Nuprl Lemma : select_member
∀[T:Type]. ∀L:T List. ∀i:ℕ||L||. (L[i] ∈ L)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_member: (x ∈ l),
exists: ∃x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
cand: A c∧ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
sq_stable: SqStable(P),
squash: ↓T,
nat: ℕ
Lemmas referenced :
int_seg_subtype_nat,
length_wf,
false_wf,
select_wf,
sq_stable__le,
less_than_wf,
equal_wf,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
cumulativity,
hypothesis,
independent_isectElimination,
sqequalRule,
independent_pairFormation,
setElimination,
rename,
productElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
because_Cache,
productEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}i:\mBbbN{}||L||. (L[i] \mmember{} L)
Date html generated:
2017_04_14-AM-08_37_19
Last ObjectModification:
2017_02_27-PM-03_28_48
Theory : list_0
Home
Index