Gatherer Text:
Rather than pay the mana cost for a spell, its controller may discard a card that shares a color with that spell.
Rules Text:
Each split card that consists of two halves with different colored mana symbols in their mana costs is a multicolored card while it’s not a spell on the stack. While it’s a spell on the stack, it’s only the color or colors of the half being played.
It follows from these two facts that one cannot use Dream Halls to play the Bound spell on the split card Bound/Determined by discarding a blue card.
