T:Type, l:IdLnk, ds1, ds2:x:Id fp Type, P:(State(ds1)Prop), Q:(State(ds2)Prop),
f:(State(ds1)T).
Normal(T)
 Normal(ds1)
 Normal(ds2)
 destination(l) = source(l)  Id
 (s:State(ds1). Dec(k:. P(s,k)))
 (s:State(ds2). Dec(k:. Q(s,k)))
 (s:State(ds1), k:. Dec(P(s,k)))
 (s:State(ds2), k:. Dec(Q(s,k)))
 R-Feasible(sendMinimalR{a:ut2, tg:ut2}
 R-Feasible(sendMinimalR(T; l; ds1; ds2; P; Q; f)) 

latex

Definitions

x:A. B(x), Prop, P  Q, x:A. B(x), x(s1,s2), t  T, x. t(x), Id, , Normal(T), A, P & Q, sendMinimalR{$a:ut2, $tg:ut2}(T; l; ds1; ds2; P; Q; f), (L), at src(l):action $a(m) precondition P sends [$tg,f] on link l, (x,yL.P(x;y)), A || B, xL. P(x), A & B, AB, False, IdDeq, Top, ||as||, l[i], Y, SQType(T), {T}, hd(l), nth_tl(n;as), if b t else f fi, ij, tl(l), b, i<j, true, false, "$x", locl(a), reduce(f;k;as), DeclaredType(ds;x), Rplus?(x1), Rplus-left(x1), Rplus-right(x1), Rnone?(x1), True, a = b, R-loc(R), Rds(R), Rda(R), p = q, R-base-domain(R), R-frame-compat(A;B), R-interface-compat(A;B), p  q, i=j, 1of(t), p  q, 2of(t), Reffect?(x1), Rframe?(x1), Rframe-x(x1), Reffect-x(x1), Reffect-knd(x1), Rframe-L(x1), Raframe?(x1), Raframe-k(x1), Raframe-L(x1), Rrframe?(x1), b, Rrframe-x(x1), Reffect-ds(x1), Rrframe-L(x1), Rsends?(x1), Rsframe?(x1), Rsframe-lnk(x1), Rsends-l(x1), Rsframe-tag(x1), map(f;as), Rsends-g(x1), Rsends-knd(x1), Rsframe-L(x1), Rbframe?(x1), Rbframe-k(x1), Rbframe-L(x1), Rsends-ds(x1), Rpre?(x1), Rpre-ds(x1), Rpre-a(x1), let x = a in b(x), isrcv(k), Rsends-dt(x1), Reffect-T(x1), Rsends-T(x1), eqof(d), Atom2Deq, eq_atom$n(x;y), P  Q, P  Q, T, isl(x), x(s), State(ds), Dec(P), Realizer, {i..j}, P  Q, (x  l), , Unit,

Lemmas

decidable-min-lemma, lsrc-inv, decl-state wf, nat wf, decidable wf, not wf, Id wf, ldst wf, lsrc wf, normal-ds wf, normal-type wf, fpf wf, IdLnk wf, R-feasible-Rlist, weakPrecondSendR wf, le wf, decidable int equal, int seg wf, R-compat-Rplus-sq, Rpre wf, Rplus wf, Rsends wf, locl wf, fpf-single wf, fpf-cap-single1, id-deq wf, decl-type wf, Rsframe wf, Knd wf, Rnone wf, R-compat-symmetry, eq id wf, bool wf, iff transitivity, assert wf, eqtt to assert, assert-eq-id, bnot wf, eqff to assert, assert of bnot, not functionality wrt iff, R-compat-none, assert of band, and functionality wrt iff, assert-eq-lnk, assert-eq-knd, squash wf, true wf, bnot thru band, assert of bor, or functionality wrt iff, weakPrecondSendR feasible, R-Feasible wf, l member wf