Nuprl Lemma : vs-add-comm-nu
∀K:RngSig. ∀vs:VectorSpace(K). ∀x,y:Point(vs). (x + y = y + x ∈ Point(vs))
Proof
Definitions occuring in Statement :
vs-add: x + y,
vector-space: VectorSpace(K),
vs-point: Point(vs),
all: ∀x:A. B[x],
equal: s = t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
vector-space: VectorSpace(K),
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
guard: {T},
infix_ap: x f y,
vs-add: x + y,
squash: ↓T,
true: True,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
subtype_rel_self,
vs-point_wf,
all_wf,
equal_wf,
rng_car_wf,
rng_one_wf,
rng_zero_wf,
infix_ap_wf,
rng_times_wf,
rng_plus_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesisEquality,
hypothesis,
because_Cache,
sqequalHypSubstitution,
dependentIntersectionElimination,
sqequalRule,
dependentIntersectionEqElimination,
thin,
applyEquality,
tokenEquality,
instantiate,
introduction,
extract_by_obid,
isectElimination,
universeEquality,
setEquality,
functionEquality,
productEquality,
lambdaEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
dependent_functionElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}K:RngSig. \mforall{}vs:VectorSpace(K). \mforall{}x,y:Point(vs). (x + y = y + x)
Date html generated:
2018_05_22-PM-09_40_25
Last ObjectModification:
2018_05_20-PM-10_41_27
Theory : linear!algebra
Home
Index