Nuprl Lemma : C_Void?_wf
∀[v:C_TYPE()]. (C_Void?(v) ∈ 𝔹)
Proof
Definitions occuring in Statement :
C_Void?: C_Void?(v),
C_TYPE: C_TYPE(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
C_Void: C_Void(),
C_Void?: C_Void?(v),
pi1: fst(t),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
C_Int: C_Int(),
C_Struct: C_Struct(fields),
C_Array: C_Array(length;elems),
C_Pointer: C_Pointer(to)
Lemmas referenced :
C_TYPE-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_subtype_base,
it_wf,
btrue_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
bfalse_wf,
C_TYPE_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
promote_hyp,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis_subsumption,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalRule,
isectElimination,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
dependent_pairFormation,
voidElimination,
equalityEquality
Latex:
\mforall{}[v:C\_TYPE()]. (C\_Void?(v) \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-08_44_47
Last ObjectModification:
2015_12_28-PM-06_58_10
Theory : C-semantics
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