A question about positive feedback resistor in a Schmitt trigger
You guys failed to recognize OP issue.
If those explanation works. He won't ask about this in the first place. (methinks)
Let's see the most simplest form of explanation  

How R3 parallel with R1?

Anything wrong with that?

Ditto for R2


Now you can read other answers which have good explanation why op-amp work this way.  

Some note on R4:
Why it is there?
In actual cheap op-amp component the op-amp cannot drive voltage to Vcc. (max at Vcc - 1.5V for instance)
There are rail-to-rail op-amp which have higher cost in general.
The op-amp in question is likely to be Open-drain op-amp hence the pull-up resistor.
It will work perfectly fine without much calculation because it will connect to digital input pin that likely to be a height impedance pin.