Nuprl Lemma : MultiTree_ind_wf_simple
∀[T,A:Type]. ∀[v:MultiTree(T)]. ∀[Node:labels:{L:Atom List| 0 < ||L||}
─→ children:({a:Atom| (a ∈ labels)} ─→ MultiTree(T))
─→ (u:{a:Atom| (a ∈ labels)} ─→ A)
─→ A]. ∀[Leaf:val:T ─→ A].
(MultiTree_ind(v;
MTree_Node(labels,children)⇒ rec1.Node[labels;children;rec1];
MTree_Leaf(val)⇒ Leaf[val]) ∈ A)
Proof
Definitions occuring in Statement :
MultiTree_ind: MultiTree_ind,
MultiTree: MultiTree(T),
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
natural_number: $n,
atom: Atom,
universe: Type
Lemmas :
MultiTree_ind_wf,
true_wf,
MultiTree_wf,
subtype_rel_dep_function,
less_than_wf,
length_wf,
l_member_wf,
set_wf,
list_wf
\mforall{}[T,A:Type]. \mforall{}[v:MultiTree(T)]. \mforall{}[Node:labels:\{L:Atom List| 0 < ||L||\}
{}\mrightarrow{} children:(\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} MultiTree(T))
{}\mrightarrow{} (u:\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} A)
{}\mrightarrow{} A]. \mforall{}[Leaf:val:T {}\mrightarrow{} A].
(MultiTree\_ind(v;
MTree\_Node(labels,children){}\mRightarrow{} rec1.Node[labels;children;rec1];
MTree\_Leaf(val){}\mRightarrow{} Leaf[val]) \mmember{} A)
Date html generated:
2015_07_17-AM-07_46_21
Last ObjectModification:
2015_01_27-AM-09_45_05
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