ultrametric_replaces_card (theorem)

/-- [I.P37] Ultrametric structure replaces cardinality hierarchy. In ZF, the chain aleph_0 < aleph_1 < aleph_2 < ... measures "how many" elements a set has. In tau, this hierarchy collapses: there is only one infinity (omega), and the notion of "size" is replaced by PROXIMITY in the divergence ultrametric. Two omega-tails are "close" if they agree to deep primorial depth, and "far" if they diverge early. This is an ultrametric (satisfies the strong triangle inequality), providing a finer structure than cardinality. The replacement has three pillars: 1. The ultrametric exists (from OmegaGerms) 2. It satisfies the strong triangle inequality (ultra_triangle) 3. There is no second infinity to compare against (unique_infinity) We package these as a single theorem. -/