Romans 4:13

‘For not through the law was the promise to Abraham or to his seed that he should be heir of the world, but through the righteousness of faith.'

The ‘for' may refer back to walking in the steps of the faith of Abraham while he was uncircumcised (Romans 4:12), or to the whole previous narrative. Or it may simply be introductory. But the gist of the verse is clear, and that is that the promise given to Abraham that he would be heir of the world was not connected with obedience to the Law but was through the righteousness of faith (Genesis 15:6). Any connection with the Law has to be read in, because there is not even a hint of it, whilst the connection with the righteousness of faith is immediately apparent from the narrative.

‘Should be heir of the world.' From the beginning the promise to Abraham was that in him and his descendants all the families of the earth would be blessed (or would bless themselves - Genesis 12:3). In terms of those days that indicated that they would rule over them in some way. Their inheritance was to be the world. Thus Abraham was seen as ‘heir of the world'. The thought of an heir arises from the context in Genesis 15 which is all about the promise of Abraham's heir who would, of course inherit the promises. As Isaac was Abraham's heir, so Abraham was God's heir. This promise of being heir of the world is further amplified in later promises where Abraham is to be the father of many nations, and the producer of kings (Genesis 17:5). But the promises were not made because of his own righteous living, they were made because God had chosen him and he was obedient to voice of the Lord. It was God's choice of Abraham that was constantly seen as the basis for his behaviour, something which indicated that his blessing came through God's sovereign grace (Genesis 15:7; Genesis 18:19). That that should  result  in godly living can then be accepted without question.