Nuprl Lemma : C_TYPE-induction
∀[P:C_TYPE() ─→ ℙ]
(P[C_Void()]
⇒ P[C_Int()]
⇒ (∀fields:(Atom × C_TYPE()) List. ((∀u∈fields.let u1,u2 = u in P[u2]) ⇒ P[C_Struct(fields)]))
⇒ (∀length:ℕ. ∀elems:C_TYPE(). (P[elems] ⇒ P[C_Array(length;elems)]))
⇒ (∀to:C_TYPE(). (P[to] ⇒ P[C_Pointer(to)]))
⇒ {∀v:C_TYPE(). P[v]})
Proof
Definitions occuring in Statement :
C_Pointer: C_Pointer(to),
C_Array: C_Array(length;elems),
C_Struct: C_Struct(fields),
C_Int: C_Int(),
C_Void: C_Void(),
C_TYPE: C_TYPE(),
l_all: (∀x∈L.P[x]),
list: T List,
nat: ℕ,
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],
spread: spread def,
product: x:A × B[x],
atom: Atom
Lemmas :
uniform-comp-nat-induction,
all_wf,
isect_wf,
le_wf,
C_TYPE_size_wf,
less_than_wf,
C_TYPE-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,
stuck-spread,
base_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
sum-nat,
length_wf_nat,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
decidable__lt,
sum_wf,
C_TYPE_wf,
nat_wf,
false_wf,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
sum-nat-less,
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,
C_Pointer_wf,
C_Array_wf,
list_wf,
l_all_wf2,
l_member_wf,
C_Struct_wf,
C_Int_wf,
C_Void_wf
\mforall{}[P:C\_TYPE() {}\mrightarrow{} \mBbbP{}]
(P[C\_Void()]
{}\mRightarrow{} P[C\_Int()]
{}\mRightarrow{} (\mforall{}fields:(Atom \mtimes{} C\_TYPE()) List. ((\mforall{}u\mmember{}fields.let u1,u2 = u in P[u2]) {}\mRightarrow{} P[C\_Struct(fields)]))
{}\mRightarrow{} (\mforall{}length:\mBbbN{}. \mforall{}elems:C\_TYPE(). (P[elems] {}\mRightarrow{} P[C\_Array(length;elems)]))
{}\mRightarrow{} (\mforall{}to:C\_TYPE(). (P[to] {}\mRightarrow{} P[C\_Pointer(to)]))
{}\mRightarrow{} \{\mforall{}v:C\_TYPE(). P[v]\})
Date html generated:
2015_07_17-AM-07_42_25
Last ObjectModification:
2015_01_29-PM-04_40_26
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