let x, y be set ; :: 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 of F st x,v ==>* y,w,TS 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 of F st x,v ==>* y,w,TS 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 of F st x,v ==>* y,w,TS 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 of F st x,v ==>* y,w,TS holds
ex u being Element of E ^omega st v = u ^ w
let TS be non empty transition-system of F; :: thesis: ( x,v ==>* y,w,TS implies ex u being Element of E ^omega st v = u ^ w )
assume x,v ==>* y,w,TS ; :: thesis: ex u being Element of E ^omega st v = u ^ w
then ==>.-relation TS reduces [x,v],[y,w] by DefTran;
hence ex u being Element of E ^omega st v = u ^ w by ThRed60; :: thesis: verum