Def |R| == {i:Id| (R(i)) }

is mentioned by

Thm* T:(Id), to,from:(|T|(IdLnk List)), f:(Edge(T)). Thm* bi-tree(T;to;from) Thm*  Thm* spanner(f;T;to;from) Thm*  Thm* (i,j:|T|. Thm* (spanner-root(f;T;to;from;i)  spanner-root(f;T;to;from;j)  i = j)	[spanner-root-unique]
Thm* T:(Id), to,from:(|T|(IdLnk List)), f:(Edge(T)). Thm* bi-tree(T;to;from) Thm*  Thm* spanner(f;T;to;from)  (i:|T|. spanner-root(f;T;to;from;i))	[spanner-root-exists]
Thm* T:(Id), to,from:(|T|(IdLnk List)), f:(Edge(T)). Thm* bi-graph(T;to;from)  spanner(f;T;to;from)  Prop	[spanner_wf]
Thm* T:(Id), to,from:(|T|(IdLnk List)). Thm* bi-tree(T;to;from)  (n:. p:Edge(T) List. lpath(p)  ||p||n)	[bi-tree-diameter]
Thm* G:(Id), to,from:(|G|(IdLnk List)). bi-tree(G;to;from)  Prop	[bi-tree_wf]
Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|. Thm* bi-graph(G;to;from)  ((inverse(e)  from(i))  destination(e) = i)	[edge-inv-from]
Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|. Thm* bi-graph(G;to;from)  ((inverse(e)  to(i))  source(e) = i)	[edge-inv-to]
Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|. Thm* bi-graph(G;to;from)  ((e  from(i))  source(e) = i)	[edge-from]
Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|. Thm* bi-graph(G;to;from)  ((e  to(i))  destination(e) = i)	[edge-to]
Thm* G:(Id), to,from:(|G|(IdLnk List)), l:Edge(G). Thm* bi-graph(G;to;from)  inverse(l)  Edge(G)	[bi-graph-inv_wf]
Thm* G:(Id), to,from:(|G|(IdLnk List)), i:|G|. Thm* bi-graph(G;to;from)  from(i)  Edge(G) List	[bi-graph-from_wf]
Thm* G:(Id), to,from:(|G|(IdLnk List)), i:|G|. Thm* bi-graph(G;to;from)  to(i)  Edge(G) List	[bi-graph-to_wf]
Thm* T:(Id), to,from:(|T|(IdLnk List)), u:Edge(T). Thm* bi-graph(T;to;from)  destination(u)  |T|	[dst-edge]
Thm* T:(Id), to,from:(|T|(IdLnk List)), u:Edge(T). Thm* bi-graph(T;to;from)  source(u)  |T|	[src-edge]
Thm* G:(Id), to,from:(|G|(IdLnk List)), l:Edge(G). Thm* bi-graph(G;to;from)  lnk-inv(l)  Edge(G)	[inv-is-edge]
Thm* G:(Id), to,from:(|G|(IdLnk List)). bi-graph(G;to;from)  Prop	[bi-graph_wf]
Thm* R:(Id), uid:(|R|), out,in:(|R|IdLnk). Thm* ring(R;in;out) Thm*  Thm* Inj(|R|; ; uid) Thm*  Thm* loc.(ring-leader1(loc;R;uid;out;in))  Thm* realizes es.ldr:|R|.  Thm* realizes es.e@ldr.kind(e) = locl("leader") Thm* realizes es.& (i:|R|. e@i.kind(e) = locl("leader")  i = ldr  |R|)	[ring-leader1__realizes]
Thm* R:(Id), uid:(|R|), out,in:(|R|IdLnk). Thm* ring(R;in;out) Thm*  Thm* Inj(|R|; ; uid)  d-feasible(loc.(ring-leader1(loc;R;uid;out;in)))	[ring-leader1__feasible]
Thm* loc:Id, R:(Id), uid:(|R|), out,in:(|R|IdLnk). Thm* ring(R;in;out) Thm*  Thm* Inj(|R|; ; uid)  ring-leader1(loc;R;uid;out;in)  MsgA List	[ring-leader1_wf]
Thm* loc:Id, R:(Id), uid:(|R|), out,in:(|R|IdLnk). Thm* ring(R;in;out) Thm*  Thm* Inj(|R|; ; uid)  (A,Bring-leader1(loc;R;uid;out;in).A ||+ B)	[ring-leader1__compatible]
Thm* R:(Id), x,y:|R|. Dec(x = y)	[decidable__rset_equal]
Thm* R:(Id). SQType(|R|)	[rset_sq]
Thm* R:(Id), in,out:(|R|IdLnk). Thm* ring(R;in;out)  (L:|R| List. 0<||L|| & (i:|R|. (i  L)))	[ring-list]
Thm* R:(Id), in,out:(|R|IdLnk), i,j:|R|. Thm* ring(R;in;out)  i = p(j)  d(i;p(j)) = d(i;j)-1	[rdist-rprev]
Thm* R:(Id), in,out:(|R|IdLnk). Thm* ring(R;in;out)  (i,j:|R|. n(i) = n(j)  i = j)	[rnext-one-one]
Thm* R:(Id), in,out:(|R|IdLnk), j:|R|. ring(R;in;out)  n(p(j)) = j	[rnext-rprev]
Thm* R:(Id), in,out:(|R|IdLnk), i,j:|R|. Thm* ring(R;in;out) Thm*  Thm* x.n(x)^d(i;j)(i) = j & (k:. k<d(i;j)  x.n(x)^k(i) = j)	[rdist-property]
Thm* R:(Id), in,out:(|R|IdLnk), i,j:|R|. ring(R;in;out)  d(i;j)	[rdist_wf]
Thm* R:(Id), in,out:(|R|IdLnk), i:|R|. ring(R;in;out)  p(i)  |R|	[rprev_wf]
Thm* R:(Id), in,out:(|R|IdLnk), i:|R|. ring(R;in;out)  n(i)  |R|	[rnext_wf]
Thm* R:(Id), in,out:(|R|IdLnk). ring(R;in;out)  Prop	[ring_wf]
Def spanner(f;T;to;from) Def == (l:Edge(T). f(l) = f(inverse(l))) Def == & (i:|T|, l1,l2:Edge(T). Def == & ((l1  to(i)) Def == & ( Def == & ((l2  to(i))  l1 = l2  IdLnk  (f(l1))  (f(l2)))	[spanner]
Def bi-tree(T;to;from) Def == bi-graph(T;to;from) Def == & (i,j:|T|. Def == & (p:Edge(T) List.  Def == & (lconnects(p;i;j) & (q:Edge(T) List. lconnects(q;i;j)  q = p)) Def == & (L:|T| List. i:|T|. (i  L)) Def == & |T|	[bi-tree]
Def Edge(G) == {l:IdLnk| i:|G|. (l  from(i)) }	[bi-graph-edge]
Def bi-graph(G;to;from) Def == i:|G|.  Def == (lto(i).destination(l) = i Def == & (G(source(l))) Def == & (l  from(source(l))) Def == & (lnk-inv(l)  from(i))) Def == & (lfrom(i).source(l) = i Def == & & (G(destination(l))) Def == & & (l  to(destination(l))) Def == & & (lnk-inv(l)  to(i)))	[bi-graph]
Def ring(R;in;out) Def == (i:|R|.  Def == ((R(source(in(i)))) & (R(destination(out(i)))) Def == (& source(out(i)) = i Def == (& & destination(in(i)) = i Def == (& & in(destination(out(i))) = out(i)  IdLnk Def == (& & out(source(in(i))) = in(i)  IdLnk) Def == & (i,j:|R|. k:. x.destination(out(x))^k(i) = j  Id) Def == & |R|	[ring]

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