Nuprl Lemma : MTree_Node_wf
∀[T:Type]. ∀[labels:{L:Atom List| 0 < ||L||} ]. ∀[children:{a:Atom| (a ∈ labels)} ─→ MultiTree(T)].
(MTree_Node(labels;children) ∈ MultiTree(T))
Proof
Definitions occuring in Statement :
MTree_Node: MTree_Node(labels;children),
MultiTree: MultiTree(T),
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
natural_number: $n,
atom: Atom,
universe: Type
Lemmas :
MultiTreeco-ext,
less_than_wf,
length_wf,
subtype_rel_dep_function,
l_member_wf,
MultiTree_wf,
MultiTreeco_wf,
set_wf,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
add_nat_wf,
false_wf,
le_wf,
sum-nat,
length_wf_nat,
MultiTree_size_wf,
select_wf,
list-subtype,
sq_stable__le,
int_seg_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
has-value_wf-partial,
MultiTreeco_size_wf,
list_wf
\mforall{}[T:Type]. \mforall{}[labels:\{L:Atom List| 0 < ||L||\} ]. \mforall{}[children:\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} MultiTree(T)].
(MTree\_Node(labels;children) \mmember{} MultiTree(T))
Date html generated:
2015_07_17-AM-07_45_50
Last ObjectModification:
2015_01_27-AM-09_45_11
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