let x, y be object ; 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 over 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 ; for u, v being Element of E ^omega
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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
let u, v be Element of E ^omega ; 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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
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) & [[x,u],[y,v]] in ==>.-relation TS holds
len u > len v
let TS be non empty transition-system over F; ( not <%> E in rng (dom the Tran of TS) & [[x,u],[y,v]] in ==>.-relation TS implies len u > len v )
assume A1:
not <%> E in rng (dom the Tran of TS)
; ( not [[x,u],[y,v]] in ==>.-relation TS or len u > len v )
assume
[[x,u],[y,v]] in ==>.-relation TS
; len u > len v
then
x,u ==>. y,v,TS
by Def4;
hence
len u > len v
by A1, Th29; verum