let A be preIfWhileAlgebra; :: thesis: for S being non empty set
for T being Subset of S
for f being ExecutionFunction of A,S,T
for I being absolutely-terminating Element of A holds I is_terminating_wrt f
let S be non empty set ; :: thesis: for T being Subset of S
for f being ExecutionFunction of A,S,T
for I being absolutely-terminating Element of A holds I is_terminating_wrt f
let T be Subset of S; :: thesis: for f being ExecutionFunction of A,S,T
for I being absolutely-terminating Element of A holds I is_terminating_wrt f
let f be ExecutionFunction of A,S,T; :: thesis: for I being absolutely-terminating Element of A holds I is_terminating_wrt f
let I be absolutely-terminating Element of A; :: thesis: I is_terminating_wrt f
let s be Element of S; :: according to AOFA_000:def 37 :: thesis: [s,I] in TerminatingPrograms (A,S,T,f)
thus [s,I] in TerminatingPrograms (A,S,T,f) by Def36; :: thesis: verum