Nuprl Lemma : vs-map-kernel_wf
∀[K:RngSig]. ∀[B:VectorSpace(K)]. ∀[T:Type]. ∀[f:T ⟶ Point(B)]. ∀[a:T]. (a ∈ Ker(f) ∈ ℙ)
Proof
Definitions occuring in Statement :
vs-map-kernel: a ∈ Ker(f),
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
vs-map-kernel: a ∈ Ker(f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
vector-space_wf,
vs-0_wf,
vs-point_wf,
equal_wf
Rules used in proof :
dependent_functionElimination,
universeEquality,
functionEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
functionExtensionality,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[B:VectorSpace(K)]. \mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} Point(B)]. \mforall{}[a:T]. (a \mmember{} Ker(f) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-09_43_05
Last ObjectModification:
2018_01_09-PM-01_38_47
Theory : linear!algebra
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