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erdOne committed Jul 3, 2024
1 parent 178507e commit 8c134d9
Showing 1 changed file with 2 additions and 1 deletion.
3 changes: 2 additions & 1 deletion Mathlib/RingTheory/LocalRing/Module.lean
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Expand Up @@ -58,7 +58,8 @@ theorem LocalRing.map_mkQ_eq {N₁ N₂ : Submodule R M} (h : N₁ ≤ N₂) (h'
N₁.map (Submodule.mkQ (𝔪 • N₂)) = N₂.map (Submodule.mkQ (𝔪 • N₂)) ↔ N₁ = N₂ := by
constructor
· intro hN
have : N₂ ≤ 𝔪 • N₂ ⊔ N₁ := by simpa using Submodule.comap_mono (f := Submodule.mkQ (𝔪 • N₂)) hN.ge
have : N₂ ≤ 𝔪 • N₂ ⊔ N₁ := by
simpa using Submodule.comap_mono (f := Submodule.mkQ (𝔪 • N₂)) hN.ge
rw [sup_comm] at this
exact h.antisymm (Submodule.le_of_le_smul_of_le_jacobson_bot h'
(by rw [jacobson_eq_maximalIdeal]; exact bot_ne_top) this)
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