Nuprl Lemma : qmul_zero_qrng
∀[a:ℚ]. (((0 * a) = 0 ∈ ℚ) ∧ ((a * 0) = 0 ∈ ℚ))
Proof
Definitions occuring in Statement :
qmul: r * s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n,
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_zero: 0,
infix_ap: x f y
Lemmas referenced :
rng_times_zero,
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:\mBbbQ{}]. (((0 * a) = 0) \mwedge{} ((a * 0) = 0))
Date html generated:
2020_05_20-AM-09_15_30
Last ObjectModification:
2020_02_03-PM-03_23_43
Theory : rationals
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