Nuprl Lemma : C_type_of_field_wf
∀[ctyp:{t:C_TYPE()| ↑C_Struct?(t)} ]. ∀[a:{c:Atom| ↑C_field_of(c;ctyp)} ].  (C_type_of_field(a;ctyp) ∈ C_TYPE())
Proof
Definitions occuring in Statement : 
C_type_of_field: C_type_of_field(a;ctyp)
, 
C_field_of: C_field_of(a;ctyp)
, 
C_Struct?: C_Struct?(v)
, 
C_TYPE: C_TYPE()
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
atom: Atom
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
C_type_of_field: C_type_of_field(a;ctyp)
, 
uimplies: b supposing a
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
C_field_of: C_field_of(a;ctyp)
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
top: Top
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
exists: ∃x:A. B[x]
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
nat: ℕ
, 
le: A ≤ B
, 
less_than: a < b
, 
not: ¬A
, 
false: False
, 
guard: {T}
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
ge: i ≥ j 
, 
true: True
, 
squash: ↓T
, 
pi1: fst(t)
, 
select: L[n]
, 
C_Struct-fields: C_Struct-fields(v)
, 
pi2: snd(t)
, 
isl: isl(x)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
Lemmas referenced : 
iff_weakening_equal, 
map_select, 
true_wf, 
squash_wf, 
not_wf, 
int_seg_wf, 
atom_subtype_base, 
int_formula_prop_eq_lemma, 
int_formula_prop_less_lemma, 
intformeq_wf, 
intformless_wf, 
decidable__lt, 
map_length, 
non_neg_length, 
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, 
select_wf, 
equal-wf-T-base, 
length_wf, 
lelt_wf, 
less_than_wf, 
nat_wf, 
equal_wf, 
and_wf, 
length_wf_nat, 
map-length, 
l_member-first, 
subtype_rel_list, 
apply-alist-cases, 
top_wf, 
subtype_rel_product, 
pi1_wf_top, 
map_wf, 
assert-deq-member, 
C_Struct?_wf, 
C_field_of_wf, 
assert_wf, 
set_wf, 
C_Struct-fields_wf, 
atom-deq_wf, 
apply-alist_wf, 
unit_wf2, 
C_TYPE_wf, 
outl_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
setElimination, 
thin, 
rename, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesis, 
atomEquality, 
hypothesisEquality, 
because_Cache, 
independent_isectElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
lambdaEquality, 
isect_memberEquality, 
dependent_functionElimination, 
productEquality, 
applyEquality, 
lambdaFormation, 
voidElimination, 
voidEquality, 
productElimination, 
independent_functionElimination, 
dependent_set_memberEquality, 
independent_pairFormation, 
setEquality, 
substitution, 
natural_numberEquality, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
computeAll, 
equalityEquality, 
imageElimination, 
universeEquality, 
imageMemberEquality, 
baseClosed
Latex:
\mforall{}[ctyp:\{t:C\_TYPE()|  \muparrow{}C\_Struct?(t)\}  ].  \mforall{}[a:\{c:Atom|  \muparrow{}C\_field\_of(c;ctyp)\}  ].
    (C\_type\_of\_field(a;ctyp)  \mmember{}  C\_TYPE())
Date html generated:
2016_05_16-AM-08_48_02
Last ObjectModification:
2016_01_17-AM-09_43_42
Theory : C-semantics
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