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 over F st x,<%e%> ==>* y, <%> E, _bool TS holds
x,<%e%> ==>. y, <%> E, _bool TS
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 x,<%e%> ==>* y, <%> E, _bool TS holds
x,<%e%> ==>. y, <%> E, _bool TS
let e be Element of E; :: thesis: for F being Subset of (E ^omega)
for TS being non empty transition-system over F st x,<%e%> ==>* y, <%> E, _bool TS holds
x,<%e%> ==>. y, <%> E, _bool TS
let F be Subset of (E ^omega); :: thesis: for TS being non empty transition-system over F st x,<%e%> ==>* y, <%> E, _bool TS holds
x,<%e%> ==>. y, <%> E, _bool TS
let TS be non empty transition-system over F; :: thesis: ( x,<%e%> ==>* y, <%> E, _bool TS implies x,<%e%> ==>. y, <%> E, _bool TS )
not <%> E in rng (dom the Tran of (_bool TS)) by REWRITE3:def 1;
hence ( x,<%e%> ==>* y, <%> E, _bool TS implies x,<%e%> ==>. y, <%> E, _bool TS ) by REWRITE3:92; :: thesis: verum