Nuprl Lemma : ispolyform_wf
∀[p:tree(ℤ)]. (ispolyform(p) ∈ ℤ ⟶ 𝔹)
Proof
Definitions occuring in Statement :
ispolyform: ispolyform(p),
tree: tree(E),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ispolyform: ispolyform(p),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
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,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
prop: ℙ,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
nat: ℕ,
assert: ↑b,
false: False,
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
tree_ind_wf_simple,
top_wf,
bool_wf,
tree_subtype,
btrue_wf,
subtract_wf,
eqtt_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
le_int_wf,
tree-height_wf,
nat_wf,
assert_of_le_int,
tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
functionEquality,
intEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
functionExtensionality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
setElimination,
rename,
axiomEquality
Latex:
\mforall{}[p:tree(\mBbbZ{})]. (ispolyform(p) \mmember{} \mBbbZ{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2017_10_01-AM-08_32_14
Last ObjectModification:
2017_05_02-AM-11_40_53
Theory : integer!polynomial!trees
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