Nuprl Lemma : isPolyOne_wf
∀[p:iPolynomial()]. (isPolyOne(p) ∈ 𝔹)
Proof
Definitions occuring in Statement :
isPolyOne: isPolyOne(p),
iPolynomial: iPolynomial(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
isPolyOne: isPolyOne(p),
iPolynomial: iPolynomial(),
all: ∀x:A. B[x],
or: P ∨ Q,
nil: [],
it: ⋅,
cons: [a / b],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
iPolynomial_wf,
iMonomial_wf,
list-cases,
bfalse_wf,
product_subtype_list,
spread_cons_lemma,
band_wf,
null_wf,
isMonomialOne_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
setElimination,
thin,
rename,
isectElimination,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[p:iPolynomial()]. (isPolyOne(p) \mmember{} \mBbbB{})
Date html generated:
2017_09_29-PM-05_52_12
Last ObjectModification:
2017_05_03-AM-11_31_13
Theory : omega
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