let x, y, z be object ; :: thesis: 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 ; :: thesis: 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); :: thesis: 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; :: thesis: ( 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) ; :: thesis: 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; :: thesis: verum