let x, y be object ; :: thesis: 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 ; :: thesis: 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 ; :: thesis: 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); :: thesis: 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; :: thesis: ( 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) ; :: thesis: ( not ==>.-relation TS reduces [x,u],[y,u] or x = y )
assume ==>.-relation TS reduces [x,u],[y,u] ; :: thesis: x = y
then ( len u > len u or x = y ) by A1, Th77;
hence x = y ; :: thesis: verum