Nuprl Lemma : poly-zero-val
∀[p:tree(ℤ)]. ∀[l:Top]. (p@l = 0 ∈ ℤ) supposing ↑poly-zero(p)
Proof
Definitions occuring in Statement :
poly-int-val: p@l,
poly-zero: poly-zero(p),
tree: tree(E),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
tree_leaf: tree_leaf(value),
poly-zero: poly-zero(p),
tree_leaf?: tree_leaf?(v),
pi1: fst(t),
tree_leaf-value: tree_leaf-value(v),
pi2: snd(t),
band: p ∧b q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
tree_node: tree_node(left;right),
polyconst: polyconst(k),
top: Top
Lemmas referenced :
top_wf,
assert_wf,
poly-zero_wf,
tree_wf,
tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
polyconst_val_lemma,
assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
applyEquality,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
voidElimination,
voidEquality,
natural_numberEquality
Latex:
\mforall{}[p:tree(\mBbbZ{})]. \mforall{}[l:Top]. (p@l = 0) supposing \muparrow{}poly-zero(p)
Date html generated:
2017_10_01-AM-08_32_36
Last ObjectModification:
2017_05_02-PM-04_02_27
Theory : integer!polynomial!trees
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