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 x,v -->. y,TS holds
==>.-relation TS reduces [x,(v ^ w)],[y,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 x,v -->. y,TS holds
==>.-relation TS reduces [x,(v ^ w)],[y,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 x,v -->. y,TS holds
==>.-relation TS reduces [x,(v ^ w)],[y,w]
let F be Subset of (E ^omega); :: thesis: for TS being non empty transition-system over F st x,v -->. y,TS holds
==>.-relation TS reduces [x,(v ^ w)],[y,w]
let TS be non empty transition-system over F; :: thesis: ( x,v -->. y,TS implies ==>.-relation TS reduces [x,(v ^ w)],[y,w] )
assume x,v -->. y,TS ; :: thesis: ==>.-relation TS reduces [x,(v ^ w)],[y,w]
then <*[x,(v ^ w)],[y,w]*> is RedSequence of ==>.-relation TS by Th58;
then [[x,(v ^ w)],[y,w]] in ==>.-relation TS by Th8;
hence ==>.-relation TS reduces [x,(v ^ w)],[y,w] by REWRITE1:15; :: thesis: verum