Nuprl Lemma : select_cons_tl
∀[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ]. ([a / as][i] = as[i - 1] ∈ T) supposing ((i ≤ ||as||) and 0 < i)
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
cons: [a / b],
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
subtract: n - m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
le: A ≤ B,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
select-cons-tl,
select_wf,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
not-lt-2,
length_wf,
le-add-cancel-alt,
le_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
independent_isectElimination,
hypothesis,
cumulativity,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_pairFormation,
lambdaFormation,
independent_functionElimination,
addEquality,
applyEquality,
lambdaEquality,
because_Cache,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[as:T List]. \mforall{}[i:\mBbbZ{}].
([a / as][i] = as[i - 1]) supposing ((i \mleq{} ||as||) and 0 < i)
Date html generated:
2016_05_14-AM-06_36_30
Last ObjectModification:
2015_12_26-PM-00_34_03
Theory : list_0
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