Nuprl Lemma : poly-int_wf
∀[p:tree(ℤ)]. (poly-int(p) ∈ 𝔹)
Proof
Definitions occuring in Statement :
poly-int: poly-int(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],
poly-int: poly-int(p),
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
tree_ind_wf_simple,
bool_wf,
btrue_wf,
istype-int,
eqtt_to_assert,
poly-zero_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bfalse_wf,
tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
equalityIsType1,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
because_Cache,
voidElimination,
universeIsType
Latex:
\mforall{}[p:tree(\mBbbZ{})]. (poly-int(p) \mmember{} \mBbbB{})
Date html generated:
2019_10_15-AM-10_52_12
Last ObjectModification:
2018_10_11-PM-06_52_03
Theory : integer!polynomial!trees
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