Nuprl Lemma : MMTree-induction
∀[T:Type]. ∀[P:MMTree(T) ─→ ℙ].
((∀val:T. P[MMTree_Leaf(val)])
⇒ (∀forest:MMTree(T) List List. ((∀u∈forest.(∀u1∈u.P[u1])) ⇒ P[MMTree_Node(forest)]))
⇒ {∀v:MMTree(T). P[v]})
Proof
Definitions occuring in Statement :
MMTree_Node: MMTree_Node(forest),
MMTree_Leaf: MMTree_Leaf(val),
MMTree: MMTree(T),
l_all: (∀x∈L.P[x]),
list: T List,
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,
isect_wf,
le_wf,
MMTree_size_wf,
nat_wf,
less_than_wf,
MMTree-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,
sum-nat,
length_wf_nat,
sum_wf,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
non_neg_sum,
zero-le-nat,
decidable__lt,
list_wf,
MMTree_wf,
false_wf,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
sum-nat-less,
sum-nat-le,
subtract_wf,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-zero,
subtract-is-less,
lelt_wf,
uall_wf,
le_weakening,
l_all_wf2,
l_member_wf,
MMTree_Node_wf,
MMTree_Leaf_wf
\mforall{}[T:Type]. \mforall{}[P:MMTree(T) {}\mrightarrow{} \mBbbP{}].
((\mforall{}val:T. P[MMTree\_Leaf(val)])
{}\mRightarrow{} (\mforall{}forest:MMTree(T) List List. ((\mforall{}u\mmember{}forest.(\mforall{}u1\mmember{}u.P[u1])) {}\mRightarrow{} P[MMTree\_Node(forest)]))
{}\mRightarrow{} \{\mforall{}v:MMTree(T). P[v]\})
Date html generated:
2015_07_17-AM-07_47_18
Last ObjectModification:
2015_01_27-AM-09_39_43
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