Nuprl Lemma : C_DVALUEp-induction
∀[P:C_DVALUEp() ─→ ℙ]
((∀x:Unit. P[DVp_Null(x)])
⇒ (∀int:ℤ. P[DVp_Int(int)])
⇒ (∀ptr:C_LVALUE()?. P[DVp_Pointer(ptr)])
⇒ (∀lower,upper:ℤ. ∀arr:{lower..upper-} ─→ C_DVALUEp().
((∀u:{lower..upper-}. P[arr u]) ⇒ P[DVp_Array(lower;upper;arr)]))
⇒ (∀lbls:Atom List. ∀struct:{a:Atom| (a ∈ lbls)} ─→ C_DVALUEp().
((∀u:{a:Atom| (a ∈ lbls)} . P[struct u]) ⇒ P[DVp_Struct(lbls;struct)]))
⇒ {∀v:C_DVALUEp(). P[v]})
Proof
Definitions occuring in Statement :
DVp_Struct: DVp_Struct(lbls;struct),
DVp_Array: DVp_Array(lower;upper;arr),
DVp_Pointer: DVp_Pointer(ptr),
DVp_Int: DVp_Int(int),
DVp_Null: DVp_Null(x),
C_DVALUEp: C_DVALUEp(),
C_LVALUE: C_LVALUE(),
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
unit: Unit,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
union: left + right,
int: ℤ,
atom: Atom
Lemmas :
uniform-comp-nat-induction,
all_wf,
C_DVALUEp_wf,
isect_wf,
le_wf,
C_DVALUEp_size_wf,
nat_wf,
less_than_wf,
C_DVALUEp-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,
sum-nat,
le_int_wf,
assert_of_le_int,
subtract_wf,
zero-le-nat,
false_wf,
bool_cases,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
less_than_transitivity1,
less_than_irreflexivity,
lelt_wf,
int_seg_wf,
decidable__lt,
condition-implies-le,
sum_wf,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
decidable__le,
not-le-2,
less-iff-le,
zero-add,
minus-minus,
add-associates,
add-zero,
subtract-is-less,
sum-nat-less,
trivial-int-eq1,
length_wf_nat,
select_wf,
l_member_wf,
list-subtype,
sq_stable__le,
length_wf,
nat_properties,
set_wf,
uall_wf,
le_weakening,
list_wf,
DVp_Struct_wf,
DVp_Array_wf,
C_LVALUE_wf,
DVp_Pointer_wf,
DVp_Int_wf,
DVp_Null_wf,
and_wf
\mforall{}[P:C\_DVALUEp() {}\mrightarrow{} \mBbbP{}]
((\mforall{}x:Unit. P[DVp\_Null(x)])
{}\mRightarrow{} (\mforall{}int:\mBbbZ{}. P[DVp\_Int(int)])
{}\mRightarrow{} (\mforall{}ptr:C\_LVALUE()?. P[DVp\_Pointer(ptr)])
{}\mRightarrow{} (\mforall{}lower,upper:\mBbbZ{}. \mforall{}arr:\{lower..upper\msupminus{}\} {}\mrightarrow{} C\_DVALUEp().
((\mforall{}u:\{lower..upper\msupminus{}\}. P[arr u]) {}\mRightarrow{} P[DVp\_Array(lower;upper;arr)]))
{}\mRightarrow{} (\mforall{}lbls:Atom List. \mforall{}struct:\{a:Atom| (a \mmember{} lbls)\} {}\mrightarrow{} C\_DVALUEp().
((\mforall{}u:\{a:Atom| (a \mmember{} lbls)\} . P[struct u]) {}\mRightarrow{} P[DVp\_Struct(lbls;struct)]))
{}\mRightarrow{} \{\mforall{}v:C\_DVALUEp(). P[v]\})
Date html generated:
2015_07_17-AM-07_44_57
Last ObjectModification:
2015_01_27-AM-09_47_34
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