Nuprl Lemma : no_repeats-firstn
∀[T:Type]. ∀[l:T List]. ∀[n:ℤ]. no_repeats(T;firstn(n;l)) supposing no_repeats(T;l)
Proof
Definitions occuring in Statement :
firstn: firstn(n;as),
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
firstn: firstn(n;as),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Lemmas referenced :
list_induction,
isect_wf,
no_repeats_wf,
uall_wf,
firstn_wf,
list_wf,
list_ind_nil_lemma,
no_repeats_witness,
nil_wf,
list_ind_cons_lemma,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
no_repeats_cons,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
no_repeats_nil,
ifthenelse_wf,
cons_wf,
subtract_wf,
member-firstn-implies-member,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
intEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaFormation,
rename,
natural_numberEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
independent_pairFormation,
dependent_pairFormation,
promote_hyp,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[n:\mBbbZ{}]. no\_repeats(T;firstn(n;l)) supposing no\_repeats(T;l)
Date html generated:
2017_04_17-AM-07_29_17
Last ObjectModification:
2017_02_27-PM-04_07_28
Theory : list_1
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