Nuprl Lemma : fps-Pascal_wf
∀[r:CRng]. ∀[x,y:Atom]. ∀[f:PowerSeries(r)]. (fps-Pascal(r;x;y;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
fps-Pascal: fps-Pascal(r;x;y;f),
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
atom: Atom,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-Pascal: fps-Pascal(r;x;y;f),
so_lambda: λ2x.t[x],
crng: CRng,
rng: Rng,
all: ∀x:A. B[x],
so_apply: x[s]
Lemmas referenced :
all_wf,
bag_wf,
equal_wf,
rng_car_wf,
fps-coeff_wf,
bag-append_wf,
single-bag_wf,
infix_ap_wf,
rng_plus_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,
hypothesis,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[x,y:Atom]. \mforall{}[f:PowerSeries(r)]. (fps-Pascal(r;x;y;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-09_58_25
Last ObjectModification:
2015_12_27-PM-04_35_27
Theory : power!series
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