let k, loc be Nat; :: thesis: IncAddr ((SCM-goto loc),k) = SCM-goto (loc + k)
A1: InsCode (IncAddr ((SCM-goto loc),k)) = InsCode (SCM-goto loc) by COMPOS_0:def 9
.= 6
.= InsCode (SCM-goto (loc + k)) ;
A2: AddressPart (IncAddr ((SCM-goto loc),k)) = AddressPart (SCM-goto loc) by COMPOS_0:def 9
.= {}
.= AddressPart (SCM-goto (loc + k)) ;
A3: JumpPart (IncAddr ((SCM-goto loc),k)) = k + (JumpPart (SCM-goto loc)) by COMPOS_0:def 9;
JumpPart (IncAddr ((SCM-goto loc),k)) = JumpPart (SCM-goto (loc + k))

proof

thus A4: dom (JumpPart (IncAddr ((SCM-goto loc),k))) = dom (JumpPart (SCM-goto (loc + k))) by A1, COMPOS_0:def 5; :: according to FUNCT_1:def 11 :: thesis: for b₁ being object holds
( not b₁ in proj1 (JumpPart (IncAddr ((SCM-goto loc),k))) or (JumpPart (IncAddr ((SCM-goto loc),k))) . b₁ = (JumpPart (SCM-goto (loc + k))) . b₁ )
let x be object ; :: thesis: ( not x in proj1 (JumpPart (IncAddr ((SCM-goto loc),k))) or (JumpPart (IncAddr ((SCM-goto loc),k))) . x = (JumpPart (SCM-goto (loc + k))) . x )
assume A5: x in dom (JumpPart (IncAddr ((SCM-goto loc),k))) ; :: thesis: (JumpPart (IncAddr ((SCM-goto loc),k))) . x = (JumpPart (SCM-goto (loc + k))) . x
dom <*(loc + k)*> = {1} by FINSEQ_1:2, FINSEQ_1:38;
then A6: x = 1 by A5, A4, TARSKI:def 1;
thus (JumpPart (IncAddr ((SCM-goto loc),k))) . x = k + ((JumpPart (SCM-goto loc)) . x) by A3, A5, VALUED_1:def 2
.= loc + k by A6
.= (JumpPart (SCM-goto (loc + k))) . x by A6 ; :: thesis: verum

end;

hence IncAddr ((SCM-goto loc),k) = SCM-goto (loc + k) by A1, A2, COMPOS_0:1; :: thesis: verum