let x, y be object ; :: thesis: for E being non empty set
for v, w being Element of E ^omega
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st ==>.-relation TS reduces [x,v],[y,w] holds
ex u being Element of E ^omega st v = u ^ w
let E be non empty set ; :: thesis: for v, w being Element of E ^omega
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st ==>.-relation TS reduces [x,v],[y,w] holds
ex u being Element of E ^omega st v = u ^ w
let v, w be Element of E ^omega ; :: thesis: for F being Subset of (E ^omega)
for TS being non empty transition-system over F st ==>.-relation TS reduces [x,v],[y,w] holds
ex u being Element of E ^omega st v = u ^ w
let F be Subset of (E ^omega); :: thesis: for TS being non empty transition-system over F st ==>.-relation TS reduces [x,v],[y,w] holds
ex u being Element of E ^omega st v = u ^ w
let TS be non empty transition-system over F; :: thesis: ( ==>.-relation TS reduces [x,v],[y,w] implies ex u being Element of E ^omega st v = u ^ w )
assume ==>.-relation TS reduces [x,v],[y,w] ; :: thesis: ex u being Element of E ^omega st v = u ^ w
then ex P being RedSequence of ==>.-relation TS st
( P . 1 = [x,v] & P . (len P) = [y,w] ) by REWRITE1:def 3;
hence ex u being Element of E ^omega st v = u ^ w by Th53; :: thesis: verum