Nuprl Lemma : local-prior-state-accumulate
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,T:Type]. ∀[X:EClass(A)]. ∀[base:T]. ∀[f:T ─→ A ─→ T]. ∀[e:E].
(prior-state(f;base;X;e)
= accumulate (with value x and list item a):
f x a
over list:
X(<e)
with starting value:
base)
∈ T)
Proof
Definitions occuring in Statement :
es-local-prior-state: prior-state(f;base;X;e),
es-prior-interface-vals: X(<e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
list_accum: list_accum,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
es-local-prior-state_wf,
in-eclass_wf,
es-prior-interface_wf1,
es-interface-subtype_rel2,
top_wf,
subtype_top,
es-E-interface_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
list_accum_nil_lemma,
list_accum_wf,
squash_wf,
true_wf,
list_wf,
es-prior-interface-vals-property,
iff_weakening_equal,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-prior-interface_wf,
list_accum_append,
es-prior-interface-vals_wf,
eclass-val_wf2,
subtype_rel_list,
list_accum_cons_lemma,
es-prior-interface-causl,
eclass-val_wf,
es-E-interface-property
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,T:Type]. \mforall{}[X:EClass(A)]. \mforall{}[base:T]. \mforall{}[f:T {}\mrightarrow{} A {}\mrightarrow{} T]. \mforall{}[e:E].
(prior-state(f;base;X;e)
= accumulate (with value x and list item a):
f x a
over list:
X(<e)
with starting value:
base))
Date html generated:
2015_07_21-PM-03_43_29
Last ObjectModification:
2015_02_04-PM-06_10_59
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