Nuprl Lemma : zero-bfs_wf
∀[S:Type]. ∀[K:RngSig]. ∀[ss:bag(S)]. (0 * ss ∈ basic-formal-sum(K;S))
Proof
Definitions occuring in Statement :
zero-bfs: 0 * ss,
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig,
bag: bag(T)
Definitions unfolded in proof :
basic-formal-sum: basic-formal-sum(K;S),
subtype_rel: A ⊆r B,
zero-bfs: 0 * ss,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
bag_wf,
rng_zero_wf,
rng_car_wf,
bag-map_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
independent_pairEquality,
lambdaEquality,
cumulativity,
hypothesis,
hypothesisEquality,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:RngSig]. \mforall{}[ss:bag(S)]. (0 * ss \mmember{} basic-formal-sum(K;S))
Date html generated:
2018_05_22-PM-09_44_33
Last ObjectModification:
2018_01_08-PM-01_01_52
Theory : linear!algebra
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