Nuprl Lemma : l_tree_ind_wf_simple
∀[L,T,A:Type]. ∀[v:l_tree(L;T)]. ∀[leaf:val:L ─→ A]. ∀[node:val:T
─→ left_subtree:l_tree(L;T)
─→ right_subtree:l_tree(L;T)
─→ A
─→ A
─→ A].
(l_tree_ind(v;
l_tree_leaf(val)⇒ leaf[val];
l_tree_node(val,left_subtree,right_subtree)⇒ rec1,rec2.node[val;left_subtree;right_subtree;rec1;rec2])
∈ A)
Proof
Definitions occuring in Statement :
l_tree_ind: l_tree_ind,
l_tree: l_tree(L;T),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4;s5],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
l_tree_ind_wf,
true_wf,
l_tree_wf,
subtype_rel_dep_function,
set_wf
\mforall{}[L,T,A:Type]. \mforall{}[v:l\_tree(L;T)]. \mforall{}[leaf:val:L {}\mrightarrow{} A]. \mforall{}[node:val:T
{}\mrightarrow{} left$_{subtree}$:\000Cl\_tree(L;T)
{}\mrightarrow{} right$_{subtree}$\000C:l\_tree(L;T)
{}\mrightarrow{} A
{}\mrightarrow{} A
{}\mrightarrow{} A].
(l\_tree\_ind(v;
l\_tree\_leaf(val){}\mRightarrow{} leaf[val];
l\_tree\_node(val,left$_{subtree}$,right$_{subtree}\mbackslash{}\000Cff24){}\mRightarrow{} rec1,rec2.node[val;...;...;rec1;rec2])
\mmember{} A)
Date html generated:
2015_07_17-AM-07_41_42
Last ObjectModification:
2015_01_27-AM-09_31_08
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