Nuprl Lemma : no_repeats_l_index
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. ∀[i:ℕ||L||].  index(L;L[i]) ~ i supposing no_repeats(T;L)
Proof
Definitions occuring in Statement : 
l_index: index(L;x)
, 
no_repeats: no_repeats(T;l)
, 
select: L[n]
, 
length: ||as||
, 
list: T List
, 
deq: EqDecider(T)
, 
int_seg: {i..j-}
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
natural_number: $n
, 
universe: Type
, 
sqequal: s ~ t
Definitions unfolded in proof : 
l_index: index(L;x)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
sq_type: SQType(T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
prop: ℙ
Lemmas referenced : 
no_repeats_mu_index, 
subtype_base_sq, 
int_subtype_base, 
no_repeats_wf, 
int_seg_wf, 
length_wf, 
list_wf, 
deq_wf
Rules used in proof : 
cut, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
instantiate, 
cumulativity, 
intEquality, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
because_Cache, 
natural_numberEquality, 
universeEquality, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
sqequalRule, 
isect_memberEquality
Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[L:T  List].  \mforall{}[i:\mBbbN{}||L||].
    index(L;L[i])  \msim{}  i  supposing  no\_repeats(T;L)
Date html generated:
2016_05_14-PM-03_32_18
Last ObjectModification:
2015_12_26-PM-06_01_19
Theory : decidable!equality
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