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,v]] in ==>.-relation TS holds
ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ 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 non empty transition-system of F st [[x,u],[y,v]] in ==>.-relation TS holds
ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v )
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,v]] in ==>.-relation TS holds
ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v )
let F be Subset of (E ^omega ); :: thesis: for TS being non empty transition-system of F st [[x,u],[y,v]] in ==>.-relation TS holds
ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v )
let TS be non empty transition-system of F; :: thesis: ( [[x,u],[y,v]] in ==>.-relation TS implies ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v ) )
assume [[x,u],[y,v]] in ==>.-relation TS ; :: thesis: ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v )
then x,u ==>. y,v,TS by DefRel;
hence ex w being Element of E ^omega st
( x,w -->. y,TS & u = w ^ v ) by ThDir25; :: thesis: verum