feat(cont): prove CONT-1 checkpoint ordering is determined by slot - #38
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…or pronic Prove justifiable_iff: the executable Slot.isJustifiableAfter holds iff the slot distance from the finalized slot is at most 5, a perfect square, or a pronic number. The core is correctness of the hand-rolled isqrt (isqrt_le / isqrt_lt_succ by functional induction on the base-4 recursion, uniqueness via isqrt_eq), plus the square-expansion helpers sq_succ / odd_sq and the pronic discriminant identity 4k(k+1) + 1 = (2k+1)^2 that justifies the upstream odd-square trick. Axiom-free, no Mathlib.
Give Checkpoint its slot-based strict order — the comparison in use inside advance_to, since upstream defines no explicit __lt__ — and prove checkpoint_lt_iff_slot_lt (definitional) plus advanceTo_eq_ite connecting the order to the forward-only progression. Axiom-free. Closes #36
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Summary
Discharges CONT-1 from
docs/lean4-proof-propositions.md, completing the Containers domain (2/2 proved).LeanSpec/Forks/Lstar/Containers/Checkpoint.lean:instance : LT Checkpoint— slot-based strict order. UpstreamCheckpointhas no explicit__lt__; the ordering in use is the slot comparison insideadvance_to, which the instance packages (plus aDecidableRelinstance).checkpoint_lt_iff_slot_lt(CONT-1) — definitional (Iff.rfl).advanceTo_eq_ite—advanceTois exactlyif self < candidate then candidate else self, keeping the instance honest against the in-use comparison.Stacked on #37 — merge order: #37 → this (retarget to
mainbefore merging #37).Verification
lake buildgreen with zero warnings; nosorry, no new axioms.Closes #36