Nuprl Lemma : polyalg_poly_wf
∀S:DSet. ∀A:CRng. ∀p:polynom_alg{i:l}(S;A). (p.poly ∈ FMonAlg(p.mo.mon;A))
Proof
Definitions occuring in Statement :
polyalg_poly: p.poly,
polyalg_mo: p.mo,
polynom_alg: polynom_alg{i:l}(S;A),
fmonalg: FMonAlg(g;a),
free_abmon_mon: f.mon,
all: ∀x:A. B[x],
member: t ∈ T,
crng: CRng,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
polynom_alg: polynom_alg{i:l}(S;A),
polyalg_poly: p.poly,
polyalg_mo: p.mo,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
polynom_alg_wf,
crng_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
lemma_by_obid,
dependent_functionElimination
Latex:
\mforall{}S:DSet. \mforall{}A:CRng. \mforall{}p:polynom\_alg\{i:l\}(S;A). (p.poly \mmember{} FMonAlg(p.mo.mon;A))
Date html generated:
2016_05_16-AM-08_14_37
Last ObjectModification:
2015_12_28-PM-06_09_16
Theory : polynom_1
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