let x, y, z be object ; for E being non empty set
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
not [[x,z],[y,z]] in ==>.-relation TS
let E be non empty set ; for F being Subset of (E ^omega)
for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
not [[x,z],[y,z]] in ==>.-relation TS
let F be Subset of (E ^omega); for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
not [[x,z],[y,z]] in ==>.-relation TS
let TS be non empty transition-system over F; ( not <%> E in rng (dom the Tran of TS) implies not [[x,z],[y,z]] in ==>.-relation TS )
assume
not <%> E in rng (dom the Tran of TS)
; not [[x,z],[y,z]] in ==>.-relation TS
then
not x,z ==>. y,z,TS
by Th28;
hence
not [[x,z],[y,z]] in ==>.-relation TS
by Def4; verum