let s be State of ; :: thesis: ( ProgramPart s halts_on s implies for k being Element of NAT st LifeSpan s <= k holds
CurInstr (Computation s,k) = halt SCMPDS )
assume ProgramPart s halts_on s ; :: thesis: for k being Element of NAT st LifeSpan s <= k holds
CurInstr (Computation s,k) = halt SCMPDS
then A1: CurInstr (Computation s,(LifeSpan s)) = halt SCMPDS by AMI_1:def 46;
let k be Element of NAT ; :: thesis: ( LifeSpan s <= k implies CurInstr (Computation s,k) = halt SCMPDS )
assume LifeSpan s <= k ; :: thesis: CurInstr (Computation s,k) = halt SCMPDS
hence CurInstr (Computation s,k) = halt SCMPDS by A1, AMI_1:52; :: thesis: verum