let I be Instruction of SCMPDS ; :: thesis: ( InsCode I = 2 implies ex a being Int_position ex k1 being Integer st I = a := k1 )
assume A1: InsCode I = 2 ; :: thesis: ex a being Int_position ex k1 being Integer st I = a := k1
( I in { [0 ,{} ,<*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 14, 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 14, 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 14, 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 14, d1 being Element of SCM-Data-Loc , k1 being Element of INT such that
A2: I = [I1,{} ,<*d1,k1*>] and
A3: I1 in {2,3} by A1, Lm2, Lm3, Lm5, Lm6;
( I1 = 2 or I1 = 3 ) by A3, TARSKI:def 2;
then consider d1 being Element of SCM-Data-Loc , k1 being Integer such that
A4: I = [2,{} ,<*d1,k1*>] by A1, A2, RECDEF_2:def 1;
reconsider a = d1 as Int_position by Def2;
take a ; :: thesis: ex k1 being Integer st I = a := k1
take k1 ; :: thesis: I = a := k1
thus I = a := k1 by A4; :: thesis: verum