Thm* E:EventStruct, tr:|E| List, ls: ||tr||.
is-send(E)(tr[ls]) 
( j: ||tr||. ls < j  is-send(E)(tr[j])) 
( i,j: ||tr||. i j  is-send(E)(tr[j])  (i (switchR(tr)^*) ls)  (j (switchR(tr)^*) ls)) | [switch_inv_rel_closure_lemma1] |
Thm* E:TaggedEventStruct, tr:|E| List, ls: ||tr||.
switch_inv(E)(tr) 
( i,j: ||tr||. (i (switchR(tr)^*) ls)  (j (switchR(tr)^*) ls)  tag(E)(tr[i]) = tag(E)(tr[j])) | [switch_inv_rel_closure] |
Thm* E:TaggedEventStruct, tr:|E| List.
switch_inv(E)(tr)  ( i,j: ||tr||. (i switchR(tr) j)  tag(E)(tr[i]) = tag(E)(tr[j])) | [switch_inv_rel_same_tag] |
Thm* E:EventStruct, tr:|E| List, ls,i: ||tr||.
is-send(E)(tr[ls])  (i (switchR(tr)^*) ls)  is-send(E)(tr[i]) | [switch_inv_rel_closure_send] |
Thm* E:EventStruct, x:|E| List, j,z: ||x||. Dec(j switchR(x) z) | [decidable__switch_inv_rel] |