I'm teaching myself Analysis, using Steven Lay's Analysis, With an Introduction to Proof.

I need to establish a conclusion given a hypothesis, using a list of tautologies, I've attached an image below of the given tautologies.

[![enter image description here](https://i.stack.imgur.com/HAgrb.jpg)](https://i.stack.imgur.com/HAgrb.jpg)

Hypothesis: $ r,\sim t,(r \land s) \implies t $

Conclusion: $ \sim s $

I first used (c) the contrapositive,

$ \sim t \implies ( \sim r \lor \sim s ) $

I'm well aware that since $ \sim t $ is True, as stated in the hypothesis, then we can eliminate it and get to $ ( \sim r \lor \sim s ) $ but I'm stuck there and I'm not understanding also what they're doing in the solutions provided.

The solution provided by the book states the following steps:

1. $ \sim t \implies ( \sim r \lor \sim s ) $ contrapositive of
hypothesis 3.12(c)
2. $ \sim r \lor \sim s $ by 3.12(h)
3. $ \sim s $ by 3.12(j)

I'm not understanding how he went from 1 to 2 using h, and 2 to 3 using j, some assistance would be much appreciated.