let x, y be object ; :: thesis: for E being non empty set
for e being Element of E
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
for P being RedSequence of ==>.-relation TS st P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] holds
len P = 2
let E be non empty set ; :: thesis: for e being Element of E
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
for P being RedSequence of ==>.-relation TS st P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] holds
len P = 2
let e be Element of E; :: thesis: for F being Subset of (E ^omega)
for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
for P being RedSequence of ==>.-relation TS st P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] holds
len P = 2
let F be Subset of (E ^omega); :: thesis: for TS being non empty transition-system over F st not <%> E in rng (dom the Tran of TS) holds
for P being RedSequence of ==>.-relation TS st P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] holds
len P = 2
let TS be non empty transition-system over F; :: thesis: ( not <%> E in rng (dom the Tran of TS) implies for P being RedSequence of ==>.-relation TS st P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] holds
len P = 2 )
assume A1: not <%> E in rng (dom the Tran of TS) ; :: thesis: for P being RedSequence of ==>.-relation TS st P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] holds
len P = 2
let P be RedSequence of ==>.-relation TS; :: thesis: ( P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] implies len P = 2 )
assume A2: ( P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] ) ; :: thesis: len P = 2
len P <= (len <%e%>) + 1 by A1, A2, Th62;
then len P <= 1 + 1 by AFINSQ_1:34;
then A3: not not len P = 0 & ... & not len P = 2 ;
len P <> 1 by A2, XTUPLE_0:1;
hence len P = 2 by A3; :: thesis: verum