Nuprl Lemma : fps-pascal_wf
∀[r:CRng]. ∀[x,y:Atom]. (Δ(x,y) ∈ PowerSeries(r))
Proof
Definitions occuring in Statement :
fps-pascal: Δ(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,
fps-pascal: Δ(x,y),
uimplies: b supposing a,
crng: CRng,
rng: Rng,
all: ∀x:A. B[x]
Lemmas referenced :
fps-div_wf,
atom-valueall-type,
atom-deq_wf,
rng_one_wf,
fps-one_wf,
fps-sub_wf,
fps-add_wf,
fps-single_wf,
single-bag_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,
setElimination,
rename,
because_Cache,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[x,y:Atom]. (\mDelta{}(x,y) \mmember{} PowerSeries(r))
Date html generated:
2016_05_15-PM-09_58_30
Last ObjectModification:
2015_12_27-PM-04_35_21
Theory : power!series
Home
Index