Nuprl Lemma : vs-0-map_wf
∀[K:Rng]. ∀[vs,ws:VectorSpace(K)]. (0 ∈ ws ⟶ vs)
Proof
Definitions occuring in Statement :
vs-0-map: 0,
vs-map: A ⟶ B,
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vs-0-map: 0,
vs-map: A ⟶ B,
rng: Rng,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x]
Lemmas referenced :
vs-0_wf,
vs-point_wf,
vs-zero-add,
vs-zero-mul,
rng_car_wf,
vs-add_wf,
rng_properties,
vs-mul_wf,
vector-space_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
universeIsType,
lambdaFormation_alt,
equalitySymmetry,
inhabitedIsType,
independent_pairFormation,
productIsType,
functionIsType,
equalityIstype,
applyEquality,
axiomEquality,
equalityTransitivity,
isect_memberEquality_alt,
isectIsTypeImplies,
dependent_functionElimination
Latex:
\mforall{}[K:Rng]. \mforall{}[vs,ws:VectorSpace(K)]. (0 \mmember{} ws {}\mrightarrow{} vs)
Date html generated:
2019_10_31-AM-06_26_57
Last ObjectModification:
2019_08_12-AM-10_55_01
Theory : linear!algebra
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