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 transition-system over F st not <%> E in rng (dom the Tran of TS) & x,u ==>. y,v,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 transition-system over F st not <%> E in rng (dom the Tran of TS) & x,u ==>. y,v,TS holds
len u > len v
let u, v be Element of E ^omega ; for F being Subset of (E ^omega)
for TS being transition-system over F st not <%> E in rng (dom the Tran of TS) & x,u ==>. y,v,TS holds
len u > len v
let F be Subset of (E ^omega); for TS being transition-system over F st not <%> E in rng (dom the Tran of TS) & x,u ==>. y,v,TS holds
len u > len v
let TS be transition-system over F; ( not <%> E in rng (dom the Tran of TS) & x,u ==>. y,v,TS implies len u > len v )
assume A1:
not <%> E in rng (dom the Tran of TS)
; ( not x,u ==>. y,v,TS or len u > len v )
assume A2:
x,u ==>. y,v,TS
; len u > len v
then consider w being Element of E ^omega such that
A3:
x,w -->. y,TS
and
A4:
u = w ^ v
;
A5:
w in rng (dom the Tran of TS)
by A3, Th15;