Nuprl Lemma : fps-add-comm
∀[X:Type]. ∀[r:CRng]. ∀[f,g:PowerSeries(X;r)]. ((f+g) = (g+f) ∈ 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,
comm: Comm(T;op),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
fps-add: (f+g),
fps-coeff: f[b],
power-series: PowerSeries(X;r),
infix_ap: x f y
Lemmas referenced :
rng_plus_comm,
fps-ext,
fps-add_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
lambdaFormation,
sqequalRule,
applyEquality,
because_Cache,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[X:Type]. \mforall{}[r:CRng]. \mforall{}[f,g:PowerSeries(X;r)]. ((f+g) = (g+f))
Date html generated:
2016_05_15-PM-09_47_51
Last ObjectModification:
2015_12_27-PM-04_40_47
Theory : power!series
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