Nuprl Lemma : fps-add-assoc
∀[X:Type]. ∀[r:CRng]. ∀[f,g,h:PowerSeries(X;r)]. (((f+g)+h) = (f+(g+h)) ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-add: (f+g),
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
crng: CRng,
rng: Rng,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
fps-add: (f+g),
fps-coeff: f[b],
infix_ap: x f y,
ring_p: IsRing(T;plus;zero;neg;times;one),
group_p: IsGroup(T;op;id;inv),
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
crng_properties,
rng_properties,
fps-ext,
fps-add_wf,
equal_wf,
squash_wf,
true_wf,
rng_car_wf,
rng_plus_assoc,
fps-coeff_wf,
infix_ap_wf,
rng_plus_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
because_Cache,
sqequalRule,
isect_memberEquality,
axiomEquality,
cumulativity,
productElimination,
independent_isectElimination,
lambdaFormation,
equalitySymmetry,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[X:Type]. \mforall{}[r:CRng]. \mforall{}[f,g,h:PowerSeries(X;r)]. (((f+g)+h) = (f+(g+h)))
Date html generated:
2018_05_21-PM-09_55_05
Last ObjectModification:
2017_07_26-PM-06_32_36
Theory : power!series
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