Nuprl Lemma : run-lt-step-less
∀[M:Type ─→ Type]. ∀[r:pRunType(P.M[P])].
∀[x,y:runEvents(r)]. run-event-step(x) < run-event-step(y) supposing x run-lt(r) y
supposing ∀e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
Proof
Definitions occuring in Statement :
run-lt: run-lt(r),
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRunType: pRunType(T.M[T]),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
pi1: fst(t),
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
run-pred-step-less,
rel_exp_one,
runEvents_wf,
run-pred_wf,
infix_ap_wf,
rel_exp_wf,
false_wf,
le_wf,
nat_plus_properties,
rel_exp_iff,
less_than_transitivity2,
run-event-step_wf,
le_weakening2,
less-iff-le,
le_antisymmetry_iff,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
decidable__le,
not-le-2,
add-swap,
all_wf,
less_than_wf,
nat_plus_wf,
primrec-wf-nat-plus,
nat_plus_subtype_nat,
run-lt_wf,
member-less_than,
nat_wf,
run-info_wf,
Id_wf,
pMsg_wf,
pRunType_wf,
less_than_transitivity1,
subtract_wf,
le_weakening,
squash_wf,
true_wf,
and_wf,
equal_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[r:pRunType(P.M[P])].
\mforall{}[x,y:runEvents(r)]. run-event-step(x) < run-event-step(y) supposing x run-lt(r) y
supposing \mforall{}e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
Date html generated:
2015_07_23-AM-11_15_23
Last ObjectModification:
2015_01_29-AM-00_05_54
Home
Index