Nuprl Lemma : es-interface-buffer-as-accum
∀[Info,A1:Type]. ∀[n:ℕ]. ∀[X:EClass(A1)].
(Buffer(n;X) = es-interface-accum(λL,v. if ||L|| <z n then L @ [v] else tl(L @ [v]) fi ;[];X) ∈ EClass(A1 List))
Proof
Definitions occuring in Statement :
es-interface-buffer: Buffer(n;X),
es-interface-accum: es-interface-accum(f;x;X),
eclass: EClass(A[eo; e]),
tl: tl(l),
length: ||as||,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
nat: ℕ,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
lastn-as-accum,
eclass-vals_wf,
es-interface-predecessors_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_rel_list,
es-E-interface_wf,
Id_wf,
es-loc_wf,
list_wf,
list_induction,
all_wf,
equal_wf,
list_accum_wf,
map_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
lt_int_wf,
length_wf,
eqtt_to_assert,
assert_of_lt_int,
append_wf,
cons_wf,
nil_wf,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
less_than_wf,
tl_wf,
map_nil_lemma,
list_accum_nil_lemma,
map_cons_lemma,
list_accum_cons_lemma,
set_wf,
sq_stable__assert,
iff_weakening_equal
Latex:
\mforall{}[Info,A1:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[X:EClass(A1)].
(Buffer(n;X) = es-interface-accum(\mlambda{}L,v. if ||L|| <z n then L @ [v] else tl(L @ [v]) fi ;[];X))
Date html generated:
2015_07_21-PM-04_23_25
Last ObjectModification:
2015_02_04-PM-06_00_44
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