let x, y be set ; :: thesis: for E being non empty set
for u, v 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,TS holds
x,u ^ v ==>* y,v,TS
let E be non empty set ; :: thesis: for u, v 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,TS holds
x,u ^ v ==>* y,v,TS
let u, v 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,TS holds
x,u ^ v ==>* y,v,TS
let F be Subset of (E ^omega ); :: thesis: for TS being non empty transition-system of F st x,u ==>* y,TS holds
x,u ^ v ==>* y,v,TS
let TS be non empty transition-system of F; :: thesis: ( x,u ==>* y,TS implies x,u ^ v ==>* y,v,TS )
assume x,u ==>* y,TS ; :: thesis: x,u ^ v ==>* y,v,TS
then x,u ==>* y, <%> E,TS by DefAcc;
then x,u ^ v ==>* y,(<%> E) ^ v,TS by ThTran30;
hence x,u ^ v ==>* y,v,TS by AFINSQ_1:32; :: thesis: verum