let x, y be object ; for E being non empty set
for u 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) & ==>.-relation TS reduces [x,u],[y,u] holds
x = y
let E be non empty set ; for u 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) & ==>.-relation TS reduces [x,u],[y,u] holds
x = y
let u 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) & ==>.-relation TS reduces [x,u],[y,u] holds
x = y
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) & ==>.-relation TS reduces [x,u],[y,u] holds
x = y
let TS be non empty transition-system over F; ( not <%> E in rng (dom the Tran of TS) & ==>.-relation TS reduces [x,u],[y,u] implies x = y )
assume A1:
not <%> E in rng (dom the Tran of TS)
; ( not ==>.-relation TS reduces [x,u],[y,u] or x = y )
assume
==>.-relation TS reduces [x,u],[y,u]
; x = y
then
( len u > len u or x = y )
by A1, Th77;
hence
x = y
; verum