Nuprl Lemma : l_tree-induction
∀[L,T:Type]. ∀[P:l_tree(L;T) ─→ ℙ].
((∀val:L. P[l_tree_leaf(val)])
⇒ (∀val:T. ∀left_subtree,right_subtree:l_tree(L;T).
(P[left_subtree] ⇒ P[right_subtree] ⇒ P[l_tree_node(val;left_subtree;right_subtree)]))
⇒ {∀v:l_tree(L;T). P[v]})
Proof
Definitions occuring in Statement :
l_tree_node: l_tree_node(val;left_subtree;right_subtree),
l_tree_leaf: l_tree_leaf(val),
l_tree: l_tree(L;T),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
uniform-comp-nat-induction,
all_wf,
l_tree_wf,
isect_wf,
le_wf,
l_tree_size_wf,
nat_wf,
less_than_wf,
l_tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtract-is-less,
lelt_wf,
uall_wf,
int_seg_wf,
le_weakening,
l_tree_node_wf,
l_tree_leaf_wf
\mforall{}[L,T:Type]. \mforall{}[P:l\_tree(L;T) {}\mrightarrow{} \mBbbP{}].
((\mforall{}val:L. P[l\_tree\_leaf(val)])
{}\mRightarrow{} (\mforall{}val:T. \mforall{}left$_{subtree}$,right$_{subtree}$:l\_tree(L;T\000C).
(P[left$_{subtree}$] {}\mRightarrow{} P[right$_{subtree}$] {}\mRightarrow{} P[l\_\000Ctree\_node(val;left$_{subtree}$;right$_{subtree}$)]))
{}\mRightarrow{} \{\mforall{}v:l\_tree(L;T). P[v]\})
Date html generated:
2015_07_17-AM-07_41_39
Last ObjectModification:
2015_01_27-AM-09_31_15
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