let x, y be set ; :: 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 of 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 of 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 of 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 of 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 of F; :: thesis: ( not <%> E in rng (dom the Tran of TS) & ==>.-relation TS reduces [x,u],[y,u] implies x = y )
assume A: 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 A, ThRed110;
hence x = y ; :: thesis: verum