feat(val): prove VAL-1 proposers are selected round-robin - #39
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Extract ValidatorIndex.proposerForSlot mirroring proposer_for_slot in upstream containers/identifiers.py and refactor processBlockHeader's proposer check to consume it (semantics unchanged: the UInt64 construction never wraps since slot % n <= slot < 2^64, recorded as proposerForSlot_toNat). Prove proposer_index_round_robin, the catalog form of the round-robin selection. Axiom-free, no Mathlib.
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Summary
Discharges VAL-1 from
docs/lean4-proof-propositions.md: proposers are selected round-robin (slot % n).LeanSpec/Forks/Lstar/Containers/Identifiers.lean(mirrors upstreamcontainers/identifiers.py):ValidatorIndex.proposerForSlot— round-robin selection,UInt64.ofNat (slot.toNat % n).proposer_index_round_robin(VAL-1, catalog form —ValidatorIndex.mkrealized asUInt64.ofNat).proposerForSlot_toNat— the substantive half: theUInt64construction never wraps (slot % n ≤ slot < 2^64), so the selected index is exactlyslot.toNat % nat theNatlevel.StateTransition.lean—processBlockHeader's proposer check refactored to consumeproposerForSlot(upstream comparesblock.proposer_index != proposer_for_slot(...)directly), so the theorem speaks about the deployed selection rather than an orphan definition. Equivalent to the previousNat-level check for all inputs byproposerForSlot_toNat; all ST proofs pass unchanged.Note: no GitHub issue exists for VAL-1 (issue creation is blocked in-session); the catalog entry is the tracking artifact.
Verification
lake buildgreen with zero warnings; nosorry, no new axioms.Part of the Validator domain (VAL-3 follows in a stacked PR).