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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