7.2.81 आतो ङितः
संधि विच्छेद : none
अनु वृत्ती : सार्वधातुके इय अतः
Meaning: from सार्वधातु, ङितः of आत from अतः इय
सार्वधातु, ङितः of आत - are आते , आथे and आताम् and आथाम्
So meaning is = from आते , आथे and आताम् and आथाम्; at अ, आ becomes इ

Physical:
आते = upto receiving float
आथे = upto receicing platform
आताम् = upto float untill inside
आथाम् = upto platform till inside
In these situations, if preceeding is अ here,आ becomes इ। .e. untill becomes inward.

commentary
This rule applies to आप while forming समीप, although आप is not a prtyay here.