let x1, x2, y1, y2 be set ; :: thesis: for E being non empty set
for F being Subset of (E ^omega )
for TS being non empty transition-system of F st x1,x2 ==>. y1,y2,TS holds
x1,x2 ==>* y1,y2,TS
let E be non empty set ; :: thesis: for F being Subset of (E ^omega )
for TS being non empty transition-system of F st x1,x2 ==>. y1,y2,TS holds
x1,x2 ==>* y1,y2,TS
let F be Subset of (E ^omega ); :: thesis: for TS being non empty transition-system of F st x1,x2 ==>. y1,y2,TS holds
x1,x2 ==>* y1,y2,TS
let TS be non empty transition-system of F; :: thesis: ( x1,x2 ==>. y1,y2,TS implies x1,x2 ==>* y1,y2,TS )
assume x1,x2 ==>. y1,y2,TS ; :: thesis: x1,x2 ==>* y1,y2,TS
then ==>.-relation TS reduces [x1,x2],[y1,y2] by ThRed83;
hence x1,x2 ==>* y1,y2,TS by DefTran; :: thesis: verum