Thm* M:sm{i:l}(), P:(M.state (M.action List) Prop).
(M |= always s,t.P(s,t))  (M |= s,t.P(s,t) while True) & (M |= initially s,t.P(s,t)) | [trace_inv_as_while] |
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}(), l:M.action List, s,s':M.state.
trace_reachable(M;s;l;s') Prop | [trace_reachable_wf] |
Thm* M:sm{i:l}(). M.trans M.state M.action M.state Prop | [sm_trans_wf] |
Thm* M:sm{i:l}(). M.init M.state Prop | [sm_init_wf] |
Def sm{i:l}() == da:Decl ds:Decl ({ds} Prop) ({ds} ( da) {ds} Prop) | [sm] |