let x, y be object ; for E being non empty set
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st [x,y] in ==>.-relation TS holds
ex s being Element of TS ex v being Element of E ^omega ex t being Element of TS ex w being Element of E ^omega st
( x = [s,v] & y = [t,w] )
let E be non empty set ; for F being Subset of (E ^omega)
for TS being non empty transition-system over F st [x,y] in ==>.-relation TS holds
ex s being Element of TS ex v being Element of E ^omega ex t being Element of TS ex w being Element of E ^omega st
( x = [s,v] & y = [t,w] )
let F be Subset of (E ^omega); for TS being non empty transition-system over F st [x,y] in ==>.-relation TS holds
ex s being Element of TS ex v being Element of E ^omega ex t being Element of TS ex w being Element of E ^omega st
( x = [s,v] & y = [t,w] )
let TS be non empty transition-system over F; ( [x,y] in ==>.-relation TS implies ex s being Element of TS ex v being Element of E ^omega ex t being Element of TS ex w being Element of E ^omega st
( x = [s,v] & y = [t,w] ) )
assume A1:
[x,y] in ==>.-relation TS
; ex s being Element of TS ex v being Element of E ^omega ex t being Element of TS ex w being Element of E ^omega st
( x = [s,v] & y = [t,w] )
then
y in [: the carrier of TS,(E ^omega):]
by ZFMISC_1:87;
then A2:
ex y1, y2 being object st
( y1 in the carrier of TS & y2 in E ^omega & y = [y1,y2] )
by ZFMISC_1:def 2;
x in [: the carrier of TS,(E ^omega):]
by A1, ZFMISC_1:87;
then
ex x1, x2 being object st
( x1 in the carrier of TS & x2 in E ^omega & x = [x1,x2] )
by ZFMISC_1:def 2;
hence
ex s being Element of TS ex v being Element of E ^omega ex t being Element of TS ex w being Element of E ^omega st
( x = [s,v] & y = [t,w] )
by A2; verum