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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