Machine-checked proofs are becoming the standard for serious proof systems.
Different systems need different properties pinned down. For a privacy protocol, zero knowledge is the product, so that is the property to prove. For a zkVM proving a Bitcoin bridge, the property that matters most is soundness: a proof that should not exist must be impossible to construct.
Formal verification has been part of Ziren for more than a year -
@VeridiseInc formally checked constraint determinism with Picus alongside a full independent audit, before
@ConsensysAudits stress-tested the system.
Ziren 2.0 extends this with machine-checked proofs in Lean 4.