sir, why lenz’s law does not violate energy conservation law-explain

Acc to energy conservation law energy is converted from one form to other. So take a example a magnet ismoved to and fro near a coil then current in induced in it.why because the energy used to move magnet is changed into current. Simply mechanical power = electrical power. Derive it using work =f.dx here F= ILB and dx =vdt putIas bLV/R you will get work yhen divide work by dt :you will get mechanical power. Using joule heating law I= I2RT and putting I=BLV/R we will get electrical powet as B2V2L2/R .and this will be the mechanical work also. I hope it cleared your doubts as i have given mathematical as well as therotical expression