let b be BinOp of INT; :: thesis: ( b = multint iff for a, b being Element of INT holds b . (a,b) = multreal . (a,b) )

hereby :: thesis: ( ( for a, b being Element of INT holds b . (a,b) = multreal . (a,b) ) implies b = multint )

assume A1: b = multint ; :: thesis: for i1, i2 being Element of INT holds b . (i1,i2) = multreal . (i1,i2)
let i1, i2 be Element of INT ; :: thesis: b . (i1,i2) = multreal . (i1,i2)
thus b . (i1,i2) = i1 * i2 by A1, BINOP_2:def 22
.= multreal . (i1,i2) by BINOP_2:def 11 ; :: thesis: verum

end;

assume A2: for i1, i2 being Element of INT holds b . (i1,i2) = multreal . (i1,i2) ; :: thesis: b = multint

now :: thesis: for i1, i2 being Element of INT holds b . (i1,i2) = multint . (i1,i2)

let i1, i2 be Element of INT ; :: thesis: b . (i1,i2) = multint . (i1,i2)
thus b . (i1,i2) = multreal . (i1,i2) by A2
.= i1 * i2 by BINOP_2:def 11
.= multint . (i1,i2) by BINOP_2:def 22 ; :: thesis: verum

end;

hence b = multint by BINOP_1:2; :: thesis: verum