let p be FinPartState of SCM+FSA ; :: thesis: for k being Element of NAT holds IC (Relocated p,k) = (IC p) + k
let k be Element of NAT ; :: thesis: IC (Relocated p,k) = (IC p) + k
A1: Relocated p,k = (Start-At ((IC p) + k),SCM+FSA ) +* ((IncAddr (Shift (ProgramPart p),k),k) +* (DataPart p)) by FUNCT_4:15;
ProgramPart (Relocated p,k) = IncAddr (Shift (ProgramPart p),k),k by Th2;
then A2: not IC SCM+FSA in dom (IncAddr (Shift (ProgramPart p),k),k) by AMI_1:101;
not IC SCM+FSA in dom (DataPart p) by AMI_1:100;
then A3: not IC SCM+FSA in dom ((IncAddr (Shift (ProgramPart p),k),k) +* (DataPart p)) by A2, FUNCT_4:13;
thus IC (Relocated p,k) = (Start-At ((IC p) + k),SCM+FSA ) . (IC SCM+FSA ) by A1, A3, FUNCT_4:12
.= (IC p) + k by FUNCOP_1:87 ; :: thesis: verum