Nuprl Lemma : no_repeats_reverse
∀[T:Type]. ∀[L:T List]. uiff(no_repeats(T;rev(L));no_repeats(T;L))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
reverse: rev(as),
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
no_repeats: no_repeats(T;l),
not: ¬A,
implies: P ⇒ Q,
false: False,
top: Top,
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
sq_stable: SqStable(P),
squash: ↓T,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
sq_type: SQType(T),
ge: i ≥ j ,
or: P ∨ Q,
nat_plus: ℕ+,
less_than: a < b,
less_than': less_than'(a;b),
decidable: Dec(P)
Lemmas referenced :
length-reverse,
length_wf,
subtract_wf,
non_neg_length,
reverse_wf,
length_wf_nat,
nat_wf,
set_subtype_base,
le_wf,
int_subtype_base,
equal_wf,
select_wf,
sq_stable__le,
not_wf,
less_than_wf,
no_repeats_witness,
no_repeats_wf,
select-reverse,
lelt_wf,
iff_weakening_equal,
list_wf,
add-associates,
minus-one-mul,
add-swap,
add-commutes,
add-mul-special,
two-mul,
mul-distributes-right,
zero-mul,
zero-add,
one-mul,
subtype_base_sq,
not-equal-implies-less,
less-iff-le,
add_functionality_wrt_le,
le_reflexive,
minus-one-mul-top,
add-zero,
not-le-2,
minus-zero,
omega-shadow,
mul-distributes,
mul-associates,
le-add-cancel,
not-lt-2,
minus-add,
minus-minus,
nat_properties,
decidable__le,
decidable__lt,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
lambdaFormation,
thin,
sqequalRule,
extract_by_obid,
isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
dependent_set_memberEquality,
cumulativity,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
dependent_pairFormation,
sqequalIntensionalEquality,
applyEquality,
intEquality,
lambdaEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
productElimination,
promote_hyp,
imageMemberEquality,
baseClosed,
imageElimination,
independent_pairEquality,
universeEquality,
addEquality,
multiplyEquality,
instantiate,
unionElimination,
minusEquality,
applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. uiff(no\_repeats(T;rev(L));no\_repeats(T;L))
Date html generated:
2017_04_14-AM-08_40_54
Last ObjectModification:
2017_02_27-PM-03_32_24
Theory : list_0
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