let i be Instruction of SCM+FSA ; :: thesis: (Directed (Macro i)) . (insloc 1) = goto (insloc 2)
A1: (Macro i) . (insloc 1) = halt SCM+FSA by SCMFSA6B:33;
insloc 1 in {(insloc 0 ),(insloc 1)} by TARSKI:def 2;
then A2: insloc 1 in dom (Macro i) by Th4;
dom ((halt SCM+FSA ) .--> (goto (insloc 2))) = {(halt SCM+FSA )} by FUNCOP_1:19;
then A3: halt SCM+FSA in dom ((halt SCM+FSA ) .--> (goto (insloc 2))) by TARSKI:def 1;
A4: dom (id the Instructions of SCM+FSA ) = the Instructions of SCM+FSA by RELAT_1:71;
( card (Macro i) = 2 & rng (Macro i) c= the Instructions of SCM+FSA ) by Th6, AMI_1:118;
hence (Directed (Macro i)) . (insloc 1) = (((id the Instructions of SCM+FSA ) +* (halt SCM+FSA ),(goto (insloc 2))) * (Macro i)) . (insloc 1) by FUNCT_7:118
.= (((id the Instructions of SCM+FSA ) +* ((halt SCM+FSA ) .--> (goto (insloc 2)))) * (Macro i)) . (insloc 1) by A4, FUNCT_7:def 3
.= ((id the Instructions of SCM+FSA ) +* ((halt SCM+FSA ) .--> (goto (insloc 2)))) . (halt SCM+FSA ) by A2, A1, FUNCT_1:23
.= ((halt SCM+FSA ) .--> (goto (insloc 2))) . (halt SCM+FSA ) by A3, FUNCT_4:14
.= goto (insloc 2) by FUNCOP_1:87 ;
:: thesis: verum