Nuprl Lemma : vs-map_wf
∀[K:RngSig]. ∀[A,B:VectorSpace(K)]. (A ⟶ B ∈ Type)
Proof
Definitions occuring in Statement :
vs-map: A ⟶ B,
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
vs-map: A ⟶ B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
vector-space_wf,
vs-mul_wf,
rng_car_wf,
vs-add_wf,
equal_wf,
all_wf,
vs-point_wf
Rules used in proof :
isect_memberEquality,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
productEquality,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
functionEquality,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[A,B:VectorSpace(K)]. (A {}\mrightarrow{} B \mmember{} Type)
Date html generated:
2018_05_22-PM-09_42_45
Last ObjectModification:
2018_01_09-AM-10_48_53
Theory : linear!algebra
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