let x, y be set ; :: thesis: for E being non empty set
for u, w, v being Element of E ^omega
for TS being non empty transition-system of (Lex E) \/ {(<%> E)} st x,u ^ w ==>* y,v ^ w,TS holds
x,u ==>* y,v,TS
let E be non empty set ; :: thesis: for u, w, v being Element of E ^omega
for TS being non empty transition-system of (Lex E) \/ {(<%> E)} st x,u ^ w ==>* y,v ^ w,TS holds
x,u ==>* y,v,TS
let u, w, v be Element of E ^omega ; :: thesis: for TS being non empty transition-system of (Lex E) \/ {(<%> E)} st x,u ^ w ==>* y,v ^ w,TS holds
x,u ==>* y,v,TS
let TS be non empty transition-system of (Lex E) \/ {(<%> E)}; :: thesis: ( x,u ^ w ==>* y,v ^ w,TS implies x,u ==>* y,v,TS )
assume x,u ^ w ==>* y,v ^ w,TS ; :: thesis: x,u ==>* y,v,TS
then ==>.-relation TS reduces [x,(u ^ w)],[y,(v ^ w)] by REWRITE3:def 6;
then ==>.-relation TS reduces [x,u],[y,v] by ThTS3k'a;
hence x,u ==>* y,v,TS by REWRITE3:def 6; :: thesis: verum