Nuprl Lemma : vs-lift_wf2
∀[K:CRng]. ∀[vs:VectorSpace(K)]. ∀[S:Type]. ∀[f:S ⟶ Point(vs)]. ∀[fs:formal-sum(K;S)]. (vs-lift(vs;f;fs) ∈ Point(vs))
Proof
Definitions occuring in Statement :
formal-sum: formal-sum(K;S),
vs-lift: vs-lift(vs;f;fs),
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
crng: CRng
Definitions unfolded in proof :
all: ∀x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
and: P ∧ Q,
quotient: x,y:A//B[x; y],
rng: Rng,
crng: CRng,
formal-sum: formal-sum(K;S),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
crng_wf,
vector-space_wf,
formal-sum_wf,
bfs-equiv_wf,
basic-formal-sum_wf,
equal-wf-base,
vs-lift-bfs-equiv,
vs-point_wf
Rules used in proof :
dependent_functionElimination,
universeEquality,
functionEquality,
cumulativity,
because_Cache,
productEquality,
independent_isectElimination,
equalitySymmetry,
equalityTransitivity,
productElimination,
pertypeElimination,
sqequalRule,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
extract_by_obid,
introduction,
pointwiseFunctionalityForEquality,
sqequalHypSubstitution,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:CRng]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[S:Type]. \mforall{}[f:S {}\mrightarrow{} Point(vs)]. \mforall{}[fs:formal-sum(K;S)].
(vs-lift(vs;f;fs) \mmember{} Point(vs))
Date html generated:
2018_05_22-PM-09_46_10
Last ObjectModification:
2018_01_09-PM-00_26_32
Theory : linear!algebra
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