C:es_realizer{i:l}. 
R-sub{i:l}
R-sub(C; C)
 (A:es_realizer{i:l}. 
 R-sub{i:l}
 R-sub(C; A)
  (B:es_realizer{i:l}. R-sub{i:l}(C; Rplus(A; B))  R-sub{i:l}(C; Rplus(B; A)))) 

latex

Definitions

guard(T), ff, tt, P  Q, Rplus-right(x1), Rplus-left(x1), Rplus?(x1), True, Rnone?(x1), if b then t else f fi , Y, x. t(x), t  T, P  Q, R-sub{i:l}(A; B), P  Q, x:A. B(x), x(s), Unit, es_realizer{i:l}, Rrframe(loc; x; L), Rbframe(loc; k; L), Raframe(loc; k; L), Rpre(loc; ds; a; p; P), Rsends(ds; knd; T; l; dt; g), Reffect(loc; ds; knd; T; x; f), Rsframe(lnk; tag; L), Rframe(loc; T; x; L), Rinit(loc; T; x; v), prop{i:l}, Rnone, , Rplus(left; right)

Lemmas

Rrframe wf, Rbframe wf, Raframe wf, Rpre wf, Rsends wf, Reffect wf, Rsframe wf, Rframe wf, Rinit wf, Rplus wf, Rnone wf, R-sub wf, es realizer wf, bool wf, finite-prob-space wf, decl-type wf, decl-state wf, fpf wf, IdLnk wf, Knd wf, rationals wf, Id wf, unit wf