aevionai/turing-sft-v1 · Datasets at Hugging Face

conversations listlengths 3 3
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : \|\|K\|\| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : \|\|K\|\| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : \|\|K\|\| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : \|\|K\|\| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : \|\|K\|\| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : \|\|K\|\| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]
[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_bounded : premium -> premium <= max_premium" }, { "from": "gpt", "value": "by linarith" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem compliance_valid : r -> is_compliant r" }, { "from": "gpt", "value": "by simp" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem monotone_pure : a <= b -> f a <= f b" }, { "from": "gpt", "value": "by linarith" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem pricing_correctness : input -> gross >= pure" }, { "from": "gpt", "value": "by linarith" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem net_premium_bounded : input -> net >= 0" }, { "from": "gpt", "value": "by linarith" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem class_has_syndicate : rc -> syndicates.length >= 1" }, { "from": "gpt", "value": "by decide" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem classes_exhaustive : rc -> displayName != \"\"" }, { "from": "gpt", "value": "by rfl" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem premium_sufficiency : loaded >= pure -> 1 - e - p <= 1" }, { "from": "gpt", "value": "by linarith" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem jsr_stability : jsr < 1 -> convergent" }, { "from": "gpt", "value": "by omega" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem spectral_bound : norm <= B -> stable" }, { "from": "gpt", "value": "by simp" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem koopman_convergent : ||K|| <= 1 -> mixing" }, { "from": "gpt", "value": "by omega" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem bacc_alarm : variance_halt -> alarm" }, { "from": "gpt", "value": "by exact" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem lyapunov_stable : V > 0 -> dV < 0 -> stable" }, { "from": "gpt", "value": "by simp" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem federated_byzantine : n >= 3f + 1 -> consensus" }, { "from": "gpt", "value": "by omega" } ]

[ { "from": "system", "value": "You are a Lean 4 expert." }, { "from": "human", "value": "Prove: theorem patent_claim_klns : M K B -> window_detected" }, { "from": "gpt", "value": "by exact" } ]