Thm*  E:EventStruct, P:TraceProperty(E), A:Type, evt:(A  |E|)
, tg:(ALabel), tr_u:Trace(E), tr_l:A List.
switchable(E)(P)  
No-dup-send(E)(tr_u)
full_switch_inv(E;A;evt;tg;tr_u;tr_l) (m:Label. P(map(evt; < tr_l > _m))) P(tr_u) | [switch_main_theorem] |
Thm* E:TaggedEventStruct, tr:Trace(E).
(switch_inv(E)  No-dup-send(E))(tr)
( tr':Trace(E). switch_inv(E)(tr') & AD-normal(E)(tr') & (tr adR(E) tr')) | [switch_normal_exists] |
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Thm* E:TaggedEventStruct, P,I,J,K:TraceProperty(E)
, R:(Trace(E)Trace(E)Prop).
tag_splitable(E;R)
(tr_1,tr_2:Trace(E). (tr_1 R tr_2) (tr_2 R tr_1))
R preserves P
R preserves K
(tr:Trace(E). (I K)(tr) (tr':Trace(E). I(tr') & J(tr') & (tr R tr')))
(((I J) K) fuses P) ((I K) fuses P) | [normal_form_fusion] |
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Def I fuses P == tr:Trace(E). (m:Label. P( < tr > _m)) I(tr) P(tr) | [fusion_condition] |
Def single-tag-decomposable(E)(L)
==  L = nil  |E| List
(L_1,L_2:Trace(E).
L = (L_1 @ L_2) |E| List
& L_2 = nil |E| List
& (xL_1.(yL_2. (x =msg=(E) y)))
& (m:Label. (xL_2.tag(E)(x) = m))) | [single_tag_decomposable] |