Nuprl Lemma : no_repeats_wf
∀[T:Type]. ∀[l:T List]. (no_repeats(T;l) ∈ ℙ)
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
no_repeats: no_repeats(T;l),
so_lambda: λ2x.t[x],
uimplies: b supposing a,
nat: ℕ,
prop: ℙ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
so_apply: x[s]
Lemmas referenced :
list_wf,
sq_stable__le,
select_wf,
equal_wf,
not_wf,
length_wf,
less_than_wf,
isect_wf,
nat_wf,
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
setElimination,
rename,
hypothesisEquality,
cumulativity,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. (no\_repeats(T;l) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_36_16
Last ObjectModification:
2016_01_14-PM-08_22_27
Theory : list_0
Home
Index