Nuprl Lemma : vs-add-assoc
∀[K:RngSig]. ∀[vs:VectorSpace(K)]. ∀[x,y,z:Point(vs)]. (x + y + z = x + y + z ∈ Point(vs))
Proof
Definitions occuring in Statement :
vs-add: x + y,
vector-space: VectorSpace(K),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
vs-add: x + y,
infix_ap: x f y,
guard: {T},
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
vector-space: VectorSpace(K)
Lemmas referenced :
rng_plus_wf,
rng_times_wf,
infix_ap_wf,
rng_zero_wf,
rng_one_wf,
rng_car_wf,
equal_wf,
all_wf,
vs-point_wf,
subtype_rel_self
Rules used in proof :
axiomEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
sqequalRule,
because_Cache,
hypothesis,
hypothesisEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productElimination,
imageElimination,
baseClosed,
imageMemberEquality,
applyLambdaEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
functionExtensionality,
lambdaEquality,
productEquality,
functionEquality,
setEquality,
universeEquality,
extract_by_obid,
instantiate,
tokenEquality,
applyEquality,
dependentIntersectionEqElimination,
dependentIntersectionElimination,
dependent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[x,y,z:Point(vs)]. (x + y + z = x + y + z)
Date html generated:
2018_05_22-PM-09_40_29
Last ObjectModification:
2018_01_09-AM-10_22_05
Theory : linear!algebra
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