Nuprl Lemma : C_TYPE-ext
C_TYPE() ≡ lbl:Atom × if lbl =a "Void" then Unit
if lbl =a "Int" then Unit
if lbl =a "Struct" then (Atom × C_TYPE()) List
if lbl =a "Array" then length:ℕ × C_TYPE()
if lbl =a "Pointer" then C_TYPE()
else Void
fi
Proof
Definitions occuring in Statement :
C_TYPE: C_TYPE(),
list: T List,
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
ext-eq: A ≡ B,
unit: Unit,
product: x:A × B[x],
token: "$token",
atom: Atom,
void: Void
Definitions unfolded in proof :
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
C_TYPE: C_TYPE(),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
C_TYPEco_size: C_TYPEco_size(p),
has-value: (a)↓,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
nequal: a ≠ b ∈ T ,
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
pi2: snd(t),
C_TYPE_size: C_TYPE_size(p),
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
nat_properties,
C_TYPE_size_wf,
sum-nat,
false_wf,
add-nat,
subtype_rel_product,
subtype_rel_list,
list_wf,
unit_wf2,
ifthenelse_wf,
C_TYPE_wf,
base_wf,
value-type-has-value,
int_subtype_base,
set_subtype_base,
subtype_partial_sqtype_base,
sum-partial-nat,
int_seg_wf,
pi2_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
length_wf,
int_seg_properties,
select_wf,
length_wf_nat,
sum-partial-has-value,
C_TYPEco_size_wf,
int-value-type,
le_wf,
set-value-type,
nat_wf,
has-value_wf-partial,
C_TYPEco_wf,
list-prod-set-type,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
it_wf,
unit_subtype_base,
atom_subtype_base,
subtype_base_sq,
assert_of_eq_atom,
eqtt_to_assert,
bool_wf,
eq_atom_wf,
C_TYPEco-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
hypothesis,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesisEquality,
applyEquality,
sqequalRule,
dependent_pairEquality,
isectElimination,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
because_Cache,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
voidElimination,
intEquality,
natural_numberEquality,
productEquality,
int_eqEquality,
isect_memberEquality,
voidEquality,
computeAll,
imageElimination,
equalityEquality,
callbyvalueAdd,
baseClosed,
dependent_set_memberEquality,
baseApply,
closedConclusion,
universeEquality,
sqleReflexivity
Latex:
C\_TYPE() \mequiv{} lbl:Atom \mtimes{} if lbl =a "Void" then Unit
if lbl =a "Int" then Unit
if lbl =a "Struct" then (Atom \mtimes{} C\_TYPE()) List
if lbl =a "Array" then length:\mBbbN{} \mtimes{} C\_TYPE()
if lbl =a "Pointer" then C\_TYPE()
else Void
fi
Date html generated:
2016_05_16-AM-08_44_31
Last ObjectModification:
2016_01_17-AM-09_44_00
Theory : C-semantics
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