Nuprl Lemma : binary_map-induction
∀[T,Key:Type]. ∀[P:binary_map(T;Key) ─→ ℙ].
(P[bm_E()]
⇒ (∀key:Key. ∀value:T. ∀cnt:ℤ. ∀left,right:binary_map(T;Key).
(P[left] ⇒ P[right] ⇒ P[bm_T(key;value;cnt;left;right)]))
⇒ {∀v:binary_map(T;Key). P[v]})
Proof
Definitions occuring in Statement :
bm_T: bm_T(key;value;cnt;left;right),
bm_E: bm_E(),
binary_map: binary_map(T;Key),
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,
universe: Type
Lemmas :
uniform-comp-nat-induction,
all_wf,
binary_map_wf,
isect_wf,
le_wf,
binary_map_size_wf,
nat_wf,
less_than_wf,
binary_map-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
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,
bm_T_wf,
bm_E_wf
\mforall{}[T,Key:Type]. \mforall{}[P:binary\_map(T;Key) {}\mrightarrow{} \mBbbP{}].
(P[bm\_E()]
{}\mRightarrow{} (\mforall{}key:Key. \mforall{}value:T. \mforall{}cnt:\mBbbZ{}. \mforall{}left,right:binary\_map(T;Key).
(P[left] {}\mRightarrow{} P[right] {}\mRightarrow{} P[bm\_T(key;value;cnt;left;right)]))
{}\mRightarrow{} \{\mforall{}v:binary\_map(T;Key). P[v]\})
Date html generated:
2015_07_17-AM-08_17_53
Last ObjectModification:
2015_01_27-PM-00_40_26
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