Nuprl Lemma : MultiTree-ext
∀[T:Type]
MultiTree(T) ≡ lbl:Atom × if lbl =a "Node" then labels:{L:Atom List| 0 < ||L||} × ({a:Atom| (a ∈ labels)} ─→ MultiTr\000Cee(T))
if lbl =a "Leaf" then T
else Void
fi
Proof
Definitions occuring in Statement :
MultiTree: MultiTree(T),
l_member: (x ∈ l),
length: ||as||,
list: T List,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
ext-eq: A ≡ B,
less_than: a < b,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
product: x:A × B[x],
natural_number: $n,
token: "$token",
atom: Atom,
void: Void,
universe: Type
Lemmas :
MultiTreeco-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
value-type-has-value,
int-value-type,
less_than_wf,
length_wf,
equal-wf-base-T,
select_wf,
sq_stable__le,
l_member_wf,
sum-partial-has-value,
length_wf_nat,
MultiTreeco_size_wf,
list-subtype,
int_seg_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
MultiTree_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
list_wf,
subtype_rel_dep_function,
MultiTreeco_wf,
set_wf,
add-nat,
false_wf,
sum-nat,
MultiTree_size_wf,
nat_properties,
lelt_wf,
and_wf,
squash_wf,
value-type_wf,
partial_wf
\mforall{}[T:Type]
MultiTree(T) \mequiv{} lbl:Atom \mtimes{} if lbl =a "Node"
then labels:\{L:Atom List| 0 < ||L||\}
\mtimes{} (\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} MultiTree(T))
if lbl =a "Leaf" then T
else Void
fi
Date html generated:
2015_07_17-AM-07_45_48
Last ObjectModification:
2015_01_29-PM-04_39_14
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