let x1, x2, y1, y2 be set ; :: thesis: for E being non empty set
for F being Subset of (E ^omega)
for TS being non empty transition-system of F st TS is deterministic & x1,x2 ==>* y1,TS & x1,x2 ==>* y2,TS holds
y1 = y2
let E be non empty set ; :: thesis: for F being Subset of (E ^omega)
for TS being non empty transition-system of F st TS is deterministic & x1,x2 ==>* y1,TS & x1,x2 ==>* y2,TS holds
y1 = y2
let F be Subset of (E ^omega); :: thesis: for TS being non empty transition-system of F st TS is deterministic & x1,x2 ==>* y1,TS & x1,x2 ==>* y2,TS holds
y1 = y2
let TS be non empty transition-system of F; :: thesis: ( TS is deterministic & x1,x2 ==>* y1,TS & x1,x2 ==>* y2,TS implies y1 = y2 )
assume A1: TS is deterministic ; :: thesis: ( not x1,x2 ==>* y1,TS or not x1,x2 ==>* y2,TS or y1 = y2 )
assume ( x1,x2 ==>* y1,TS & x1,x2 ==>* y2,TS ) ; :: thesis: y1 = y2
then ( x1,x2 ==>* y1, <%> E,TS & x1,x2 ==>* y2, <%> E,TS ) by Def7;
hence y1 = y2 by A1, Th93; :: thesis: verum