Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
784972462a
while trying to help a user who was facing an unhelpful ``` omega did not find a contradiction: [0, 0, 0, 0, 1, -1] ∈ [1, ∞) [0, 0, 0, 0, 0, 1] ∈ [0, ∞) [0, 0, 0, 0, 1] ∈ [0, ∞) [1, -1] ∈ [1, ∞) [0, 0, 0, 1] ∈ [0, ∞) [0, 1] ∈ [0, ∞) [1] ∈ [0, ∞) [0, 0, 0, 1, 1] ∈ [-1, ∞) ``` I couldn’t resist and wrote a pretty-printer for these problem that shows the linear combination as such, and includes the recognized atoms. This is especially useful since oftem `omega` failures stem from failure to recognize atoms as equal. In this case, we now get: ``` omega-failure.lean:19:2-19:7: error: omega could not prove the goal: a possible counterexample may satisfy the constraints d - e ≥ 1 e ≥ 0 d ≥ 0 a - b ≥ 1 c ≥ 0 b ≥ 0 a ≥ 0 c + d ≥ -1 where a := ↑(sizeOf xs) b := ↑(sizeOf x) c := ↑(sizeOf x.fst) d := ↑(sizeOf x.snd) e := ↑(sizeOf xs) ``` and this might help the user make progress (e.g. by using `case x` first, and investingating why `sizeOf xs` shows up twice) |
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