Nuprl Lemma : select-qv-mul
∀[as:Top List]. ∀[r:Top]. ∀[i:ℕdimension(as)]. (qv-mul(r;as)[i] ~ r * as[i])
Proof
Definitions occuring in Statement :
qv-mul: qv-mul(r;bs),
qv-dim: dimension(as),
qmul: r * s,
select: L[n],
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
qv-dim: dimension(as),
uall: ∀[x:A]. B[x],
member: t ∈ T,
qv-mul: qv-mul(r;bs),
top: Top
Lemmas referenced :
select-map,
int_seg_wf,
length_wf,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
sqequalAxiom,
natural_numberEquality,
because_Cache
Latex:
\mforall{}[as:Top List]. \mforall{}[r:Top]. \mforall{}[i:\mBbbN{}dimension(as)]. (qv-mul(r;as)[i] \msim{} r * as[i])
Date html generated:
2016_05_15-PM-11_20_47
Last ObjectModification:
2015_12_27-PM-07_33_04
Theory : rationals
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