Nuprl Lemma : Pascal-completion_wf
∀[r:CRng]. ∀[f,g:PowerSeries(r)]. ∀[x,y:Atom]. (Pascal-completion(r;f;g;x;y) ∈ PowerSeries(r))
Proof
Definitions occuring in Statement :
Pascal-completion: Pascal-completion(r;f;g;x;y),
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Pascal-completion: Pascal-completion(r;f;g;x;y),
uimplies: b supposing a
Lemmas referenced :
fps-mul_wf,
atom-valueall-type,
atom-deq_wf,
fps-sub_wf,
fps-add_wf,
fps-one_wf,
fps-atom_wf,
fps-elim-x_wf,
fps-pascal_wf,
power-series_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[f,g:PowerSeries(r)]. \mforall{}[x,y:Atom]. (Pascal-completion(r;f;g;x;y) \mmember{} PowerSeries(r))
Date html generated:
2016_05_15-PM-09_59_09
Last ObjectModification:
2015_12_27-PM-04_35_09
Theory : power!series
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