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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