Nuprl Lemma : LV_Index_wf
∀[lval:C_LVALUE()]. ∀[idx:ℤ]. (LV_Index(lval;idx) ∈ C_LVALUE())
Proof
Definitions occuring in Statement :
LV_Index: LV_Index(lval;idx),
C_LVALUE: C_LVALUE(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
C_LVALUE: C_LVALUE(),
LV_Index: LV_Index(lval;idx),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
C_LVALUEco_size: C_LVALUEco_size(p),
C_LVALUE_size: C_LVALUE_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
C_LVALUEco-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
C_LOCATION_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
C_LVALUEco_wf,
add_nat_wf,
false_wf,
le_wf,
C_LVALUE_size_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
has-value_wf-partial,
C_LVALUEco_size_wf,
C_LVALUE_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality,
tokenEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
intEquality,
isectElimination,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
productEquality,
atomEquality,
voidEquality,
equalityEquality,
applyEquality,
natural_numberEquality,
independent_pairFormation,
lambdaEquality
Latex:
\mforall{}[lval:C\_LVALUE()]. \mforall{}[idx:\mBbbZ{}]. (LV\_Index(lval;idx) \mmember{} C\_LVALUE())
Date html generated:
2016_05_16-AM-08_46_54
Last ObjectModification:
2015_12_28-PM-06_57_12
Theory : C-semantics
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