Nuprl Lemma : null-formal-sum_wf
∀[K:RngSig]. ∀[S:Type]. ∀[fs:basic-formal-sum(K;S)]. (null-formal-sum(K;S;fs) ∈ ℙ)
Proof
Definitions occuring in Statement :
null-formal-sum: null-formal-sum(K;S;fs),
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
so_apply: x[s],
subtype_rel: A ⊆r B,
basic-formal-sum: basic-formal-sum(K;S),
so_lambda: λ2x.t[x],
null-formal-sum: null-formal-sum(K;S;fs),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
basic-formal-sum_wf,
neg-bfs_wf,
bag-append_wf,
equal_wf,
rng_car_wf,
bag_wf,
exists_wf
Rules used in proof :
universeEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
applyEquality,
lambdaEquality,
cumulativity,
hypothesis,
hypothesisEquality,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. \mforall{}[fs:basic-formal-sum(K;S)]. (null-formal-sum(K;S;fs) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-09_47_09
Last ObjectModification:
2018_01_08-AM-11_44_59
Theory : linear!algebra
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