let x, y be set ; :: thesis: for E being non empty set
for u, 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,u ==>* y,v,TS holds
x,u ^ w ==>* y,v ^ w,TS
let E be non empty set ; :: thesis: for u, 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,u ==>* y,v,TS holds
x,u ^ w ==>* y,v ^ w,TS
let u, 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,u ==>* y,v,TS holds
x,u ^ w ==>* y,v ^ w,TS
let F be Subset of (E ^omega ); :: thesis: for TS being non empty transition-system of F st x,u ==>* y,v,TS holds
x,u ^ w ==>* y,v ^ w,TS
let TS be non empty transition-system of F; :: thesis: ( x,u ==>* y,v,TS implies x,u ^ w ==>* y,v ^ w,TS )
assume x,u ==>* y,v,TS ; :: thesis: x,u ^ w ==>* y,v ^ w,TS
then ==>.-relation TS reduces [x,u],[y,v] by DefTran;
then ==>.-relation TS reduces [x,(u ^ w)],[y,(v ^ w)] by ThRed70;
hence x,u ^ w ==>* y,v ^ w,TS by DefTran; :: thesis: verum