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
Home
Index