Nuprl Lemma : sq_stable__no_repeats
∀[T:Type]. ∀[l:T List]. SqStable(no_repeats(T;l))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
no_repeats: no_repeats(T;l),
uall: ∀[x:A]. B[x],
member: t ∈ T,
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],
not: ¬A,
false: False
Lemmas referenced :
sq_stable__uall,
nat_wf,
uall_wf,
isect_wf,
less_than_wf,
length_wf,
not_wf,
equal_wf,
select_wf,
sq_stable__le,
sq_stable__not,
squash_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
because_Cache,
cumulativity,
hypothesisEquality,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
voidElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. SqStable(no\_repeats(T;l))
Date html generated:
2017_04_14-AM-08_37_40
Last ObjectModification:
2017_02_27-PM-03_29_29
Theory : list_0
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