| Rank | Theorem | Name |
| 6 | Thm* the_w:World.
Thm* FairFifo
Thm* 
Thm* ESAxioms{i:l}
Thm* ESAxioms(E;
Thm* ESAxioms(( i,x. vartype(i;x));
Thm* ESAxioms(the_w.M;
Thm* ESAxioms(( e.loc(e));
Thm* ESAxioms(( e.kind(e));
Thm* ESAxioms(( e.val(e));
Thm* ESAxioms(( x,e. (x when e));
Thm* ESAxioms(( x,e. (x after e));
Thm* ESAxioms(( l,e. sends(l;e));
Thm* ESAxioms(( e.sender(e));
Thm* ESAxioms(( e.index(e));
Thm* ESAxioms(( e.first(e));
Thm* ESAxioms(( e.pred(e));
Thm* ESAxioms(( e,e'. e <c e')) | [world-event-system] |
| cites the following: |
| 0 | Thm* the_w:World, e:E. isnull(act(e)) | [w-act-not-null] |
| 1 | Thm* the_w:World, e:E. first(e)  ( t': . t'<time(e)  isnull(a(loc(e);t'))) | [assert-w-first] |
| 0 | Thm* the_w:World, t: , i:Id. first(<i,t>)  pred(<i,t>) E | [w-pred-aux] |
| 0 | Thm* the_w:World, i:Id, t: . first(<i,t>)  | [w-first-aux] |
| 0 | Thm* the_w:World, e:E. <loc(e),time(e)> ~ e | [w-loc-time] |
| 1 | Thm* R:(T T Prop). Trans x,y:T. x R^+ y | [rel_plus_trans] |
| 4 | Thm* the_w:World, e,e':E. FairFifo  e <c e'  time(e)<time(e') | [w-causl-time] |
| 5 | Thm* the_w:World, e:E, t: .
Thm* FairFifo
Thm* 
Thm* isrcv(kind(e))
Thm* 
Thm* match(lnk(kind(e));t;time(e))
Thm* 
Thm* onlnk(lnk(kind(e));m(source(lnk(kind(e)));t))[(||rcvs(lnk(kind(e));time(e))||
Thm* -||snds(lnk(kind(e));t)||)]
Thm* =
Thm* msg(a(loc(e);time(e)))
Thm* Msg | [w-match-property] |
| 0 | Thm* R:(T T Prop), x,y:T. (x R^+ y)  (x R y) ( z:T. (x R^+ z) & (z R y)) | [rel_plus_implies] |
| 0 | Thm* T:Type, P:(T  ), l:T List. filter(P;l) {x:T| P(x) } List | [filter_type] |
| 3 | Thm* the_w:World, e:E.
Thm* FairFifo  isrcv(kind(e))  ( t: time(e). match(lnk(kind(e));t;time(e))) | [w-match-exists] |
| 4 | Thm* i,j: .
Thm* i<j
Thm* 
Thm* ( f:(  T), P:(T  ).
Thm* (P(f(i))  ||filter(P;map(f;upto(i)))||<||filter(P;map(f;upto(j)))||) | [filter_map_upto] |
| 5 | Thm* the_w:World, e,e':E.
Thm* FairFifo  (e <loc e'  loc(e) = loc(e') Id & e <c e') | [w-locl-iff] |
| 0 | Thm* P:(T  ), A:T List, B:Top. filter(P;A @ B) ~ (filter(P;A) @ filter(P;B)) | [filter_append_sq] |
| 1 | Thm* P:(T  ), L2,L1:T List. L1 L2  filter(P;L1) filter(P;L2) | [filter_iseg] |
| 1 | Thm* r: , L:Top List. ||nth_tl(r;L)|| = if r< ||L|| ||L||-r else 0 fi | [general_length_nth_tl] |
| 2 | Thm* i,j: . i j  upto(i) upto(j) | [upto_iseg] |
| 0 | Thm* f:(A B), L1,L2:A List. L1 L2  map(f;L1) map(f;L2) | [iseg_map] |
| 2 | Thm* ll1,ll2:(T List) List. ll1 ll2  concat(ll1) concat(ll2) | [concat_iseg] |
| 1 | Thm* l1,l2:T List. l1 l2  ||l1|| ||l2|| | [iseg_length] |
| 0 | Thm* f,as':Top, A:Type, as:A List. map(f;as @ as') ~ (map(f;as) @ map(f;as')) | [map_append_sq] |
| 0 | Thm* l:T List. (l @ nil) ~ l | [append_nil_sq] |
| 0 | Thm* l:Top List, ll:(Top List) List. concat([l / ll]) ~ (l @ concat(ll)) | [concat-cons] |
| 1 | Thm* ll1,ll2:(Top List) List. concat(ll1 @ ll2) ~ (concat(ll1) @ concat(ll2)) | [concat_append] |
| 0 | Thm* as,bs:T List. ||as @ bs|| = ||as||+||bs||  | [length_append] |
| 1 | Thm* t',m: , T:Type, f:(  T), P:(T  ).
Thm* m+1 ||filter(P;map(f;upto(t')))||
Thm* 
Thm* ( t: . P(f(t)) & ||filter(P;map(f;upto(t)))|| = m ) | [filter_map_upto2] |
| 0 | Thm* the_w:World, l:IdLnk, t,t': .
Thm* match(l;t;t')
Thm* 
Thm* ||snds(l;t)|| ||rcvs(l;t')||
Thm* & ||rcvs(l;t')||<||snds(l;t)||+||onlnk(l;m(source(l);t))|| | [assert-w-match] |
| 0 | Thm* w:World, t: , l:IdLnk, i:Id. ||onlnk(l;m(i;t))||  | [w-onlnk-m] |
| 0 | Thm* f:(   ). ( n: . f(n))  f(mu(f)) & ( i: . i<mu(f)  f(i)) | [mu-property] |
| 4 | Thm* the_w:World, e:E, t,t': .
Thm* FairFifo
Thm* 
Thm* isrcv(kind(e))
Thm* 
Thm* match(lnk(kind(e));t;time(e))  match(lnk(kind(e));t';time(e))  t = t' | [w-match-unique] |