Nuprl Lemma : loop-class-memory-no-input
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
loop-class-memory(X;init)(e) = Prior(loop-class-memory(X;init))?init(e) ∈ bag(B)
supposing (¬↑first(e)) ⇒ (¬↑pred(e) ∈b X)
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
primed-class-opt: Prior(X)?b,
member-eclass: e ∈b X,
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
not_wf,
assert_wf,
es-first_wf2,
member-eclass_wf,
es-pred_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,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
bag-size_wf,
es-loc_wf,
eclass3_wf,
top_wf,
es-interface-subtype_rel2,
subtype_rel_dep_function,
loop-class-memory_wf,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
lt_int_wf,
class-ap_wf,
assert_of_lt_int,
le_int_wf,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
es-pred-loc-base,
iff_weakening_equal,
loop-class-memory-size,
primed-class-opt-cases,
bag-member-iff-size,
eclass3-classrel,
assert-member-eclass,
squash_wf,
exists_wf,
classrel_wf,
loop-class-memory-exists,
loop-class-memory-exists-prior,
primed-class-opt_wf,
bag-size-bag-member,
assert_of_eq_int,
null-bag-size,
null-bag
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
loop-class-memory(X;init)(e) = Prior(loop-class-memory(X;init))?init(e)
supposing (\mneg{}\muparrow{}first(e)) {}\mRightarrow{} (\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X)
Date html generated:
2015_07_21-PM-02_36_09
Last ObjectModification:
2015_02_04-PM-06_22_00
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