Nuprl Lemma : vs-subtract_wf
∀[K:RngSig]. ∀[vs:VectorSpace(K)]. ∀[x,y:Point(vs)]. ((x - y) ∈ Point(vs))
Proof
Definitions occuring in Statement :
vs-subtract: (x - y),
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
vs-subtract: (x - y),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
vector-space_wf,
vs-point_wf,
rng_one_wf,
rng_minus_wf,
vs-mul_wf,
vs-add_wf
Rules used in proof :
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[x,y:Point(vs)]. ((x - y) \mmember{} Point(vs))
Date html generated:
2018_05_22-PM-09_42_53
Last ObjectModification:
2018_01_09-PM-02_06_37
Theory : linear!algebra
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