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structure definition def or abbrev

ExtinctionCascadeCert

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formal statement (Lean)

 214structure ExtinctionCascadeCert where
 215  Z_life_pos : 0 < Z_life
 216  Z_life_gt_one : 1 < Z_life
 217  totalRung_pos :
 218    ∀ n (E : Ecosystem n) (L : Finset (Fin n)) (j : Fin n),
 219      0 < totalRung E L j
 220  isBankrupt_antimono :
 221    ∀ n (E : Ecosystem n) (L₁ L₂ : Finset (Fin n)),
 222      L₁ ⊆ L₂ → ∀ j : Fin n,
 223        IsBankrupt E L₂ j → IsBankrupt E L₁ j
 224  cascadeStep_subset :
 225    ∀ n (E : Ecosystem n) (L : Finset (Fin n)),
 226      cascadeStep E L ⊆ L
 227  cascadeStep_card_le :
 228    ∀ n (E : Ecosystem n) (L : Finset (Fin n)),
 229      (cascadeStep E L).card ≤ L.card
 230  cascadeIterate_subset :
 231    ∀ n (E : Ecosystem n) (L : Finset (Fin n)) (k : ℕ),
 232      cascadeIterate E L (k + 1) ⊆ cascadeIterate E L k
 233  cascadeIterate_card_monotone :
 234    ∀ n (E : Ecosystem n) (L : Finset (Fin n)) (k : ℕ),
 235      (cascadeIterate E L (k + 1)).card ≤ (cascadeIterate E L k).card
 236  recoveryTime_pos : ∀ k : ℕ, 0 < recoveryTime k
 237  recoveryTime_strict_mono :
 238    ∀ k : ℕ, recoveryTime k < recoveryTime (k + 1)
 239  deep_cascade_recovery_lower : phi ^ 16 < recoveryTime 17
 240

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