Nuprl Lemma : select_tl
∀[A:Type]. ∀[as:A List]. ∀[n:ℕ||as|| - 1]. (tl(as)[n] = as[n + 1] ∈ A)
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
tl: tl(l),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
guard: {T},
so_apply: x[s],
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
add-subtract-cancel,
select-cons-tl,
reduce_tl_cons_lemma,
length_of_cons_lemma,
le-add-cancel2,
base_wf,
stuck-spread,
reduce_tl_nil_lemma,
length_of_nil_lemma,
list_wf,
not-lt-2,
decidable__lt,
add-zero,
not-le-2,
iff_weakening_equal,
le-add-cancel,
add_functionality_wrt_le,
zero-add,
add-commutes,
minus-one-mul-top,
add-swap,
minus-one-mul,
minus-add,
add-associates,
condition-implies-le,
less-iff-le,
not-ge-2,
false_wf,
decidable__le,
length_tl,
true_wf,
squash_wf,
less_than_wf,
sq_stable__le,
tl_wf,
select_wf,
equal_wf,
length_wf,
subtract_wf,
int_seg_wf,
uall_wf,
list_induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
natural_numberEquality,
cumulativity,
hypothesis,
because_Cache,
setElimination,
rename,
independent_isectElimination,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
dependent_functionElimination,
unionElimination,
independent_pairFormation,
lambdaFormation,
voidElimination,
addEquality,
minusEquality,
isect_memberEquality,
voidEquality,
universeEquality,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[as:A List]. \mforall{}[n:\mBbbN{}||as|| - 1]. (tl(as)[n] = as[n + 1])
Date html generated:
2016_05_14-AM-06_36_37
Last ObjectModification:
2016_01_06-PM-08_33_28
Theory : list_0
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