Nuprl Lemma : assert_of_null
∀[T:Type]. ∀[as:T List]. uiff(↑null(as);as = [] ∈ (T List))
Proof
Definitions occuring in Statement :
null: null(as),
nil: [],
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
top: Top,
bfalse: ff,
false: False,
prop: ℙ,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
true: True
Lemmas referenced :
list-cases,
null_nil_lemma,
nil_wf,
product_subtype_list,
null_cons_lemma,
assert_wf,
null_wf,
and_wf,
equal_wf,
list_wf,
btrue_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
axiomEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
sqequalRule,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
natural_numberEquality,
independent_pairEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as:T List]. uiff(\muparrow{}null(as);as = [])
Date html generated:
2016_05_14-AM-06_30_34
Last ObjectModification:
2015_12_26-PM-00_39_08
Theory : list_0
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