question about the comparator's operation regions

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istyle

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It's a fig of operation reagion of comparator.
And the formula describes the vout when the comparator work in the REG_MIN region (which is a Linear region).
My question is :
1. How could we derive the formula? I think the relationship of Vout and A in the formula is strange.
2. Does the Hmin point mean the first corner (from left to right) in the picture?And its a value correspond to Vin?[/quote]
 

it doesn't make sense
 

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