Nuprl Lemma : MultiTree_ind_wf
∀[T,A:Type]. ∀[R:A ─→ MultiTree(T) ─→ ℙ]. ∀[v:MultiTree(T)]. ∀[Node:labels:{L:Atom List| 0 < ||L||}
─→ children:({a:Atom| (a ∈ labels)} ─→ MultiTree(T)\000C)
─→ (u:{a:Atom| (a ∈ labels)} ─→ {x:A| R[x;children \000Cu]} )
─→ {x:A| R[x;MTree_Node(labels;children)]} ].
∀[Leaf:val:T ─→ {x:A| R[x;MTree_Leaf(val)]} ].
(MultiTree_ind(v;
MTree_Node(labels,children)⇒ rec1.Node[labels;children;rec1];
MTree_Leaf(val)⇒ Leaf[val]) ∈ {x:A| R[x;v]} )
Proof
Definitions occuring in Statement :
MultiTree_ind: MultiTree_ind,
MTree_Leaf: MTree_Leaf(val),
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],
prop: ℙ,
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
atom: Atom,
universe: Type
Lemmas :
top_wf,
has-value_wf_base,
lifting-strict-atom_eq,
base_wf,
MultiTree_wf,
list_wf,
less_than_wf,
length_wf,
l_member_wf,
MTree_Node_wf,
MTree_Leaf_wf,
all_wf,
set_wf,
subtype_rel-equal
\mforall{}[T,A:Type]. \mforall{}[R:A {}\mrightarrow{} MultiTree(T) {}\mrightarrow{} \mBbbP{}]. \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{} \{x:A| R[x;children u]\} )
{}\mrightarrow{} \{x:A| R[x;MTree\_Node(labels;children)]\} ]. \mforall{}[Leaf:val:T {}\mrightarrow{} \{x:A| R[x;MTree\_Leaf(val)]\} ].
(MultiTree\_ind(v;
MTree\_Node(labels,children){}\mRightarrow{} rec1.Node[labels;children;rec1];
MTree\_Leaf(val){}\mRightarrow{} Leaf[val]) \mmember{} \{x:A| R[x;v]\} )
Date html generated:
2015_07_17-AM-07_46_19
Last ObjectModification:
2015_01_29-PM-04_39_16
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