Nuprl Lemma : total-run-lt
∀[M:Type ─→ Type]
∀r:pRunType(P.M[P]). ∀e1,e2:runEvents(r).
(e1 = e2 ∈ runEvents(r)) ∨ (e1 run-lt(r) e2) ∨ (e2 run-lt(r) e1)
supposing run-event-loc(e1) = run-event-loc(e2) ∈ Id
Proof
Definitions occuring in Statement :
run-lt: run-lt(r),
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
run-pred_wf,
rel_plus_wf,
runEvents_wf,
infix_ap_wf,
or_wf,
assert_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
is-run-event_wf,
assert_elim,
le_wf,
le_antisymmetry,
nat_plus_subtype_nat,
rel_exp_wf,
pMsg_wf,
run-info_wf,
subtype_rel_self,
subtype_rel_product,
Id_wf,
equal_wf,
le-add-cancel,
add_functionality_wrt_le,
add-commutes,
add-swap,
minus-one-mul,
minus-add,
condition-implies-le,
not-le-2,
false_wf,
nat_wf,
run-event-step_wf,
decidable__lt,
rel_exp_one,
less_than_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}r:pRunType(P.M[P]). \mforall{}e1,e2:runEvents(r).
(e1 = e2) \mvee{} (e1 run-lt(r) e2) \mvee{} (e2 run-lt(r) e1)
supposing run-event-loc(e1) = run-event-loc(e2)
Date html generated:
2015_07_23-AM-11_15_34
Last ObjectModification:
2015_07_16-AM-09_38_36
Home
Index