उपसर्गप्रादुर्भ्यामस्तिर्यच्परः

ष् is substituted for the स् of the verb अस् 'to be' when it is followed by a vowel or य् and is preceded by प्रादुः or an उपसर्ग (Preposition) इ or उ having in it.
The word यच् परः means 'followed by य् or अच्' ॥ The word प्रादुः is an Indeclinable, meaning 'evidently'.

Thus अभिषन्ति, निषन्ति, विषन्ति, प्रादुःषन्ति; अभिष्यात्, निष्यात्, विष्यात्, प्रादुःष्यात् ॥

Why do we say "when preceded by an Upasarga having an इ or उ?" Observe दधिस्यात्, मधुस्यात् ॥ Why do we say 'of the verb अस्'? Observe अनुसृतम्, विसृतम् ॥

Question:- How is there any occasion for the application of the rule here? The context here relates to स, and the word "upasarga" qualifies that स, but here the upasarga is not applied to स् but to the whole verb सृ, therefore this is no counter-example. In fact, what is the necessity of using the word अस् at all in the sutra: for even without it, the word 'upasarga' would qualify that verb which consists of स् only, and such a verb is अस्, with its अ elided and no other verb? Nor is the employment of अस् necessary for प्रादुः, for it comes only in connection with the verbs कृ, भू and अस् ॥

Answer:- All that you urge, is true, yet the following counter-example should be given, as अनुसू, the son of Anusu will be आनुसेयः with ढक् as it belongs to Subhradi class. Thus अनुसू + ढक् = आनुसू + एय = आनुस् + एय ॥ Here the ऊ is elided by 6.4.147. Now when ऊ is elided, the स् is the only verb-element that remains, अनु is upasarga, and एय is affix; so that had अस् not been taken in the sutra, the rule would apply to this स् also.

Why do we say "when it is followed by a vowel or य्"? Observe निस्तः, विस्तः, प्रादुस्तः ॥