is mentioned by
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}(), 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] |
Thm* M:sm{i:l}(), a:M.action, s,s':M.state. trace_reachable(M;s;[a];s') M.trans(s,a,s') | [trace_reachable_one] |
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:(Ism{i:l}()), j:I, x:i:IM(i).action. x M(j).action | [small_action] |
Thm* M:sm{i:l}(). M.trans M.stateM.actionM.stateProp | [sm_trans_wf] |
Thm* M:sm{i:l}(), a:M.action. kind(a) Label & kind(a) Pattern | [kind_wf2] |
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] |
Def (M |= always s,t.P(s;t)) == t:M.action List, s0,s:M.state. M.init(s0) trace_reachable(M;s0;t;s) P(s;t) | [trace_inv] |
Try larger context: GenAutomata