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,TS holds
x,v ^ w ==>* y,w,TS
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,TS holds
x,v ^ w ==>* y,w,TS
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,TS holds
x,v ^ w ==>* y,w,TS
let F be Subset of (E ^omega ); :: thesis: for TS being non empty transition-system of F st x,v -->. y,TS holds
x,v ^ w ==>* y,w,TS
let TS be non empty transition-system of F; :: thesis: ( x,v -->. y,TS implies x,v ^ w ==>* y,w,TS )
assume x,v -->. y,TS ; :: thesis: x,v ^ w ==>* y,w,TS
then ==>.-relation TS reduces [x,(v ^ w)],[y,w] by ThRed82;
hence x,v ^ w ==>* y,w,TS by DefTran; :: thesis: verum