Nuprl Lemma : qmul_assoc_qrng

∀[a,b,c:ℚ].  ((a * b * c) = ((a * b) * c) ∈ ℚ)


Proof




Definitions occuring in Statement :  qmul: r * s,  rationals: ℚ,  uall: ∀[x:A]. B[x],  equal: s = t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  subtype_rel: A ⊆r B,  qrng: <ℚ+*>,  rng_car: |r|,  pi1: fst(t),  rng_times: *,  pi2: snd(t),  infix_ap: x f y
Lemmas referenced :  rng_times_assoc,  qrng_wf,  crng_subtype_rng
Rules used in proof :  cut,  introduction,  extract_by_obid,  sqequalHypSubstitution,  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isectElimination,  thin,  hypothesis,  applyEquality,  sqequalRule

Latex:
\mforall{}[a,b,c:\mBbbQ{}].    ((a  *  b  *  c)  =  ((a  *  b)  *  c))



Date html generated: 2020_05_20-AM-09_15_33
Last ObjectModification: 2020_02_04-PM-01_49_40

Theory : rationals


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