Nuprl Lemma : select-reverse
∀[T:Type]. ∀[L:T List]. ∀[i:ℕ||rev(L)||]. (rev(L)[i] = L[||L|| - 1 - i] ∈ T)
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
reverse: rev(as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reverse: rev(as),
top: Top,
squash: ↓T,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
select: L[n],
nil: [],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtract: n - m,
nat_plus: ℕ+,
less_than': less_than'(a;b),
decidable: Dec(P)
Lemmas referenced :
length-reverse,
equal_wf,
squash_wf,
true_wf,
select-rev-append,
nil_wf,
length-nil,
add-zero,
length_wf,
lelt_wf,
select_wf,
subtract_wf,
non_neg_length,
length_wf_nat,
nat_wf,
set_subtype_base,
le_wf,
int_subtype_base,
iff_weakening_equal,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
stuck-spread,
base_wf,
int_seg_wf,
reverse_wf,
add-associates,
minus-one-mul,
add-swap,
add-commutes,
less-iff-le,
add_functionality_wrt_le,
le_reflexive,
minus-one-mul-top,
one-mul,
add-mul-special,
two-mul,
mul-distributes-right,
zero-mul,
not-le-2,
minus-zero,
zero-add,
omega-shadow,
mul-distributes,
mul-associates,
le-add-cancel,
not-lt-2,
minus-add,
minus-minus,
int_seg_properties,
nat_properties,
decidable__le,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
cumulativity,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
addEquality,
natural_numberEquality,
independent_isectElimination,
lambdaFormation,
dependent_pairFormation,
sqequalIntensionalEquality,
intEquality,
dependent_functionElimination,
independent_functionElimination,
promote_hyp,
imageMemberEquality,
baseClosed,
universeEquality,
unionElimination,
equalityElimination,
instantiate,
axiomEquality,
multiplyEquality,
minusEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[i:\mBbbN{}||rev(L)||]. (rev(L)[i] = L[||L|| - 1 - i])
Date html generated:
2017_04_14-AM-08_40_31
Last ObjectModification:
2017_02_27-PM-03_31_04
Theory : list_0
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