let x, y be set ; :: thesis: for E being non empty set
for u, v being Element of E ^omega
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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
let E be non empty set ; :: thesis: for u, v being Element of E ^omega
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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
let u, v be Element of E ^omega ; :: 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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
let TS be non empty transition-system of F; :: thesis: ( not <%> E in rng (dom the Tran of TS) & [[x,u],[y,v]] in ==>.-relation TS implies len u > len v )
assume A: not <%> E in rng (dom the Tran of TS) ; :: thesis: ( not [[x,u],[y,v]] in ==>.-relation TS or len u > len v )
assume [[x,u],[y,v]] in ==>.-relation TS ; :: thesis: len u > len v
then x,u ==>. y,v,TS by DefRel;
hence len u > len v by A, ThDir50; :: thesis: verum