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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
run-lt: run-lt(r),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
infix_ap: x f y,
runEvents: runEvents(r),
top: Top,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
run-event-step: run-event-step(e),
pi1: fst(t),
run-event-loc: run-event-loc(e),
pi2: snd(t),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
and: P ∧ Q,
rel_plus: R+,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
run-pred: run-pred(r),
cand: A c∧ B,
le: A ≤ B
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:
2016_05_17-AM-10_50_44
Last ObjectModification:
2016_01_18-AM-00_12_42
Theory : process-model
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