is mentioned by

Thm* E:TaggedEventStruct, x:|E| List, i:(||x||-1). switch_inv(E)(x) is-send(E)(x[(i+1)]) is-send(E)(x[i]) loc(E)(x[i]) = loc(E)(x[(i+1)]) switch_inv(E)(swap(x;i;i+1))	[switch_inv_swap]
Thm* E:EventStruct, a,b:|E|, tr:|E| List. a somewhere delivered before b (k:||tr||. a delivered at time k (k':||tr||. k' < k & b delivered at time k' & loc(E)(tr[k']) = loc(E)(tr[k])))	[not_delivered_before_somewhere]
Thm* E:EventStruct, tr:|E| List. No-dup-deliver(E)(tr) (x,y:|E|. is-send(E)(x) is-send(E)(y) (y =msg=(E) x) loc(E)(x) = loc(E)(y) sublist(|E|;[x; y];tr))	[P_no_dup_iff]
Def switch_inv(E)(tr) == i,j,k:||tr||. i < j (is-send(E)(tr[i])) (is-send(E)(tr[j])) tag(E)(tr[i]) = tag(E)(tr[j]) tr[j] delivered at time k (k':||tr||. k' < k & tr[i] delivered at time k' & loc(E)(tr[k']) = loc(E)(tr[k]))	[switch_inv]
Def asyncR(E) == swap adjacent[loc(E)(x) = loc(E)(y) & (is-send(E)(x)) & (is-send(E)(y)) (is-send(E)(x)) & (is-send(E)(y))]	[R_async]
Def AD-normal(E)(tr) == i:(||tr||-1). ((is-send(E)(tr[i])) (is-send(E)(tr[(i+1)])) (tr[i] =msg=(E) tr[(i+1)])) & ((x,y:||tr||. x < y & (is-send(E)(tr[x])) & (is-send(E)(tr[y])) & tr[x] delivered at time i+1 & tr[y] delivered at time i) loc(E)(tr[i]) = loc(E)(tr[(i+1)]))	[switch_normal]
Def x somewhere delivered before y == k:||tr||. x delivered at time k & (k':||tr||. y delivered at time k' loc(E)(tr[k']) = loc(E)(tr[k]) kk')	[delivered_before_somewhere]
Def R_ad_normal(tr)(a,b) == ((is-send(E)(a)) (is-send(E)(b)) (a =msg=(E) b)) & ((is-send(E)(a)) (is-send(E)(b)) (x,y:||tr||. x < y & (is-send(E)(tr[x])) & (is-send(E)(tr[y])) & (tr[x] =msg=(E) b) & (tr[y] =msg=(E) a)) loc(E)(a) = loc(E)(b))	[R_ad_normal]
Def No-dup-deliver(E)(tr) == i,j:||tr||. (is-send(E)(tr[i])) (is-send(E)(tr[j])) (tr[j] =msg=(E) tr[i]) loc(E)(tr[i]) = loc(E)(tr[j]) i = j	[P_no_dup]
Def tr delivered at p == filter(e.is-send(E)(e)loc(E)(e) = p;tr)	[deliveries_at]
Def switch_inv(E; tr) == i,j,k:||tr||. i < j (is-send(E)(tr[i])) (is-send(E)(tr[j])) tag(E)(tr[i]) = tag(E)(tr[j]) (tr[j] =msg=(E) tr[k]) (is-send(E)(tr[k])) (k':||tr||. k' < k & loc(E)(tr[k']) = loc(E)(tr[k]) & (tr[i] =msg=(E) tr[k']) & (is-send(E)(tr[k'])))	[switch_inv2001_03_15_DASH_PM_DASH_12_53_21]

In prior sections: mb structures

Try larger context: GenAutomata