  ([u]{|r / d|} = [v]{|r / d|} ∈ |r / d| `⇐⇒` a (u +r (-r v)))))`

Proof

Definitions occuring in Statement :  quot_ring: `r / d` ideal: `Ideal(r){i}` crng: `CRng` rng_minus: `-r` rng_plus: `+r` rng_car: `|r|` detach_fun: `detach_fun(T;A)` type_inj: `[x]{T}` sq_stable: `SqStable(P)` infix_ap: `x f y` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` implies: `P `` Q` apply: `f a` equal: `s = t ∈ T`
Definitions unfolded in proof :  type_inj: `[x]{T}`
Lemmas referenced :  quot_ring_car_elim_a
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lemma_by_obid

Latex:
\mforall{}r:CRng.  \mforall{}a:Ideal(r)\{i\}.  \mforall{}d:detach\_fun(|r|;a).
((\mforall{}w:|r|.  SqStable(a  w))  {}\mRightarrow{}  (\mforall{}u,v:|r|.    ([u]\{|r  /  d|\}  =  [v]\{|r  /  d|\}  \mLeftarrow{}{}\mRightarrow{}  a  (u  +r  (-r  v)))))

Date html generated: 2016_05_15-PM-00_24_31
Last ObjectModification: 2015_12_27-AM-00_00_24

Theory : rings_1

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