let x, y be set ; :: 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 of 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 of 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 of 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 of 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 of 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 A: 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 B: ( P . 1 = [x,<%e%>] & P . (len P) = [y,(<%> E)] ) ; :: thesis: len P = 2
C: len P <> 1 by B, ZFMISC_1:33;
len P <= (len <%e%>) + 1 by A, B, ThRedSeq90;
then len P <= 1 + 1 by AFINSQ_1:38;
hence len P = 2 by C, NAT_1:27; :: thesis: verum