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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