Nuprl Lemma : ml-select_wf
∀[T:Type]. ∀[L:T List]. ∀[n:ℕ||L||]. (ml-select(n;L) ∈ T) supposing valueall-type(T)
Proof
Definitions occuring in Statement :
ml-select: ml-select(n;L),
length: ||as||,
list: T List,
int_seg: {i..j-},
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T
Lemmas referenced :
ml-select-sq,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
list_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
setElimination,
rename,
cumulativity,
because_Cache,
natural_numberEquality,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[n:\mBbbN{}||L||]. (ml-select(n;L) \mmember{} T) supposing valueall-type(T)
Date html generated:
2017_09_29-PM-05_51_27
Last ObjectModification:
2017_05_19-PM-05_58_44
Theory : ML
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