Nuprl Lemma : qmul_comm_qrng
∀[a,b:ℚ]. ((a * b) = (b * a) ∈ 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,
qrng: <ℚ+*>,
rng_car: |r|,
pi1: fst(t),
rng_times: *,
pi2: snd(t),
infix_ap: x f y
Lemmas referenced :
crng_times_comm,
qrng_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[a,b:\mBbbQ{}]. ((a * b) = (b * a))
Date html generated:
2020_05_20-AM-09_15_39
Last ObjectModification:
2020_02_03-PM-02_14_00
Theory : rationals
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