Nuprl Lemma : C_TYPE-valueall-type
valueall-type(C_TYPE())
Proof
Definitions occuring in Statement :
C_TYPE: C_TYPE(),
valueall-type: valueall-type(T)
Definitions unfolded in proof :
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
C_Void: C_Void(),
C_TYPE_size: C_TYPE_size(p),
select: L[n],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
evalall: evalall(t),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
C_Int: C_Int(),
C_Struct: C_Struct(fields),
so_lambda: λ2x.t[x],
less_than: a < b,
squash: ↓T,
so_apply: x[s],
cand: A c∧ B,
C_Array: C_Array(length;elems),
pi2: snd(t),
C_Pointer: C_Pointer(to),
nil: [],
subtract: n - m,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
true: True,
cons: [a / b]
Lemmas referenced :
int-valueall-type,
set-valueall-type,
atom-valueall-type,
add-is-int-iff,
nat_plus_properties,
nat_plus_wf,
add_nat_plus,
add-subtract-cancel,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
assert_of_le_int,
bool_cases,
not_wf,
bnot_wf,
assert_wf,
le_int_wf,
select-cons,
add-member-int_seg2,
evalall-cons,
length_of_cons_lemma,
length_of_nil_lemma,
int_subtype_base,
set_subtype_base,
subtype_rel_self,
product_subtype_base,
list_subtype_base,
all_wf,
list_induction,
list_wf,
C_TYPE_subtype_base,
subtype_rel_product,
subtype_rel_list,
is-exception_wf,
has-value_wf_base,
nat_wf,
sum-nat-less,
int_term_value_add_lemma,
itermAdd_wf,
pi2_wf,
decidable__lt,
length_wf,
select_wf,
length_wf_nat,
sum-nat,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
stuck-spread,
it_wf,
unit_subtype_base,
atom_subtype_base,
subtype_base_sq,
assert_of_eq_atom,
eqtt_to_assert,
bool_wf,
eq_atom_wf,
C_TYPE-ext,
int_formula_prop_eq_lemma,
intformeq_wf,
lelt_wf,
false_wf,
int_seg_subtype,
decidable__equal_int,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
int_seg_properties,
int_seg_wf,
C_TYPE_size_wf,
le_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
base_wf,
equal-wf-base,
C_TYPE_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
lemma_by_obid,
lambdaFormation,
equalityEquality,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
axiomSqleEquality,
isectElimination,
because_Cache,
isect_memberEquality,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
productElimination,
unionElimination,
setEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
promote_hyp,
tokenEquality,
equalityElimination,
instantiate,
cumulativity,
atomEquality,
baseClosed,
productEquality,
imageElimination,
callbyvalueReduce,
sqleReflexivity,
addEquality,
divergentSqle,
functionEquality,
baseApply,
closedConclusion,
impliesFunctionality,
imageMemberEquality,
pointwiseFunctionality
Latex:
valueall-type(C\_TYPE())
Date html generated:
2016_05_16-AM-08_46_17
Last ObjectModification:
2016_01_17-AM-09_44_10
Theory : C-semantics
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