Thm* M:sm{i:l}(), I:(M.state (M.action List) Prop).
( x:M.state. M.init(x)  I(x,nil)) 
( s0,x:M.state, act:M.action, x':M.state, l:M.action List.
M.init(s0)  trace_reachable(M;s0;l;x)  I(x,l)  M.trans(x,act,x')  I(x',l @ [act]))

(M |= always s,t.I(s,t)) | [trace_inv_induction] |
Thm* M:sm{i:l}(), l1,l2:M.action List, s,s':M.state.
trace_reachable(M;s;l1 @ l2;s')

( x:M.state. trace_reachable(M;s;l1;x) & trace_reachable(M;x;l2;s')) | [trace_reachable_append] |
Def (M |= x,x',tr,tr'.R(x;x';tr;tr'))
== x,x':M.state, tr:M.action List, a:M.action.
(M -tr- > x)  M.trans(x,a,x')  R(x;x';tr;tr @ [a]) | [tla] |