Nuprl Lemma : DVp_Array_wf
∀[lower,upper:ℤ]. ∀[arr:{lower..upper-} ⟶ C_DVALUEp()]. (DVp_Array(lower;upper;arr) ∈ C_DVALUEp())
Proof
Definitions occuring in Statement :
DVp_Array: DVp_Array(lower;upper;arr),
C_DVALUEp: C_DVALUEp(),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
C_DVALUEp: C_DVALUEp(),
DVp_Array: DVp_Array(lower;upper;arr),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
ext-eq: A ≡ B,
C_DVALUEpco_size: C_DVALUEpco_size(p),
pi1: fst(t),
pi2: snd(t),
C_DVALUEp_size: C_DVALUEp_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
C_DVALUEpco_size_wf,
has-value_wf-partial,
int-value-type,
set-value-type,
value-type-has-value,
nat_wf,
ifthenelse_wf,
int_formula_prop_less_lemma,
intformless_wf,
assert_of_bnot,
iff_weakening_uiff,
not_wf,
bnot_wf,
assert_wf,
iff_transitivity,
lelt_wf,
add-member-int_seg1,
C_DVALUEp_size_wf,
bool_cases,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__le,
assert_of_le_int,
le_int_wf,
sum-nat,
le_wf,
false_wf,
add_nat_wf,
l_member_wf,
list_wf,
C_LVALUE_wf,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
unit_wf2,
assert_of_eq_atom,
eqtt_to_assert,
bool_wf,
eq_atom_wf,
C_DVALUEpco_wf,
C_DVALUEp_wf,
int_seg_wf,
subtype_rel_dep_function,
C_DVALUEpco-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality,
tokenEquality,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
setElimination,
rename,
functionEquality,
productEquality,
intEquality,
unionElimination,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
unionEquality,
atomEquality,
setEquality,
voidEquality,
equalityEquality,
natural_numberEquality,
independent_pairFormation,
int_eqEquality,
isect_memberEquality,
computeAll,
impliesFunctionality
Latex:
\mforall{}[lower,upper:\mBbbZ{}]. \mforall{}[arr:\{lower..upper\msupminus{}\} {}\mrightarrow{} C\_DVALUEp()]. (DVp\_Array(lower;upper;arr) \mmember{} C\_DVALUEp())
Date html generated:
2016_05_16-AM-08_49_27
Last ObjectModification:
2016_01_17-AM-09_42_55
Theory : C-semantics
Home
Index