let x, z, y be set ; :: thesis: for E being non empty set
for F being Subset of (E ^omega )
for TS being non empty transition-system of 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 of 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 of 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 of 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 ThDir60;
hence not [[x,z],[y,z]] in ==>.-relation TS by DefRel; :: thesis: verum