Nuprl Lemma : C_TYPE_eq_fun_wf
∀[a:C_TYPE()]. (C_TYPE_eq_fun(a) ∈ C_TYPE() ⟶ 𝔹)
Proof
Definitions occuring in Statement : 
C_TYPE_eq_fun: C_TYPE_eq_fun(a)
, 
C_TYPE: C_TYPE()
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
C_TYPE_eq_fun: C_TYPE_eq_fun(a)
, 
so_lambda: λ2x y.t[x; y]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_apply: x[s1;s2]
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s1;s2;s3]
, 
l_all: (∀x∈L.P[x])
, 
int_seg: {i..j-}
, 
sq_stable: SqStable(P)
, 
squash: ↓T
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
not: ¬A
, 
top: Top
Lemmas referenced : 
pi2_wf, 
subtype_rel-equal, 
top_wf, 
int_formula_prop_eq_lemma, 
intformeq_wf, 
eq_atom_wf, 
subtype_rel_product, 
pi1_wf_top, 
int_formula_prop_less_lemma, 
intformless_wf, 
decidable__lt, 
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, 
decidable__equal_int_seg, 
sq_stable__l_member, 
select_wf, 
band_wf, 
bl-all_wf, 
upto_wf, 
int_seg_wf, 
C_Pointer-to_wf, 
C_Pointer?_wf, 
C_Array-elems_wf, 
nat_wf, 
C_Array-length_wf, 
C_Array?_wf, 
list_wf, 
l_member_wf, 
l_all_wf2, 
bfalse_wf, 
neg_assert_of_eq_int, 
assert-bnot, 
bool_subtype_base, 
subtype_base_sq, 
bool_cases_sqequal, 
equal_wf, 
eqff_to_assert, 
assert_of_eq_int, 
C_Struct-fields_wf, 
length_wf, 
eq_int_wf, 
eqtt_to_assert, 
C_Struct?_wf, 
C_Int?_wf, 
C_Void?_wf, 
bool_wf, 
C_TYPE_wf, 
C_TYPE_ind_wf_simple
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
functionEquality, 
hypothesis, 
hypothesisEquality, 
lambdaEquality, 
sqequalRule, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
independent_isectElimination, 
productEquality, 
atomEquality, 
because_Cache, 
dependent_pairFormation, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
cumulativity, 
independent_functionElimination, 
voidElimination, 
equalityEquality, 
spreadEquality, 
setElimination, 
rename, 
setEquality, 
applyEquality, 
axiomEquality, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidEquality, 
independent_pairFormation, 
computeAll
Latex:
\mforall{}[a:C\_TYPE()].  (C\_TYPE\_eq\_fun(a)  \mmember{}  C\_TYPE()  {}\mrightarrow{}  \mBbbB{})
Date html generated:
2016_05_16-AM-08_45_47
Last ObjectModification:
2016_01_17-AM-09_43_48
Theory : C-semantics
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