Nuprl Lemma : poly-zero_wf
∀[p:tree(ℤ)]. (poly-zero(p) ∈ 𝔹)
Proof
Definitions occuring in Statement :
poly-zero: poly-zero(p),
tree: tree(E),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
poly-zero: poly-zero(p),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
prop: ℙ
Lemmas referenced :
tree_leaf?_wf,
bool_wf,
eqtt_to_assert,
eq_int_wf,
tree_leaf-value_wf,
equal_wf,
tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[p:tree(\mBbbZ{})]. (poly-zero(p) \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-08_32_09
Last ObjectModification:
2017_05_02-PM-01_44_33
Theory : integer!polynomial!trees
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