Nuprl Lemma : fps-alg_wf
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. (fps-alg(X;eq;r) ∈ CAlg(r)) supposing valueall-type(X)
Proof
Definitions occuring in Statement :
fps-alg: fps-alg(X;eq;r)
,
calgebra: CAlg(A)
,
deq: EqDecider(T)
,
valueall-type: valueall-type(T)
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
universe: Type
,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
and: P ∧ Q
,
crng: CRng
,
rng: Rng
,
prop: ℙ
,
calgebra: CAlg(A)
,
algebra: algebra{i:l}(A)
,
module: A-Module
,
cand: A c∧ B
,
alg_car: a.car
,
pi1: fst(t)
,
fps-alg: fps-alg(X;eq;r)
,
power-series: PowerSeries(X;r)
,
alg_act: a.act
,
pi2: snd(t)
,
alg_plus: a.plus
,
all: ∀x:A. B[x]
,
alg_times: a.times
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
rng_car: |r|
,
fps-rng: fps-rng(r)
,
rng_times: *
,
ring_p: IsRing(T;plus;zero;neg;times;one)
,
rng_plus: +r
,
rng_zero: 0
,
rng_minus: -r
,
alg_zero: a.zero
,
alg_minus: a.minus
,
rng_one: 1
,
alg_one: a.one
,
algebra_sig: algebra_sig{i:l}(A)
,
comm: Comm(T;op)
,
infix_ap: x f y
,
guard: {T}
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
implies: P
⇒ Q
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. (fps-alg(X;eq;r) \mmember{} CAlg(r)) supposing valueall-type(X)
Date html generated:
2016_05_16-AM-08_12_31
Last ObjectModification:
2015_12_28-PM-06_07_36
Theory : instances
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