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 transition-system of F st x,u ==>. y,v,TS holds
len u >= len v
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 transition-system of F st x,u ==>. y,v,TS holds
len u >= len v
let u, v be Element of E ^omega ; :: thesis: for F being Subset of (E ^omega)
for TS being transition-system of F st x,u ==>. y,v,TS holds
len u >= len v
let F be Subset of (E ^omega); :: thesis: for TS being transition-system of F st x,u ==>. y,v,TS holds
len u >= len v
let TS be transition-system of F; :: thesis: ( x,u ==>. y,v,TS implies len u >= len v )
assume x,u ==>. y,v,TS ; :: thesis: len u >= len v
then ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v ) by Th22;
hence len u >= len v by Th9; :: thesis: verum