Braking distance and friction

I was taught that in conditions where there is less friction, such as on icy or wet roads, the braking distance of a car, is less than if the car was travelling in conditions with more friction, such as when the road is rocky or sandy.

Although it makes sense intuitively, I recalled that friction opposes motion and not acceleration. So, for example, when a car travels to the right, and the driver applies the brakes, the car will still travel to the right, but just decelerate until it stops completely. Since friction opposes movement, and the car is still moving to the right when braking, then the direction of the friction force is to the left — so shouldn’t a larger friction force decrease the braking distance?

Thanks for your help!

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