Nuprl Lemma : DVp_Struct_wf
∀[lbls:Atom List]. ∀[struct:{a:Atom| (a ∈ lbls)} ⟶ C_DVALUEp()]. (DVp_Struct(lbls;struct) ∈ C_DVALUEp())
Proof
Definitions occuring in Statement :
DVp_Struct: DVp_Struct(lbls;struct),
C_DVALUEp: C_DVALUEp(),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
C_DVALUEp: C_DVALUEp(),
DVp_Struct: DVp_Struct(lbls;struct),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
prop: ℙ,
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],
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,
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
Lemmas referenced :
C_DVALUEpco_size_wf,
has-value_wf-partial,
int-value-type,
set-value-type,
value-type-has-value,
nat_wf,
length_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,
int_seg_properties,
list-subtype,
select_wf,
C_DVALUEp_size_wf,
length_wf_nat,
sum-nat,
le_wf,
false_wf,
add_nat_wf,
list_wf,
int_seg_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,
set_wf,
C_DVALUEpco_wf,
C_DVALUEp_wf,
l_member_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,
setEquality,
atomEquality,
lambdaEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
setElimination,
rename,
functionEquality,
unionElimination,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
intEquality,
unionEquality,
productEquality,
voidEquality,
equalityEquality,
natural_numberEquality,
independent_pairFormation,
int_eqEquality,
isect_memberEquality,
computeAll,
imageElimination
Latex:
\mforall{}[lbls:Atom List]. \mforall{}[struct:\{a:Atom| (a \mmember{} lbls)\} {}\mrightarrow{} C\_DVALUEp()].
(DVp\_Struct(lbls;struct) \mmember{} C\_DVALUEp())
Date html generated:
2016_05_16-AM-08_49_33
Last ObjectModification:
2016_01_17-AM-09_43_06
Theory : C-semantics
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