Nuprl Lemma : mul-zero-vector
∀[i:Type]. ∀[r:Rng]. ∀[c:|r|]. ((c*0) = 0 ∈ (i ⟶ |r|))
Proof
Definitions occuring in Statement :
zero-vector: 0,
vector-mul: (c*a),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
rng: Rng,
rng_car: |r|
Definitions unfolded in proof :
rng: Rng,
and: P ∧ Q,
vector-mul: (c*a),
zero-vector: 0,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
rng_car_wf,
rng_times_zero
Rules used in proof :
universeEquality,
because_Cache,
axiomEquality,
isect_memberEquality,
rename,
setElimination,
hypothesis,
productElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
functionExtensionality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[i:Type]. \mforall{}[r:Rng]. \mforall{}[c:|r|]. ((c*0) = 0)
Date html generated:
2018_05_21-PM-09_40_46
Last ObjectModification:
2018_01_09-PM-01_00_31
Theory : matrices
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