Nuprl Lemma : neg-bfs_wf
∀[S:Type]. ∀[K:RngSig]. ∀[fs:basic-formal-sum(K;S)]. (-(fs) ∈ 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],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
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,
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,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:RngSig]. \mforall{}[fs:basic-formal-sum(K;S)]. (-(fs) \mmember{} basic-formal-sum(K;S))
Date html generated:
2018_05_22-PM-09_47_01
Last ObjectModification:
2018_01_08-AM-11_44_22
Theory : linear!algebra
Home
Index