let I be Instruction of SCMPDS; :: thesis: ( InsCode I = 12 implies ex a, b being Int_position ex k1, k2 being Integer st I = Divide (a,k1,b,k2) )
assume A1: InsCode I = 12 ; :: thesis: ex a, b being Int_position ex k1, k2 being Integer st I = Divide (a,k1,b,k2)
( I in {[0,{},{}]} or I in { [14,{},<*k1*>] where k1 is Element of INT : verum } or I in { [1,{},<*d1*>] where d1 is Element of SCM-Data-Loc : verum } or I in { [I1,{},<*d2,k2*>] where I1 is Element of Segm 15, d2 is Element of SCM-Data-Loc , k2 is Element of INT : I1 in {2,3} } or I in { [I2,{},<*d3,k3,k4*>] where I2 is Element of Segm 15, d3 is Element of SCM-Data-Loc , k3, k4 is Element of INT : I2 in {4,5,6,7,8} } or I in { [I3,{},<*d4,d5,k5,k6*>] where I3 is Element of Segm 15, d4, d5 is Element of SCM-Data-Loc , k5, k6 is Element of INT : I3 in {9,10,11,12,13} } ) by Lm1;
then consider I1 being Element of Segm 15, d1, d2 being Element of SCM-Data-Loc , k1, k2 being Element of INT such that
A2: I = [I1,{},<*d1,d2,k1,k2*>] and
I1 in {9,10,11,12,13} by A1, Lm9;
consider d1, d2 being Element of SCM-Data-Loc , k1, k2 being Integer such that
A3: I = [12,{},<*d1,d2,k1,k2*>] by A1, A2;
reconsider a = d1, b = d2 as Int_position by AMI_2:def 16;
take a ; :: thesis: ex b being Int_position ex k1, k2 being Integer st I = Divide (a,k1,b,k2)
take b ; :: thesis: ex k1, k2 being Integer st I = Divide (a,k1,b,k2)
take k1 ; :: thesis: ex k2 being Integer st I = Divide (a,k1,b,k2)
take k2 ; :: thesis: I = Divide (a,k1,b,k2)
thus I = Divide (a,k1,b,k2) by A3; :: thesis: verum