(51steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc

At: vc trace correctness 1
1. A: ioa{i:l}()
2. I: Fmla
3. rho: Decl
4. de: sig()
5. e: {[[de]] rho}
6. te: LabelLabel
7. tc_ioa(A;de)
8. ioa_mentions_trace(A)
9. trace_consistent_pred(rho;A.da;te;I)
10. guarded_trace(A.da;te;I)
11. tc_pred(I;A.ds; < > ;de)
12. covers_pred(A;I)
13. closed_pred(I)
14. single_valued_decls(A.ds)
15. s:[[A]] rho de e.state, tr:([[A.da]] rho) List. ([[A]] rho de e -tr- > s) [[VCs(A;I)]] rho A.ds A.da de e s mk_trace_env(tr, te)

([[A]] rho de e |= always s,tr.[[I]] rho A.ds < > de e s mk_trace_env(tr, te))
By: (BackThru 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))) THENA (Auto THEN (Try TrivialIoaHyp) THEN (Try ((AllHyps Subtype) THEN (Unfold `ioa_mng` 0) THEN (Reduce 0) THEN Easy)))
Generated subgoals:

116. s: [[A]] rho de e.state
17. tr: [[A]] rho de e.action List
[[I]] rho A.ds < > de e s mk_trace_env(tr, te) Prop
2 x:[[A]] rho de e.state. [[A]] rho de e.init(x) [[I]] rho A.ds < > de e x mk_trace_env(nil, te)
3 s0,x:[[A]] rho de e.state, act:[[A]] rho de e.action, x':[[A]] rho de e.state, l:[[A]] rho de e.action List. [[A]] rho de e.init(s0) trace_reachable([[A]] rho de e;s0;l;x) [[I]] rho A.ds < > de e x mk_trace_env(l, te) [[A]] rho de e.trans(x,act,x') [[I]] rho A.ds < > de e x' mk_trace_env(l @ [act], te)

About:
listconsnilboolitapplyfunctionmemberpropimpliesall

(51steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc