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def definition def or abbrev

PossibilitySpace

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formal statement (Lean)

 372def PossibilitySpace (c : Config) : Set Config :=

proof body

Definition body.

 373  {y : Config | ∃ n : ℕ, ∃ path : Fin (n+1) → Config,
 374    path ⟨0, Nat.zero_lt_succ n⟩ = c ∧
 375    path ⟨n, Nat.lt_succ_self n⟩ = y ∧
 376    ∀ i : Fin n, path ⟨i.val + 1, Nat.succ_lt_succ i.isLt⟩ ∈
 377                 Possibility (path ⟨i.val, Nat.lt_of_lt_of_le i.isLt (Nat.le_succ n)⟩)}
 378
 379/-- The identity is in every possibility space. -/

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