`diff_in_deltaSub`

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module: IndisputableMonolith.Potential
domain: Potential
line: 106 · github
papers citing: none yet

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IndisputableMonolith.Potential on GitHub at line 106.

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formal source

 103              simp [Nat.cast_add]
 104
 105/-- Corollary: the set of potential differences along reaches is the δ-generated subgroup. -/
 106lemma diff_in_deltaSub {δ : ℤ} {p : Pot M}
 107  (hp : DE (M:=M) δ p) {n x y}
 108  (h : Causality.ReachN (Kin M) n x y) : ∃ k : ℤ, p y - p x = k * δ := by
 109  refine ⟨(n : ℤ), ?_⟩
 110  simpa using increment_on_ReachN (M:=M) (δ:=δ) (p:=p) hp (n:=n) (x:=x) (y:=y) h
 111
 112end Potential
 113end IndisputableMonolith

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