Nuprl Lemma : no_repeats_witness
∀[T:Type]. ∀[l:T List]. (no_repeats(T;l) ⇒ (λx.Ax ∈ no_repeats(T;l)))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
lambda: λx.A[x],
universe: Type,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
no_repeats: no_repeats(T;l),
uimplies: b supposing a,
not: ¬A,
false: False,
nat: ℕ,
sq_stable: SqStable(P),
squash: ↓T,
prop: ℙ
Lemmas referenced :
equal_wf,
select_wf,
sq_stable__le,
not_wf,
nat_wf,
less_than_wf,
length_wf,
no_repeats_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
voidElimination,
extract_by_obid,
cumulativity,
because_Cache,
setElimination,
rename,
hypothesis,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. (no\_repeats(T;l) {}\mRightarrow{} (\mlambda{}x.Ax \mmember{} no\_repeats(T;l)))
Date html generated:
2017_04_14-AM-08_37_35
Last ObjectModification:
2017_02_27-PM-03_29_19
Theory : list_0
Home
Index