Edit: Can complete hold even if $d < u \le 1+R$ or $1+R \le d < u$ ?

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In Tomas Björk's [Arbitrage Theory in Continuous Time](http://global.oup.com/academic/product/arbitrage-theory-in-continuous-time-9780199574742?cc=nl&lang=en&) (or [here](https://rads.stackoverflow.com/amzn/click/com/019957474X)), $\exists$ this proposition

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> ![enter image description here](https://i.stack.imgur.com/8htwR.png)
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It seems that to show that the model is complete, we must show that the claims are reachable, i.e. we must find replicating portfolios for each claim.

Which part of finding the replicating portfolio makes use of the assumption, where I understand the assumption is equivalent to $d < 1+R < u$ (or $d \le 1+R \le u$, but $d<u$)? All I see so far is the $d<u$, but that's nothing really special: of course the stock price $u$ if it would go up from its current price should be higher than the stock price $d$ if it would go down from the its current price.