Nuprl Lemma : State-loc-comb-is-loop-class-state
∀[Info,A,B:Type]. ∀[init:Id ─→ bag(B)]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[X:EClass(A)].
(State-loc-comb(init;f;X) = loop-class-state((f o X);init) ∈ EClass(B))
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-comb(init;f;X),
loop-class-state: loop-class-state(X;init),
eclass1: (f o X),
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
State-loc-comb_wf,
loop-class-state_wf,
eclass1_wf,
base_sq,
eclass-ext,
es-E_wf,
event-ordering+_subtype,
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,
primed-class-opt_functionality,
bag-size-map,
class-ap_wf,
bag_wf,
null-bag-size,
top_wf,
subtype_rel_bag,
eq_int_wf,
bag-size_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eclass_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
assert-bnot,
neg_assert_of_eq_int,
bag-combine_wf,
single-bag_wf,
es-loc_wf,
bag-combine-map,
bag-map_wf,
iff_weakening_equal,
bag-combine-single-right-as-map,
squash_wf,
true_wf,
eta_conv,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
event-ordering+_wf,
Id_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
(State-loc-comb(init;f;X) = loop-class-state((f o X);init))
Date html generated:
2015_07_22-PM-00_22_59
Last ObjectModification:
2015_02_04-PM-04_39_18
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