`Reaches`

definition

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module: IndisputableMonolith.Causality.Basic
domain: Causality
line: 24 · github
papers citing: none yet

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open lean source

IndisputableMonolith.Causality.Basic on GitHub at line 24.

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depends on

used by

formal source

  21lemma reach_le_in_ball {K : Kinematics α} {x y : α} {k n : Nat}
  22  (hk : k ≤ n) (h : ReachN K k x y) : inBall K x n y := ⟨k, hk, h⟩
  23
  24def Reaches (K : Kinematics α) (x y : α) : Prop := ∃ n, ReachN K n x y
  25
  26lemma reaches_of_reachN {K : Kinematics α} {x y : α} {n : Nat}
  27  (h : ReachN K n x y) : Reaches K x y := ⟨n, h⟩
  28
  29lemma inBall_mono {K : Kinematics α} {x y : α} {n m : Nat}
  30  (hnm : n ≤ m) : inBall K x n y → inBall K x m y := by
  31  intro ⟨k, hk, hkreach⟩
  32  exact ⟨k, le_trans hk hnm, hkreach⟩
  33
  34end Causality
  35end IndisputableMonolith

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