Nuprl Lemma : fps-pascal-symmetry
∀[r:CRng]. ∀[x,y:Atom]. (Δ(x,y) = Δ(y,x) ∈ PowerSeries(r))
Proof
Definitions occuring in Statement :
fps-pascal: Δ(x,y),
power-series: PowerSeries(X;r),
uall: ∀[x:A]. B[x],
atom: Atom,
equal: s = t ∈ T,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-pascal: Δ(x,y),
squash: ↓T,
uimplies: b supposing a,
prop: ℙ,
crng: CRng,
rng: Rng,
all: ∀x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
fps-div_wf,
squash_wf,
valueall-type_wf,
power-series_wf,
rng_car_wf,
crng_wf,
deq_wf,
atom-deq_wf,
rng_one_wf,
fps-one_wf,
equal_wf,
true_wf,
fps-sub_wf,
fps-add-comm,
fps-single_wf,
single-bag_wf,
fps-add_wf,
iff_weakening_equal,
atom-valueall-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
equalityTransitivity,
equalitySymmetry,
cumulativity,
setElimination,
rename,
universeEquality,
because_Cache,
atomEquality,
dependent_functionElimination,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[x,y:Atom]. (\mDelta{}(x,y) = \mDelta{}(y,x))
Date html generated:
2018_05_21-PM-10_12_03
Last ObjectModification:
2017_07_26-PM-06_34_54
Theory : power!series
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