Nuprl Lemma : member-prior-run-events
∀[M:Type ⟶ Type]. ∀r:pRunType(P.M[P]). ∀t:ℕ. ∀e:runEvents(r). ((e ∈ prior-run-events(r;t)) ⇐⇒ run-event-step(e) < t)
Proof
Definitions occuring in Statement :
prior-run-events: prior-run-events(r;t),
run-event-step: run-event-step(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
l_member: (x ∈ l),
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prior-run-events: prior-run-events(r;t),
run-event-step: run-event-step(e),
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
pRunType: pRunType(T.M[T]),
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
top: Top,
cand: A c∧ B,
runEvents: runEvents(r),
pi1: fst(t),
pi2: snd(t),
outl: outl(x),
isl: isl(x),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
is-run-event: is-run-event(r;t;x),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
spreadn: spread3,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
squash: ↓T,
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
sq_stable: SqStable(P),
true: True
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}r:pRunType(P.M[P]). \mforall{}t:\mBbbN{}. \mforall{}e:runEvents(r).
((e \mmember{} prior-run-events(r;t)) \mLeftarrow{}{}\mRightarrow{} run-event-step(e) < t)
Date html generated:
2016_05_17-AM-10_47_44
Last ObjectModification:
2016_01_18-AM-00_16_04
Theory : process-model
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