let IL be non empty set ; :: thesis: for N being with_non-empty_elements set
for S being non empty IC-Ins-separated AMI-Struct of IL,N
for s being State of S
for l1, l2 being Instruction-Location of S holds (s +* (Start-At l1)) +* (Start-At l2) = s +* (Start-At l2)
let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated AMI-Struct of IL,N
for s being State of S
for l1, l2 being Instruction-Location of S holds (s +* (Start-At l1)) +* (Start-At l2) = s +* (Start-At l2)
let S be non empty IC-Ins-separated AMI-Struct of IL,N; :: thesis: for s being State of S
for l1, l2 being Instruction-Location of S holds (s +* (Start-At l1)) +* (Start-At l2) = s +* (Start-At l2)
let s be State of S; :: thesis: for l1, l2 being Instruction-Location of S holds (s +* (Start-At l1)) +* (Start-At l2) = s +* (Start-At l2)
let l1, l2 be Instruction-Location of S; :: thesis: (s +* (Start-At l1)) +* (Start-At l2) = s +* (Start-At l2)
A1: dom (Start-At l1) = {(IC S)} by FUNCOP_1:19
.= dom (Start-At l2) by FUNCOP_1:19 ;
thus (s +* (Start-At l1)) +* (Start-At l2) = s +* ((Start-At l1) +* (Start-At l2)) by FUNCT_4:15
.= s +* (Start-At l2) by A1, FUNCT_4:20 ; :: thesis: verum