Nuprl Lemma : vs-id-map_wf
∀[K:Rng]. ∀[vs:VectorSpace(K)]. (id ∈ vs ⟶ vs)
Proof
Definitions occuring in Statement :
vs-id-map: id,
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-id-map: id,
vs-map: A ⟶ B,
rng: Rng,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x]
Lemmas referenced :
vs-point_wf,
vs-add_wf,
vs-mul_wf,
rng_car_wf,
rng_properties,
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,
hypothesisEquality,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesis,
lambdaFormation_alt,
because_Cache,
inhabitedIsType,
independent_pairFormation,
productIsType,
functionIsType,
equalityIstype,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[K:Rng]. \mforall{}[vs:VectorSpace(K)]. (id \mmember{} vs {}\mrightarrow{} vs)
Date html generated:
2019_10_31-AM-06_27_03
Last ObjectModification:
2019_08_13-PM-01_58_18
Theory : linear!algebra
Home
Index