Nuprl Lemma : C_TYPE-of-LVALUE_wf
∀env:C_TYPE_env(). ∀lval:C_LVALUE().  (C_TYPE-of-LVALUE(env;lval) ∈ C_TYPE()?)
Proof
Definitions occuring in Statement : 
C_TYPE-of-LVALUE: C_TYPE-of-LVALUE(env;lval)
, 
C_TYPE_env: C_TYPE_env()
, 
C_LVALUE: C_LVALUE()
, 
C_TYPE: C_TYPE()
, 
all: ∀x:A. B[x]
, 
unit: Unit
, 
member: t ∈ T
, 
union: left + right
Definitions unfolded in proof : 
C_TYPE_env: C_TYPE_env()
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
C_TYPE-of-LVALUE: C_TYPE-of-LVALUE(env;lval)
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
implies: P 
⇒ Q
, 
exposed-bfalse: exposed-bfalse
, 
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)
, 
assert: ↑b
, 
bfalse: ff
, 
false: False
, 
band: p ∧b q
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
not: ¬A
, 
le: A ≤ B
, 
less_than: a < b
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
so_apply: x[s1;s2;s3]
Lemmas referenced : 
C_LVALUE_ind_wf_simple, 
C_TYPE_wf, 
unit_wf2, 
C_LOCATION_wf, 
isl_wf, 
bool_wf, 
eqtt_to_assert, 
C_Array?_wf, 
le_int_wf, 
assert_of_le_int, 
lt_int_wf, 
C_Array-length_wf, 
nat_wf, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert_of_lt_int, 
C_Array-elems_wf, 
eqff_to_assert, 
assert-bnot, 
iff_transitivity, 
assert_wf, 
le_wf, 
less_than_wf, 
iff_weakening_uiff, 
assert_of_band, 
it_wf, 
C_LVALUE_wf, 
C_Struct?_wf, 
apply-alist_wf, 
atom-deq_wf, 
C_Struct-fields_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
unionEquality, 
hypothesis, 
hypothesisEquality, 
lambdaEquality, 
applyEquality, 
because_Cache, 
unionElimination, 
equalityElimination, 
productElimination, 
independent_isectElimination, 
voidElimination, 
natural_numberEquality, 
setElimination, 
rename, 
equalityTransitivity, 
equalitySymmetry, 
equalityEquality, 
dependent_functionElimination, 
independent_functionElimination, 
dependent_pairFormation, 
promote_hyp, 
instantiate, 
cumulativity, 
inlEquality, 
productEquality, 
independent_pairFormation, 
inrEquality, 
intEquality, 
atomEquality, 
functionEquality
Latex:
\mforall{}env:C\_TYPE\_env().  \mforall{}lval:C\_LVALUE().    (C\_TYPE-of-LVALUE(env;lval)  \mmember{}  C\_TYPE()?)
Date html generated:
2016_05_16-AM-08_48_11
Last ObjectModification:
2015_12_28-PM-06_56_54
Theory : C-semantics
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