feat(val): prove VAL-3 each slot has exactly one proposer - #40
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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.
Define isProposerFor (equality with the round-robin index, phrased on Fin n so registry membership is carried by the type) and prove unique_proposer: the proposer slot % n exists and any proposer equals it. The catalog's exists-unique is written in expanded form since ExistsUnique is Mathlib-only. Axiom-free.
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Summary
Discharges VAL-3 from
docs/lean4-proof-propositions.md: each slot has exactly one proposer.LeanSpec/Forks/Lstar/Containers/Identifiers.lean:ValidatorIndex.isProposerFor— validatorvid : Fin nis the scheduled proposer ofslotiffvid.val = slot.toNat % n(the equality-with-proposer_for_slotcheck the validator service uses, e.g. invalidator_duties.py).unique_proposer(VAL-3) — existence (slot % n < nfor a nonempty registry) plus uniqueness (Fin.ext). The catalog's∃!is written in its expanded form∃ vid, P vid ∧ ∀ vid', P vid' → vid' = vid—ExistsUniquelives in Mathlib, which this repo does not depend on (noted in the catalog annotation).Stacked on #39 — merge order: #39 → this (retarget to
mainbefore merging #39).Verification
lake buildgreen with zero warnings; nosorry, no new axioms.Remaining VAL propositions (VAL-2 dual keys, VAL-4 no double vote, VAL-5 XMSS preparation monotonicity) need the ValidatorService / KeyRegistry / XMSS-state models — a separate machinery step.