No, having a sat nav doesn't obviate the need to be attentive to road signs and the size of your vehicle.
No map data supplier warrants that their data is free from errors, and even if they did the data could be out-of-date within hours as roads are being built all the time.
There is no proof - mathematical or otherwise - a sat nav won't switch off if you fail to plug it in. Neither is there any proof a bridge won't be closed due to roadworks, an accident, or other reasons.
