Nuprl Lemma : State-comb-classrel-class
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀[v:B]. (v ∈ State-comb(init;f;X)(e) ⇐⇒ v ∈ State-class(init;f;X)(e))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
State-class: State-class(init;f;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
universe: Type,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
classrel_wf,
State-comb_wf,
State-class_wf,
nat_wf,
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__lt,
es-causl_wf,
zero-le-nat,
le_wf,
add-mul-special,
zero-mul,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
State-classrel,
rec-combined-class-opt-1-classrel,
bag-null_wf,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-bag-null,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
primed-class-opt-classrel,
sq_stable__iterated_classrel,
es-locl-trichotomy,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
es-first_wf2,
es-loc-pred,
es-pred-locl,
State-comb-exists,
State-comb-exists-iff,
and_wf,
equal_wf,
bag-size_wf,
bag-member_wf,
es-loc_wf,
bool_cases_sqequal,
assert-bnot,
iterated_classrel_wf,
or_wf,
exists_wf,
all_wf,
es-causl_weakening,
squash_wf,
true_wf,
iff_weakening_equal,
uiff_transitivity,
bag-member-empty-iff,
es-pred_property,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
es-causl_transitivity2,
es-causle_weakening,
es-causl_irreflexivity,
bag-member-iff-size,
es-pred-loc-base,
bag-member-lifting-2,
primed-class-opt_wf,
atom2_subtype_base,
es-locl_wf,
es-p-local-pred_wf,
empty-bag-iff-size
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
\mforall{}[v:B]. (v \mmember{} State-comb(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} State-class(init;f;X)(e))
Date html generated:
2015_07_22-PM-00_21_10
Last ObjectModification:
2015_02_04-PM-04_41_22
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