Nuprl Lemma : vs-map-image_wf
∀[K:RngSig]. ∀[A,B:VectorSpace(K)]. ∀[f:A ⟶ B]. ∀[b:Point(B)]. (b ∈ Img(f) ∈ ℙ)
Proof
Definitions occuring in Statement :
vs-map-image: b ∈ Img(f),
vs-map: A ⟶ B,
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vs-map-image: b ∈ Img(f),
prop: ℙ,
exists: ∃x:A. B[x],
vs-map: A ⟶ B,
all: ∀x:A. B[x]
Lemmas referenced :
vs-point_wf,
equal_wf,
vs-map_wf,
vector-space_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
dependent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[A,B:VectorSpace(K)]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[b:Point(B)]. (b \mmember{} Img(f) \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-06_27_20
Last ObjectModification:
2019_08_12-PM-00_40_20
Theory : linear!algebra
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