Nuprl Lemma : vs-iso_wf
∀[K:RngSig]. ∀[A,B:VectorSpace(K)]. (A ≅ B ∈ ℙ)
Proof
Definitions occuring in Statement :
vs-iso: A ≅ B,
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_apply: x[s],
vs-map: A ⟶ B,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
vs-iso: A ≅ B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
vector-space_wf,
equal_wf,
vs-point_wf,
all_wf,
vs-map_wf,
exists_wf
Rules used in proof :
isect_memberEquality,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
applyEquality,
productEquality,
because_Cache,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[A,B:VectorSpace(K)]. (A \mcong{} B \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-09_43_17
Last ObjectModification:
2018_01_09-AM-10_50_41
Theory : linear!algebra
Home
Index