Nuprl Lemma : run-event-cases
∀[M:Type ─→ Type]
∀S0:System(P.M[P]). ∀r:pRunType(P.M[P]). ∀e1,e2:runEvents(r).
(((run-event-local-pred(r;e2) = run-event-local-pred(r;e1) ∈ (runEvents(r)?))
∧ (run-event-interval(r;e1;e2) = [e2] ∈ (runEvents(r) List)))
∨ (∃e:runEvents(r)
(run-event-step(e) < run-event-step(e2)
∧ (run-event-step(e1) ≤ run-event-step(e))
∧ ((run-event-loc(e1) = run-event-loc(e) ∈ Id) ∧ (run-event-local-pred(r;e2) = (inl e) ∈ (runEvents(r)?)))
∧ (run-event-interval(r;e1;e2) = (run-event-interval(r;e1;e) @ [e2]) ∈ (runEvents(r) List))))) supposing
((run-event-step(e1) ≤ run-event-step(e2)) and
(run-event-loc(e1) = run-event-loc(e2) ∈ Id))
Proof
Definitions occuring in Statement :
run-event-local-pred: run-event-local-pred(r;e),
run-event-interval: run-event-interval(r;e1;e2),
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
System: System(P.M[P]),
Id: Id,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
and: P ∧ Q,
unit: Unit,
function: x:A ─→ B[x],
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Lemmas :
sq_stable__assert,
is-run-event_wf,
and_wf,
equal_wf,
Id_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
atom2_subtype_base,
from-upto-split,
sq_stable__le,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero,
add-associates,
add-commutes,
le-add-cancel,
mapfilter_wf,
le_wf,
less_than_wf,
from-upto_wf,
assert_wf,
subtype_rel_sets,
set_wf,
subtype_rel_list,
top_wf,
int_seg_wf,
int_seg_subtype-nat,
lelt_wf,
list_wf,
le_transitivity,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
value-type-has-value,
int-value-type,
less_than_irreflexivity,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
filter_cons_lemma,
filter_nil_lemma,
assert_of_null,
null_wf3,
map_cons_lemma,
map_nil_lemma,
mapfilter-append,
null_append,
subtype_rel_nested_set2,
filter_type,
map_wf,
nil_wf,
cons_wf,
subtype_top,
subtype_rel_product,
subtype_rel_set,
btrue_neq_bfalse,
btrue_wf,
isl_wf,
pi2_wf,
pi1_wf_top,
bfalse_wf,
subtype_rel_list_set,
append_wf,
equal-wf-base-T,
exists_wf,
unit_wf2,
nat_wf,
it_wf,
null_nil_lemma,
null_cons_lemma,
list_ind_cons_lemma,
product_subtype_list,
list_ind_nil_lemma,
list-cases,
last_wf,
not_wf,
equal-wf-T-base,
squash_wf,
true_wf,
set_subtype_base,
product_subtype_base,
int_subtype_base,
list_subtype_base,
nat_properties,
less_than_transitivity1,
ge_wf,
add_functionality_wrt_le,
zero-add,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
pRunType_wf,
from-upto-nil,
le_antisymmetry,
le-add-cancel-alt,
mapfilter-singleton,
trivial-int-eq1,
length_of_nil_lemma,
length_of_cons_lemma,
last_append,
bnot_wf,
append-nil,
not-equal-2,
decidable__equal_int,
decidable__assert,
equal_functionality_wrt_subtype_rel2
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}S0:System(P.M[P]). \mforall{}r:pRunType(P.M[P]). \mforall{}e1,e2:runEvents(r).
(((run-event-local-pred(r;e2) = run-event-local-pred(r;e1))
\mwedge{} (run-event-interval(r;e1;e2) = [e2]))
\mvee{} (\mexists{}e:runEvents(r)
(run-event-step(e) < run-event-step(e2)
\mwedge{} (run-event-step(e1) \mleq{} run-event-step(e))
\mwedge{} ((run-event-loc(e1) = run-event-loc(e)) \mwedge{} (run-event-local-pred(r;e2) = (inl e)))
\mwedge{} (run-event-interval(r;e1;e2) = (run-event-interval(r;e1;e) @ [e2]))))) supposing
((run-event-step(e1) \mleq{} run-event-step(e2)) and
(run-event-loc(e1) = run-event-loc(e2)))
Date html generated:
2015_07_23-AM-11_12_22
Last ObjectModification:
2015_07_16-AM-09_37_56
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