Nuprl Lemma : qmul_over_plus_qrng
∀[a,b,c:ℚ]. (((a * (b + c)) = ((a * b) + (a * c)) ∈ ℚ) ∧ (((b + c) * a) = ((b * a) + (c * a)) ∈ ℚ))
Proof
Definitions occuring in Statement :
qmul: r * s,
qadd: r + s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
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),
rng_plus: +r,
infix_ap: x f y
Lemmas referenced :
rng_times_over_plus,
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) + (a * c))) \mwedge{} (((b + c) * a) = ((b * a) + (c * a))))
Date html generated:
2020_05_20-AM-09_15_23
Last ObjectModification:
2020_02_03-PM-02_49_09
Theory : rationals
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