Nuprl Lemma : C_TYPE_vs_DVALp_wf
∀env:C_TYPE_env(). ∀ctyp:C_TYPE(). (C_TYPE_vs_DVALp(env;ctyp) ∈ C_DVALUEp() ⟶ 𝔹)
Proof
Definitions occuring in Statement :
C_TYPE_vs_DVALp: C_TYPE_vs_DVALp(env;ctyp),
C_DVALUEp: C_DVALUEp(),
C_TYPE_env: C_TYPE_env(),
C_TYPE: C_TYPE(),
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
C_TYPE_vs_DVALp: C_TYPE_vs_DVALp(env;ctyp),
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
outl: outl(x),
isl: isl(x),
not: ¬A,
false: False,
bfalse: ff,
assert: ↑b,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ext-eq: A ≡ B,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
DVp_Null: DVp_Null(x),
let: let,
DVp_Struct?: DVp_Struct?(v),
pi1: fst(t),
DVp_Struct-lbls: DVp_Struct-lbls(v),
pi2: snd(t),
DVp_Struct-struct: DVp_Struct-struct(v),
DVp_Int: DVp_Int(int),
DVp_Pointer: DVp_Pointer(ptr),
DVp_Array: DVp_Array(lower;upper;arr),
DVp_Struct: DVp_Struct(lbls;struct),
has-value: (a)↓,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T,
band: p ∧b q,
iff: P ⇐⇒ Q,
l_all: (∀x∈L.P[x]),
DVp_Array?: DVp_Array?(v),
DVp_Array-upper: DVp_Array-upper(v),
DVp_Array-lower: DVp_Array-lower(v),
DVp_Array-arr: DVp_Array-arr(v),
nat: ℕ,
ge: i ≥ j
Lemmas referenced :
lelt_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
nat_properties,
add-member-int_seg1,
upto_wf,
bl-all_wf,
assert_of_eq_int,
subtract_wf,
eq_int_wf,
top_wf,
int_seg_wf,
assert-deq-member,
atom-deq_wf,
deq-member_wf,
subtype_rel_product,
pi1_wf_top,
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,
atom-value-type,
value-type-has-value,
length_wf_nat,
bdd-all_wf,
neg_assert_of_eq_atom,
it_wf,
unit_subtype_base,
atom_subtype_base,
assert_of_eq_atom,
eq_atom_wf,
C_DVALUEp-ext,
DVp_Pointer-ptr_wf,
btrue_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
btrue_neq_bfalse,
assert_elim,
equal_wf,
and_wf,
C_TYPE_eq_wf,
C_TYPE-of-LVALUE_wf,
isl_wf,
unit_wf2,
C_LVALUE_wf,
let_wf,
eqtt_to_assert,
DVp_Pointer?_wf,
nat_wf,
list_wf,
l_member_wf,
l_all_wf2,
DVp_Int?_wf,
bfalse_wf,
bool_wf,
C_DVALUEp_wf,
C_TYPE_ind_wf_simple,
C_TYPE_env_wf,
C_TYPE_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
lambdaEquality,
sqequalRule,
productEquality,
atomEquality,
spreadEquality,
setElimination,
rename,
setEquality,
because_Cache,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
unionEquality,
dependent_functionElimination,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
equalityTransitivity,
applyEquality,
independent_functionElimination,
voidElimination,
equalityEquality,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
hypothesis_subsumption,
tokenEquality,
callbyvalueReduce,
natural_numberEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll,
imageElimination
Latex:
\mforall{}env:C\_TYPE\_env(). \mforall{}ctyp:C\_TYPE(). (C\_TYPE\_vs\_DVALp(env;ctyp) \mmember{} C\_DVALUEp() {}\mrightarrow{} \mBbbB{})
Date html generated:
2016_05_16-AM-08_51_17
Last ObjectModification:
2016_01_17-AM-09_43_52
Theory : C-semantics
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