Danila Fedorin 86bc33ee26 Register cases rules on lattice carriers for aesop automation ...

Tag the finite lattice carrier types with `@[aesop safe cases]`
(`AboveBelow`, `Sign`) so aesop performs the dominant proof step in this
framework -- case-splitting a lattice element -- automatically. Combined
with the existing `@[simp]` operation lemmas, this collapses the recurring
"case-split then reduce" proofs to a bare `aesop`:

  * AboveBelow's six lattice axioms drop their explicit `rcases`
  * Sign/Constant `plus_mono₂`/`minus_mono₂` become `by aesop`
  * Constant `plus_valid`/`minus_valid` shrink to a 2-line `rcases <;> simp_all`
  * `not_mk_lt_mk` is reexpressed via `le_cases`

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

2026-06-27 20:01:01 -05:00

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