### Nuprl Lemma : rng_plus_assoc

`∀[r:Rng]. ∀[a,b,c:|r|].  ((a +r (b +r c)) = ((a +r b) +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` grp: `Group{i}` mon: `Mon` imon: `IMonoid` prop: `ℙ` add_grp_of_rng: `r↓+gp` grp_car: `|g|` pi1: `fst(t)` grp_op: `*` pi2: `snd(t)` rng: `Rng`
Lemmas referenced :  mon_assoc add_grp_of_rng_wf_a grp_sig_wf monoid_p_wf grp_car_wf grp_op_wf grp_id_wf inverse_wf grp_inv_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 lambdaEquality setElimination rename setEquality cumulativity isect_memberEquality axiomEquality

Latex:
\mforall{}[r:Rng].  \mforall{}[a,b,c:|r|].    ((a  +r  (b  +r  c))  =  ((a  +r  b)  +r  c))

Date html generated: 2016_05_15-PM-00_21_27
Last ObjectModification: 2015_12_27-AM-00_02_13

Theory : rings_1

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