Nuprl Lemma : accum-class-programmable
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[base:A ─→ B]. ∀[f:B ─→ A ─→ B].
(accum-class(b,a.f[b;a];a.base[a];X)
= λB,r. if (#(B 0) =z 1)
then if (#(r) =z 1) then {f[only(r);only(B 0)]} else {base[only(B 0)]} fi
else {}
fi |λi.X,(self)'|
∈ EClass(B))
Proof
Definitions occuring in Statement :
rec-combined-class: f|X,(self)'|,
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-only: only(bs),
bag-size: #(bs),
single-bag: {x},
empty-bag: {}
Lemmas :
rec-combined-class_wf,
false_wf,
le_wf,
int_seg_wf,
eq_int_wf,
bag-size_wf,
lelt_wf,
nat_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
single-bag_wf,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
add-zero,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
not-equal-2,
empty-bag_wf,
bag_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
squash_wf,
true_wf,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
primed-class_wf,
eclass-val_wf,
bag_size_single_lemma,
bag_size_empty_lemma,
iff_weakening_equal,
assert_wf,
es-interface-extensionality,
accum-class_wf,
is-accum-class,
accum-class-val,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
minus-add,
minus-minus,
add-associates,
add-swap,
decidable__equal_int,
subtype_rel-int_seg,
int_seg_properties,
zero-le-nat,
es-causl_wf,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
accum_list_wf,
es-E-interface_wf,
Id_wf,
es-loc_wf,
assert_elim,
es-interface-predecessors_wf,
es-interface-predecessors-nonempty,
bag_only_single_lemma,
single-valued-bag-single,
single-valued-bag_wf,
set_wf,
sq_stable__assert,
length_wf,
list_wf,
es-interface-predecessors-step,
es-prior-interface_wf1,
subtype_top,
eclass-val_wf2,
es-prior-interface_wf,
es-is-prior-interface,
es-E-interface-property,
es-locl_wf,
accum_list_cons_lemma,
list_accum_nil_lemma,
es-prior-interface-causl,
append_wf,
subtype_rel_list,
cons_wf,
nil_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_wf_nat,
length_cons,
length_append,
es-prior-interface-same,
event-ordering+_cumulative2,
list-cases,
list_ind_nil_lemma,
product_subtype_list,
list_ind_cons_lemma,
length_of_nil_lemma,
list_accum_append,
list_accum_cons_lemma,
list_accum_wf,
primed-class-prior-val,
and_wf,
not_assert_elim,
btrue_neq_bfalse
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[base:A {}\mrightarrow{} B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B].
(accum-class(b,a.f[b;a];a.base[a];X)
= \mlambda{}B,r. if (\#(B 0) =\msubz{} 1)
then if (\#(r) =\msubz{} 1) then \{f[only(r);only(B 0)]\} else \{base[only(B 0)]\} fi
else \{\}
fi |\mlambda{}i.X,(self)'|)
Date html generated:
2015_07_21-PM-04_23_09
Last ObjectModification:
2015_02_04-PM-06_02_59
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