Nuprl Lemma : formal-sum-mul_wf1
∀[S:Type]. ∀[K:RngSig]. ∀[x:basic-formal-sum(K;S)]. ∀[k:|K|]. (k * x ∈ basic-formal-sum(K;S))
Proof
Definitions occuring in Statement :
formal-sum-mul: k * x,
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
infix_ap: x f y,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-formal-sum: basic-formal-sum(K;S),
formal-sum-mul: k * x
Lemmas referenced :
rng_sig_wf,
bag_wf,
rng_times_wf,
rng_car_wf,
bag-map_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
independent_pairEquality,
productElimination,
spreadEquality,
lambdaEquality,
cumulativity,
hypothesis,
hypothesisEquality,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:RngSig]. \mforall{}[x:basic-formal-sum(K;S)]. \mforall{}[k:|K|]. (k * x \mmember{} basic-formal-sum(K;S))
Date html generated:
2018_05_22-PM-09_44_29
Last ObjectModification:
2018_01_09-PM-01_00_44
Theory : linear!algebra
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