### Nuprl Lemma : fps-slice_wf

`∀[X:Type]. ∀[r:CRng]. ∀[n:ℤ]. ∀[f:PowerSeries(X;r)].  ([f]_n ∈ PowerSeries(X;r))`

Proof

Definitions occuring in Statement :  fps-slice: `[f]_n` power-series: `PowerSeries(X;r)` uall: `∀[x:A]. B[x]` member: `t ∈ T` int: `ℤ` universe: `Type` crng: `CRng`
Definitions unfolded in proof :  power-series: `PowerSeries(X;r)` uall: `∀[x:A]. B[x]` member: `t ∈ T` fps-slice: `[f]_n` subtype_rel: `A ⊆r B` nat: `ℕ` crng: `CRng` rng: `Rng`
Lemmas referenced :  ifthenelse_wf eq_int_wf bag-size_wf nat_wf rng_car_wf rng_zero_wf bag_wf crng_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis applyEquality setElimination rename axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache intEquality universeEquality

Latex:
\mforall{}[X:Type].  \mforall{}[r:CRng].  \mforall{}[n:\mBbbZ{}].  \mforall{}[f:PowerSeries(X;r)].    ([f]\_n  \mmember{}  PowerSeries(X;r))

Date html generated: 2016_05_15-PM-09_49_13
Last ObjectModification: 2015_12_27-PM-04_40_39

Theory : power!series

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