What is the evidence for differentiating in inheritance between a full sister and a half-sister if verse 176 of Surat An-Nisa (and he has a sister) does not specify whether she is full or not?

The last verse of Surat An-Nisa', which is Allah's saying: (They ask you for a legal ruling. Say: Allah gives you a ruling concerning al-kalalah...) speaks about the inheritance of full or paternal siblings. If the deceased has no child and has a full or paternal sister, she inherits half of what he leaves. If there are two of them, they inherit two-thirds. If they are brothers and sisters, then the male gets the share of two females. As for maternal siblings, their inheritance is mentioned in verse 12 of Surat An-Nisa', where each of them inherits one-sixth. If a full sister is present with a paternal sister, the full sister gets half, and the paternal sister gets one-sixth as a complement to two-thirds. If a paternal brother is present with a paternal sister, they inherit the remainder as ‘asabah (residuaries), and the male gets the share of two females.