Nuprl Lemma : neg-bfs-append
∀[S:Type]. ∀[K:RngSig]. ∀[fs1,fs2:basic-formal-sum(K;S)]. (-(fs1 + fs2) = (-(fs1) + -(fs2)) ∈ basic-formal-sum(K;S))
Proof
Definitions occuring in Statement :
neg-bfs: -(fs),
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T,
rng_sig: RngSig,
bag-append: as + bs
Definitions unfolded in proof :
top: Top,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
basic-formal-sum: basic-formal-sum(K;S),
neg-bfs: -(fs),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
basic-formal-sum_wf,
bag_wf,
rng_minus_wf,
bag-map_wf,
bag-append_wf,
rng_car_wf,
top_wf,
subtype_rel_bag,
bag-map-append
Rules used in proof :
universeEquality,
axiomEquality,
independent_pairEquality,
productElimination,
because_Cache,
voidEquality,
voidElimination,
isect_memberEquality,
lambdaEquality,
independent_isectElimination,
cumulativity,
productEquality,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:RngSig]. \mforall{}[fs1,fs2:basic-formal-sum(K;S)]. (-(fs1 + fs2) = (-(fs1) + -(fs2)))
Date html generated:
2018_05_22-PM-09_47_04
Last ObjectModification:
2018_01_08-AM-11_47_14
Theory : linear!algebra
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