Nuprl Lemma : binary-tree-induction
∀[P:binary-tree() ─→ ℙ]
((∀val:ℤ. P[btr_Leaf(val)])
⇒ (∀left,right:binary-tree(). (P[left] ⇒ P[right] ⇒ P[btr_Node(left;right)]))
⇒ {∀v:binary-tree(). P[v]})
Proof
Definitions occuring in Statement :
btr_Node: btr_Node(left;right),
btr_Leaf: btr_Leaf(val),
binary-tree: binary-tree(),
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],
int: ℤ
Lemmas :
uniform-comp-nat-induction,
all_wf,
isect_wf,
le_wf,
binary-tree_size_wf,
nat_wf,
less_than_wf,
binary-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,
binary-tree_wf,
btr_Node_wf,
btr_Leaf_wf
\mforall{}[P:binary-tree() {}\mrightarrow{} \mBbbP{}]
((\mforall{}val:\mBbbZ{}. P[btr\_Leaf(val)])
{}\mRightarrow{} (\mforall{}left,right:binary-tree(). (P[left] {}\mRightarrow{} P[right] {}\mRightarrow{} P[btr\_Node(left;right)]))
{}\mRightarrow{} \{\mforall{}v:binary-tree(). P[v]\})
Date html generated:
2015_07_17-AM-07_52_17
Last ObjectModification:
2015_01_27-AM-09_35_51
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