Nuprl Lemma : assert-C_TYPE_eq
∀[a,b:C_TYPE()]. uiff(↑C_TYPE_eq(a;b);a = b ∈ C_TYPE())
Proof
Definitions occuring in Statement :
C_TYPE_eq: C_TYPE_eq(a;b),
C_TYPE: C_TYPE(),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
C_TYPE_eq: C_TYPE_eq(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
C_TYPE_eq_fun: C_TYPE_eq_fun(a),
C_Void: C_Void(),
C_TYPE_ind: C_TYPE_ind,
select: L[n],
uimplies: b supposing a,
all: ∀x:A. B[x],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
C_Void?: C_Void?(v),
pi1: fst(t),
eq_atom: x =a y,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
true: True,
C_Int: C_Int(),
bfalse: ff,
false: False,
C_Int?: C_Int?(v),
not: ¬A,
C_Struct: C_Struct(fields),
C_Struct?: C_Struct?(v),
C_Array: C_Array(length;elems),
C_Array?: C_Array?(v),
C_Pointer: C_Pointer(to),
C_Pointer?: C_Pointer?(v),
guard: {T},
bool: 𝔹,
unit: Unit,
band: p ∧b q,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
C_Struct-fields: C_Struct-fields(v),
pi2: snd(t),
nat: ℕ,
ge: i ≥ j ,
squash: ↓T,
sq_type: SQType(T),
bnot: ¬bb,
l_all: (∀x∈L.P[x]),
le: A ≤ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
cand: A c∧ B,
nequal: a ≠ b ∈ T ,
C_Array-length: C_Array-length(v),
C_Array-elems: C_Array-elems(v),
C_Pointer-to: C_Pointer-to(v)
Lemmas referenced :
C_Pointer-to_wf,
le_wf,
decidable__equal_int,
C_Array-elems_wf,
C_Array-length_wf,
equal-wf-base-T,
C_TYPE_subtype_base,
atom_subtype_base,
product_subtype_base,
list_subtype_base,
assert_of_band,
iff_weakening_uiff,
iff_transitivity,
band_wf,
select-upto,
lelt_wf,
length_wf_nat,
length_upto,
assert-bl-all,
less_than_wf,
neg_assert_of_eq_int,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
list_extensionality,
squash_wf,
nat_properties,
pi2_wf,
assert_of_eq_atom,
int_formula_prop_eq_lemma,
intformeq_wf,
top_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,
select_wf,
eq_atom_wf,
upto_wf,
int_seg_wf,
bl-all_wf,
assert_of_eq_int,
C_Struct-fields_wf,
length_wf,
eq_int_wf,
eqtt_to_assert,
bool_wf,
C_TYPE_eq_wf,
assert_witness,
C_Pointer_wf,
C_Pointer?_wf,
nat_wf,
C_Array_wf,
C_Array?_wf,
list_wf,
l_member_wf,
l_all_wf2,
C_Struct_wf,
C_Struct?_wf,
C_Int_wf,
btrue_neq_bfalse,
bfalse_wf,
C_Int?_wf,
and_wf,
btrue_wf,
false_wf,
true_wf,
C_Void_wf,
C_Void?_wf,
base_wf,
stuck-spread,
equal_wf,
C_TYPE_eq_fun_wf,
assert_wf,
uiff_wf,
C_TYPE_wf,
all_wf,
C_TYPE-induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
lambdaEquality,
hypothesis,
applyEquality,
hypothesisEquality,
independent_functionElimination,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
setElimination,
rename,
productElimination,
setEquality,
productEquality,
atomEquality,
spreadEquality,
because_Cache,
dependent_functionElimination,
independent_pairEquality,
unionElimination,
equalityElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll,
equalityEquality,
imageElimination,
promote_hyp,
instantiate,
cumulativity,
imageMemberEquality,
functionEquality,
addLevel,
impliesFunctionality,
substitution
Latex:
\mforall{}[a,b:C\_TYPE()]. uiff(\muparrow{}C\_TYPE\_eq(a;b);a = b)
Date html generated:
2016_05_16-AM-08_46_01
Last ObjectModification:
2016_01_17-AM-09_44_50
Theory : C-semantics
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