order.irreducible ⟷ Mathlib.Order.Irreducible

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -146,7 +146,7 @@ theorem SupIrred.finset_sup_eq (ha : SupIrred a) (h : s.sup f = a) : ∃ i ∈ s
   induction' s using Finset.induction with i s hi ih
   · simpa [ha.ne_bot] using h.symm
   simp only [exists_prop, exists_mem_insert] at ih ⊢
-  rw [sup_insert] at h 
+  rw [sup_insert] at h
   exact (ha.2 h).imp_right ih
 #align sup_irred.finset_sup_eq SupIrred.finset_sup_eq
 -/
@@ -173,7 +173,7 @@ theorem exists_supIrred_decomposition (a : α) :
   rintro a ih
   by_cases ha : SupIrred a
   · exact ⟨{a}, by simp [ha]⟩
-  rw [not_supIrred] at ha 
+  rw [not_supIrred] at ha
   obtain ha | ⟨b, c, rfl, hb, hc⟩ := ha
   · exact ⟨∅, by simp [ha.eq_bot]⟩
   obtain ⟨s, rfl, hs⟩ := ih _ hb

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -143,11 +143,20 @@ theorem SupPrime.ne_bot (ha : SupPrime a) : a ≠ ⊥ := by rintro rfl; exact no
 #print SupIrred.finset_sup_eq /-
 theorem SupIrred.finset_sup_eq (ha : SupIrred a) (h : s.sup f = a) : ∃ i ∈ s, f i = a := by
   classical
+  induction' s using Finset.induction with i s hi ih
+  · simpa [ha.ne_bot] using h.symm
+  simp only [exists_prop, exists_mem_insert] at ih ⊢
+  rw [sup_insert] at h 
+  exact (ha.2 h).imp_right ih
 #align sup_irred.finset_sup_eq SupIrred.finset_sup_eq
 -/
 
 #print SupPrime.le_finset_sup /-
-theorem SupPrime.le_finset_sup (ha : SupPrime a) : a ≤ s.sup f ↔ ∃ i ∈ s, a ≤ f i := by classical
+theorem SupPrime.le_finset_sup (ha : SupPrime a) : a ≤ s.sup f ↔ ∃ i ∈ s, a ≤ f i := by
+  classical
+  induction' s using Finset.induction with i s hi ih
+  · simp [ha.ne_bot]
+  · simp only [exists_prop, exists_mem_insert, sup_insert, ha.le_sup, ih]
 #align sup_prime.le_finset_sup SupPrime.le_finset_sup
 -/
 
@@ -157,7 +166,19 @@ variable [WellFoundedLT α]
 /-- In a well-founded lattice, any element is the supremum of finitely many sup-irreducible
 elements. This is the order-theoretic analogue of prime factorisation. -/
 theorem exists_supIrred_decomposition (a : α) :
-    ∃ s : Finset α, s.sup id = a ∧ ∀ ⦃b⦄, b ∈ s → SupIrred b := by classical
+    ∃ s : Finset α, s.sup id = a ∧ ∀ ⦃b⦄, b ∈ s → SupIrred b := by
+  classical
+  apply WellFoundedLT.induction a _
+  clear a
+  rintro a ih
+  by_cases ha : SupIrred a
+  · exact ⟨{a}, by simp [ha]⟩
+  rw [not_supIrred] at ha 
+  obtain ha | ⟨b, c, rfl, hb, hc⟩ := ha
+  · exact ⟨∅, by simp [ha.eq_bot]⟩
+  obtain ⟨s, rfl, hs⟩ := ih _ hb
+  obtain ⟨t, rfl, ht⟩ := ih _ hc
+  exact ⟨s ∪ t, sup_union, forall_mem_union.2 ⟨hs, ht⟩⟩
 #align exists_sup_irred_decomposition exists_supIrred_decomposition
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -143,20 +143,11 @@ theorem SupPrime.ne_bot (ha : SupPrime a) : a ≠ ⊥ := by rintro rfl; exact no
 #print SupIrred.finset_sup_eq /-
 theorem SupIrred.finset_sup_eq (ha : SupIrred a) (h : s.sup f = a) : ∃ i ∈ s, f i = a := by
   classical
-  induction' s using Finset.induction with i s hi ih
-  · simpa [ha.ne_bot] using h.symm
-  simp only [exists_prop, exists_mem_insert] at ih ⊢
-  rw [sup_insert] at h 
-  exact (ha.2 h).imp_right ih
 #align sup_irred.finset_sup_eq SupIrred.finset_sup_eq
 -/
 
 #print SupPrime.le_finset_sup /-
-theorem SupPrime.le_finset_sup (ha : SupPrime a) : a ≤ s.sup f ↔ ∃ i ∈ s, a ≤ f i := by
-  classical
-  induction' s using Finset.induction with i s hi ih
-  · simp [ha.ne_bot]
-  · simp only [exists_prop, exists_mem_insert, sup_insert, ha.le_sup, ih]
+theorem SupPrime.le_finset_sup (ha : SupPrime a) : a ≤ s.sup f ↔ ∃ i ∈ s, a ≤ f i := by classical
 #align sup_prime.le_finset_sup SupPrime.le_finset_sup
 -/
 
@@ -166,19 +157,7 @@ variable [WellFoundedLT α]
 /-- In a well-founded lattice, any element is the supremum of finitely many sup-irreducible
 elements. This is the order-theoretic analogue of prime factorisation. -/
 theorem exists_supIrred_decomposition (a : α) :
-    ∃ s : Finset α, s.sup id = a ∧ ∀ ⦃b⦄, b ∈ s → SupIrred b := by
-  classical
-  apply WellFoundedLT.induction a _
-  clear a
-  rintro a ih
-  by_cases ha : SupIrred a
-  · exact ⟨{a}, by simp [ha]⟩
-  rw [not_supIrred] at ha 
-  obtain ha | ⟨b, c, rfl, hb, hc⟩ := ha
-  · exact ⟨∅, by simp [ha.eq_bot]⟩
-  obtain ⟨s, rfl, hs⟩ := ih _ hb
-  obtain ⟨t, rfl, ht⟩ := ih _ hc
-  exact ⟨s ∪ t, sup_union, forall_mem_union.2 ⟨hs, ht⟩⟩
+    ∃ s : Finset α, s.sup id = a ∧ ∀ ⦃b⦄, b ∈ s → SupIrred b := by classical
 #align exists_sup_irred_decomposition exists_supIrred_decomposition
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2023 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
-import Mathbin.Data.Finset.Lattice
-import Mathbin.Data.Fintype.Card
+import Data.Finset.Lattice
+import Data.Fintype.Card
 
 #align_import order.irreducible from "leanprover-community/mathlib"@"573eea921b01c49712ac02471911df0719297349"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -324,16 +324,16 @@ theorem supPrime_ofDual {a : αᵒᵈ} : SupPrime (ofDual a) ↔ InfPrime a :=
 #align sup_prime_of_dual supPrime_ofDual
 -/
 
-alias infIrred_toDual ↔ _ SupIrred.dual
+alias ⟨_, SupIrred.dual⟩ := infIrred_toDual
 #align sup_irred.dual SupIrred.dual
 
-alias infPrime_toDual ↔ _ SupPrime.dual
+alias ⟨_, SupPrime.dual⟩ := infPrime_toDual
 #align sup_prime.dual SupPrime.dual
 
-alias supIrred_ofDual ↔ _ InfIrred.ofDual
+alias ⟨_, InfIrred.ofDual⟩ := supIrred_ofDual
 #align inf_irred.of_dual InfIrred.ofDual
 
-alias supPrime_ofDual ↔ _ InfPrime.ofDual
+alias ⟨_, InfPrime.ofDual⟩ := supPrime_ofDual
 #align inf_prime.of_dual InfPrime.ofDual
 
 end SemilatticeSup
@@ -370,16 +370,16 @@ theorem infPrime_ofDual {a : αᵒᵈ} : InfPrime (ofDual a) ↔ SupPrime a :=
 #align inf_prime_of_dual infPrime_ofDual
 -/
 
-alias supIrred_toDual ↔ _ InfIrred.dual
+alias ⟨_, InfIrred.dual⟩ := supIrred_toDual
 #align inf_irred.dual InfIrred.dual
 
-alias supPrime_toDual ↔ _ InfPrime.dual
+alias ⟨_, InfPrime.dual⟩ := supPrime_toDual
 #align inf_prime.dual InfPrime.dual
 
-alias infIrred_ofDual ↔ _ SupIrred.ofDual
+alias ⟨_, SupIrred.ofDual⟩ := infIrred_ofDual
 #align sup_irred.of_dual SupIrred.ofDual
 
-alias infPrime_ofDual ↔ _ SupPrime.ofDual
+alias ⟨_, SupPrime.ofDual⟩ := infPrime_ofDual
 #align sup_prime.of_dual SupPrime.ofDual
 
 end SemilatticeInf
@@ -404,10 +404,10 @@ theorem infPrime_iff_infIrred : InfPrime a ↔ InfIrred a :=
 #align inf_prime_iff_inf_irred infPrime_iff_infIrred
 -/
 
-alias supPrime_iff_supIrred ↔ _ SupIrred.supPrime
+alias ⟨_, SupIrred.supPrime⟩ := supPrime_iff_supIrred
 #align sup_irred.sup_prime SupIrred.supPrime
 
-alias infPrime_iff_infIrred ↔ _ InfIrred.infPrime
+alias ⟨_, InfIrred.infPrime⟩ := infPrime_iff_infIrred
 #align inf_irred.inf_prime InfIrred.infPrime
 
 attribute [protected] SupIrred.supPrime InfIrred.infPrime

mathlib commit https://github.com/leanprover-community/mathlib/commit/8047de4d911cdef39c2d646165eea972f7f9f539

@@ -6,11 +6,14 @@ Authors: Yaël Dillies
 import Mathbin.Data.Finset.Lattice
 import Mathbin.Data.Fintype.Card
 
-#align_import order.irreducible from "leanprover-community/mathlib"@"bf2428c9486c407ca38b5b3fb10b87dad0bc99fa"
+#align_import order.irreducible from "leanprover-community/mathlib"@"573eea921b01c49712ac02471911df0719297349"
 
 /-!
 # Irreducible and prime elements in an order
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines irreducible and prime elements in an order and shows that in a well-founded
 lattice every element decomposes as a supremum of irreducible elements.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module order.irreducible
-! leanprover-community/mathlib commit bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Finset.Lattice
 import Mathbin.Data.Fintype.Card
 
+#align_import order.irreducible from "leanprover-community/mathlib"@"bf2428c9486c407ca38b5b3fb10b87dad0bc99fa"
+
 /-!
 # Irreducible and prime elements in an order
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -46,32 +46,45 @@ section SemilatticeSup
 
 variable [SemilatticeSup α] {a b c : α}
 
+#print SupIrred /-
 /-- A sup-irreducible element is a non-bottom element which isn't the supremum of anything smaller.
 -/
 def SupIrred (a : α) : Prop :=
   ¬IsMin a ∧ ∀ ⦃b c⦄, b ⊔ c = a → b = a ∨ c = a
 #align sup_irred SupIrred
+-/
 
+#print SupPrime /-
 /-- A sup-prime element is a non-bottom element which isn't less than the supremum of anything
 smaller. -/
 def SupPrime (a : α) : Prop :=
   ¬IsMin a ∧ ∀ ⦃b c⦄, a ≤ b ⊔ c → a ≤ b ∨ a ≤ c
 #align sup_prime SupPrime
+-/
 
+#print SupIrred.not_isMin /-
 theorem SupIrred.not_isMin (ha : SupIrred a) : ¬IsMin a :=
   ha.1
 #align sup_irred.not_is_min SupIrred.not_isMin
+-/
 
+#print SupPrime.not_isMin /-
 theorem SupPrime.not_isMin (ha : SupPrime a) : ¬IsMin a :=
   ha.1
 #align sup_prime.not_is_min SupPrime.not_isMin
+-/
 
+#print IsMin.not_supIrred /-
 theorem IsMin.not_supIrred (ha : IsMin a) : ¬SupIrred a := fun h => h.1 ha
 #align is_min.not_sup_irred IsMin.not_supIrred
+-/
 
+#print IsMin.not_supPrime /-
 theorem IsMin.not_supPrime (ha : IsMin a) : ¬SupPrime a := fun h => h.1 ha
 #align is_min.not_sup_prime IsMin.not_supPrime
+-/
 
+#print not_supIrred /-
 @[simp]
 theorem not_supIrred : ¬SupIrred a ↔ IsMin a ∨ ∃ b c, b ⊔ c = a ∧ b < a ∧ c < a :=
   by
@@ -80,38 +93,54 @@ theorem not_supIrred : ¬SupIrred a ↔ IsMin a ∨ ∃ b c, b ⊔ c = a ∧ b <
   rw [exists₂_congr]
   simp (config := { contextual := true }) [@eq_comm _ _ a]
 #align not_sup_irred not_supIrred
+-/
 
+#print not_supPrime /-
 @[simp]
 theorem not_supPrime : ¬SupPrime a ↔ IsMin a ∨ ∃ b c, a ≤ b ⊔ c ∧ ¬a ≤ b ∧ ¬a ≤ c := by
   rw [SupPrime, not_and_or]; push_neg; rfl
 #align not_sup_prime not_supPrime
+-/
 
+#print SupPrime.supIrred /-
 protected theorem SupPrime.supIrred : SupPrime a → SupIrred a :=
   And.imp_right fun h b c ha => by simpa [← ha] using h ha.ge
 #align sup_prime.sup_irred SupPrime.supIrred
+-/
 
+#print SupPrime.le_sup /-
 theorem SupPrime.le_sup (ha : SupPrime a) : a ≤ b ⊔ c ↔ a ≤ b ∨ a ≤ c :=
   ⟨fun h => ha.2 h, fun h => h.elim le_sup_of_le_left le_sup_of_le_right⟩
 #align sup_prime.le_sup SupPrime.le_sup
+-/
 
 variable [OrderBot α] {s : Finset ι} {f : ι → α}
 
+#print not_supIrred_bot /-
 @[simp]
 theorem not_supIrred_bot : ¬SupIrred (⊥ : α) :=
   isMin_bot.not_supIrred
 #align not_sup_irred_bot not_supIrred_bot
+-/
 
+#print not_supPrime_bot /-
 @[simp]
 theorem not_supPrime_bot : ¬SupPrime (⊥ : α) :=
   isMin_bot.not_supPrime
 #align not_sup_prime_bot not_supPrime_bot
+-/
 
+#print SupIrred.ne_bot /-
 theorem SupIrred.ne_bot (ha : SupIrred a) : a ≠ ⊥ := by rintro rfl; exact not_supIrred_bot ha
 #align sup_irred.ne_bot SupIrred.ne_bot
+-/
 
+#print SupPrime.ne_bot /-
 theorem SupPrime.ne_bot (ha : SupPrime a) : a ≠ ⊥ := by rintro rfl; exact not_supPrime_bot ha
 #align sup_prime.ne_bot SupPrime.ne_bot
+-/
 
+#print SupIrred.finset_sup_eq /-
 theorem SupIrred.finset_sup_eq (ha : SupIrred a) (h : s.sup f = a) : ∃ i ∈ s, f i = a := by
   classical
   induction' s using Finset.induction with i s hi ih
@@ -120,16 +149,20 @@ theorem SupIrred.finset_sup_eq (ha : SupIrred a) (h : s.sup f = a) : ∃ i ∈ s
   rw [sup_insert] at h 
   exact (ha.2 h).imp_right ih
 #align sup_irred.finset_sup_eq SupIrred.finset_sup_eq
+-/
 
+#print SupPrime.le_finset_sup /-
 theorem SupPrime.le_finset_sup (ha : SupPrime a) : a ≤ s.sup f ↔ ∃ i ∈ s, a ≤ f i := by
   classical
   induction' s using Finset.induction with i s hi ih
   · simp [ha.ne_bot]
   · simp only [exists_prop, exists_mem_insert, sup_insert, ha.le_sup, ih]
 #align sup_prime.le_finset_sup SupPrime.le_finset_sup
+-/
 
 variable [WellFoundedLT α]
 
+#print exists_supIrred_decomposition /-
 /-- In a well-founded lattice, any element is the supremum of finitely many sup-irreducible
 elements. This is the order-theoretic analogue of prime factorisation. -/
 theorem exists_supIrred_decomposition (a : α) :
@@ -147,6 +180,7 @@ theorem exists_supIrred_decomposition (a : α) :
   obtain ⟨t, rfl, ht⟩ := ih _ hc
   exact ⟨s ∪ t, sup_union, forall_mem_union.2 ⟨hs, ht⟩⟩
 #align exists_sup_irred_decomposition exists_supIrred_decomposition
+-/
 
 end SemilatticeSup
 
@@ -154,77 +188,107 @@ section SemilatticeInf
 
 variable [SemilatticeInf α] {a b c : α}
 
+#print InfIrred /-
 /-- An inf-irreducible element is a non-top element which isn't the infimum of anything bigger. -/
 def InfIrred (a : α) : Prop :=
   ¬IsMax a ∧ ∀ ⦃b c⦄, b ⊓ c = a → b = a ∨ c = a
 #align inf_irred InfIrred
+-/
 
+#print InfPrime /-
 /-- An inf-prime element is a non-top element which isn't bigger than the infimum of anything
 bigger. -/
 def InfPrime (a : α) : Prop :=
   ¬IsMax a ∧ ∀ ⦃b c⦄, b ⊓ c ≤ a → b ≤ a ∨ c ≤ a
 #align inf_prime InfPrime
+-/
 
+#print IsMax.not_infIrred /-
 @[simp]
 theorem IsMax.not_infIrred (ha : IsMax a) : ¬InfIrred a := fun h => h.1 ha
 #align is_max.not_inf_irred IsMax.not_infIrred
+-/
 
+#print IsMax.not_infPrime /-
 @[simp]
 theorem IsMax.not_infPrime (ha : IsMax a) : ¬InfPrime a := fun h => h.1 ha
 #align is_max.not_inf_prime IsMax.not_infPrime
+-/
 
+#print not_infIrred /-
 @[simp]
 theorem not_infIrred : ¬InfIrred a ↔ IsMax a ∨ ∃ b c, b ⊓ c = a ∧ a < b ∧ a < c :=
   @not_supIrred αᵒᵈ _ _
 #align not_inf_irred not_infIrred
+-/
 
+#print not_infPrime /-
 @[simp]
 theorem not_infPrime : ¬InfPrime a ↔ IsMax a ∨ ∃ b c, b ⊓ c ≤ a ∧ ¬b ≤ a ∧ ¬c ≤ a :=
   @not_supPrime αᵒᵈ _ _
 #align not_inf_prime not_infPrime
+-/
 
+#print InfPrime.infIrred /-
 protected theorem InfPrime.infIrred : InfPrime a → InfIrred a :=
   And.imp_right fun h b c ha => by simpa [← ha] using h ha.le
 #align inf_prime.inf_irred InfPrime.infIrred
+-/
 
+#print InfPrime.inf_le /-
 theorem InfPrime.inf_le (ha : InfPrime a) : b ⊓ c ≤ a ↔ b ≤ a ∨ c ≤ a :=
   ⟨fun h => ha.2 h, fun h => h.elim inf_le_of_left_le inf_le_of_right_le⟩
 #align inf_prime.inf_le InfPrime.inf_le
+-/
 
 variable [OrderTop α] {s : Finset ι} {f : ι → α}
 
+#print not_infIrred_top /-
 @[simp]
 theorem not_infIrred_top : ¬InfIrred (⊤ : α) :=
   isMax_top.not_infIrred
 #align not_inf_irred_top not_infIrred_top
+-/
 
+#print not_infPrime_top /-
 @[simp]
 theorem not_infPrime_top : ¬InfPrime (⊤ : α) :=
   isMax_top.not_infPrime
 #align not_inf_prime_top not_infPrime_top
+-/
 
+#print InfIrred.ne_top /-
 theorem InfIrred.ne_top (ha : InfIrred a) : a ≠ ⊤ := by rintro rfl; exact not_infIrred_top ha
 #align inf_irred.ne_top InfIrred.ne_top
+-/
 
+#print InfPrime.ne_top /-
 theorem InfPrime.ne_top (ha : InfPrime a) : a ≠ ⊤ := by rintro rfl; exact not_infPrime_top ha
 #align inf_prime.ne_top InfPrime.ne_top
+-/
 
+#print InfIrred.finset_inf_eq /-
 theorem InfIrred.finset_inf_eq : InfIrred a → s.inf f = a → ∃ i ∈ s, f i = a :=
   @SupIrred.finset_sup_eq _ αᵒᵈ _ _ _ _ _
 #align inf_irred.finset_inf_eq InfIrred.finset_inf_eq
+-/
 
+#print InfPrime.finset_inf_le /-
 theorem InfPrime.finset_inf_le (ha : InfPrime a) : s.inf f ≤ a ↔ ∃ i ∈ s, f i ≤ a :=
   @SupPrime.le_finset_sup _ αᵒᵈ _ _ _ _ _ ha
 #align inf_prime.finset_inf_le InfPrime.finset_inf_le
+-/
 
 variable [WellFoundedGT α]
 
+#print exists_infIrred_decomposition /-
 /-- In a cowell-founded lattice, any element is the infimum of finitely many inf-irreducible
 elements. This is the order-theoretic analogue of prime factorisation. -/
 theorem exists_infIrred_decomposition (a : α) :
     ∃ s : Finset α, s.inf id = a ∧ ∀ ⦃b⦄, b ∈ s → InfIrred b :=
   @exists_supIrred_decomposition αᵒᵈ _ _ _ _
 #align exists_inf_irred_decomposition exists_infIrred_decomposition
+-/
 
 end SemilatticeInf
 
@@ -232,25 +296,33 @@ section SemilatticeSup
 
 variable [SemilatticeSup α]
 
+#print infIrred_toDual /-
 @[simp]
 theorem infIrred_toDual {a : α} : InfIrred (toDual a) ↔ SupIrred a :=
   Iff.rfl
 #align inf_irred_to_dual infIrred_toDual
+-/
 
+#print infPrime_toDual /-
 @[simp]
 theorem infPrime_toDual {a : α} : InfPrime (toDual a) ↔ SupPrime a :=
   Iff.rfl
 #align inf_prime_to_dual infPrime_toDual
+-/
 
+#print supIrred_ofDual /-
 @[simp]
 theorem supIrred_ofDual {a : αᵒᵈ} : SupIrred (ofDual a) ↔ InfIrred a :=
   Iff.rfl
 #align sup_irred_of_dual supIrred_ofDual
+-/
 
+#print supPrime_ofDual /-
 @[simp]
 theorem supPrime_ofDual {a : αᵒᵈ} : SupPrime (ofDual a) ↔ InfPrime a :=
   Iff.rfl
 #align sup_prime_of_dual supPrime_ofDual
+-/
 
 alias infIrred_toDual ↔ _ SupIrred.dual
 #align sup_irred.dual SupIrred.dual
@@ -270,25 +342,33 @@ section SemilatticeInf
 
 variable [SemilatticeInf α]
 
+#print supIrred_toDual /-
 @[simp]
 theorem supIrred_toDual {a : α} : SupIrred (toDual a) ↔ InfIrred a :=
   Iff.rfl
 #align sup_irred_to_dual supIrred_toDual
+-/
 
+#print supPrime_toDual /-
 @[simp]
 theorem supPrime_toDual {a : α} : SupPrime (toDual a) ↔ InfPrime a :=
   Iff.rfl
 #align sup_prime_to_dual supPrime_toDual
+-/
 
+#print infIrred_ofDual /-
 @[simp]
 theorem infIrred_ofDual {a : αᵒᵈ} : InfIrred (ofDual a) ↔ SupIrred a :=
   Iff.rfl
 #align inf_irred_of_dual infIrred_ofDual
+-/
 
+#print infPrime_ofDual /-
 @[simp]
 theorem infPrime_ofDual {a : αᵒᵈ} : InfPrime (ofDual a) ↔ SupPrime a :=
   Iff.rfl
 #align inf_prime_of_dual infPrime_ofDual
+-/
 
 alias supIrred_toDual ↔ _ InfIrred.dual
 #align inf_irred.dual InfIrred.dual
@@ -308,17 +388,21 @@ section DistribLattice
 
 variable [DistribLattice α] {a b c : α}
 
+#print supPrime_iff_supIrred /-
 @[simp]
 theorem supPrime_iff_supIrred : SupPrime a ↔ SupIrred a :=
   ⟨SupPrime.supIrred,
     And.imp_right fun h b c => by simp_rw [← inf_eq_left, inf_sup_left]; exact @h _ _⟩
 #align sup_prime_iff_sup_irred supPrime_iff_supIrred
+-/
 
+#print infPrime_iff_infIrred /-
 @[simp]
 theorem infPrime_iff_infIrred : InfPrime a ↔ InfIrred a :=
   ⟨InfPrime.infIrred,
     And.imp_right fun h b c => by simp_rw [← sup_eq_left, sup_inf_left]; exact @h _ _⟩
 #align inf_prime_iff_inf_irred infPrime_iff_infIrred
+-/
 
 alias supPrime_iff_supIrred ↔ _ SupIrred.supPrime
 #align sup_irred.sup_prime SupIrred.supPrime
@@ -334,25 +418,33 @@ section LinearOrder
 
 variable [LinearOrder α] {a : α}
 
+#print supPrime_iff_not_isMin /-
 @[simp]
 theorem supPrime_iff_not_isMin : SupPrime a ↔ ¬IsMin a :=
   and_iff_left <| by simp
 #align sup_prime_iff_not_is_min supPrime_iff_not_isMin
+-/
 
+#print infPrime_iff_not_isMax /-
 @[simp]
 theorem infPrime_iff_not_isMax : InfPrime a ↔ ¬IsMax a :=
   and_iff_left <| by simp
 #align inf_prime_iff_not_is_max infPrime_iff_not_isMax
+-/
 
+#print supIrred_iff_not_isMin /-
 @[simp]
 theorem supIrred_iff_not_isMin : SupIrred a ↔ ¬IsMin a :=
   and_iff_left fun _ _ => by simpa only [sup_eq_max, max_eq_iff] using Or.imp And.left And.left
 #align sup_irred_iff_not_is_min supIrred_iff_not_isMin
+-/
 
+#print infIrred_iff_not_isMax /-
 @[simp]
 theorem infIrred_iff_not_isMax : InfIrred a ↔ ¬IsMax a :=
   and_iff_left fun _ _ => by simpa only [inf_eq_min, min_eq_iff] using Or.imp And.left And.left
 #align inf_irred_iff_not_is_max infIrred_iff_not_isMax
+-/
 
 end LinearOrder
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -321,7 +321,7 @@ alias ⟨_, SupIrred.supPrime⟩ := supPrime_iff_supIrred
 alias ⟨_, InfIrred.infPrime⟩ := infPrime_iff_infIrred
 #align inf_irred.inf_prime InfIrred.infPrime
 
--- porting note: was attribute [protected] SupIrred.supPrime InfIrred.infPrime
+-- Porting note: was attribute [protected] SupIrred.supPrime InfIrred.infPrime
 
 end DistribLattice
 

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -188,12 +188,12 @@ theorem InfPrime.inf_le (ha : InfPrime a) : b ⊓ c ≤ a ↔ b ≤ a ∨ c ≤
 
 variable [OrderTop α] {s : Finset ι} {f : ι → α}
 
--- @[simp] Porting note: simp can prove this.
+-- @[simp] Porting note (#10618): simp can prove this.
 theorem not_infIrred_top : ¬InfIrred (⊤ : α) :=
   isMax_top.not_infIrred
 #align not_inf_irred_top not_infIrred_top
 
--- @[simp] Porting note: simp can prove this.
+-- @[simp] Porting note (#10618): simp can prove this.
 theorem not_infPrime_top : ¬InfPrime (⊤ : α) :=
   isMax_top.not_infPrime
 #align not_inf_prime_top not_infPrime_top
@@ -329,12 +329,12 @@ section LinearOrder
 
 variable [LinearOrder α] {a : α}
 
--- @[simp] Porting note: simp can prove this
+-- @[simp] Porting note (#10618): simp can prove this
 theorem supPrime_iff_not_isMin : SupPrime a ↔ ¬IsMin a :=
   and_iff_left <| by simp
 #align sup_prime_iff_not_is_min supPrime_iff_not_isMin
 
--- @[simp] Porting note: simp can prove this
+-- @[simp] Porting note (#10618): simp can prove thisrove this
 theorem infPrime_iff_not_isMax : InfPrime a ↔ ¬IsMax a :=
   and_iff_left <| by simp
 #align inf_prime_iff_not_is_max infPrime_iff_not_isMax

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
 import Mathlib.Data.Finset.Lattice
-import Mathlib.Data.Fintype.Card
 
 #align_import order.irreducible from "leanprover-community/mathlib"@"bf2428c9486c407ca38b5b3fb10b87dad0bc99fa"
 

@@ -248,16 +248,16 @@ theorem supPrime_ofDual {a : αᵒᵈ} : SupPrime (ofDual a) ↔ InfPrime a :=
   Iff.rfl
 #align sup_prime_of_dual supPrime_ofDual
 
-alias infIrred_toDual ↔ _ SupIrred.dual
+alias ⟨_, SupIrred.dual⟩ := infIrred_toDual
 #align sup_irred.dual SupIrred.dual
 
-alias infPrime_toDual ↔ _ SupPrime.dual
+alias ⟨_, SupPrime.dual⟩ := infPrime_toDual
 #align sup_prime.dual SupPrime.dual
 
-alias supIrred_ofDual ↔ _ InfIrred.ofDual
+alias ⟨_, InfIrred.ofDual⟩ := supIrred_ofDual
 #align inf_irred.of_dual InfIrred.ofDual
 
-alias supPrime_ofDual ↔ _ InfPrime.ofDual
+alias ⟨_, InfPrime.ofDual⟩ := supPrime_ofDual
 #align inf_prime.of_dual InfPrime.ofDual
 
 end SemilatticeSup
@@ -286,16 +286,16 @@ theorem infPrime_ofDual {a : αᵒᵈ} : InfPrime (ofDual a) ↔ SupPrime a :=
   Iff.rfl
 #align inf_prime_of_dual infPrime_ofDual
 
-alias supIrred_toDual ↔ _ InfIrred.dual
+alias ⟨_, InfIrred.dual⟩ := supIrred_toDual
 #align inf_irred.dual InfIrred.dual
 
-alias supPrime_toDual ↔ _ InfPrime.dual
+alias ⟨_, InfPrime.dual⟩ := supPrime_toDual
 #align inf_prime.dual InfPrime.dual
 
-alias infIrred_ofDual ↔ _ SupIrred.ofDual
+alias ⟨_, SupIrred.ofDual⟩ := infIrred_ofDual
 #align sup_irred.of_dual SupIrred.ofDual
 
-alias infPrime_ofDual ↔ _ SupPrime.ofDual
+alias ⟨_, SupPrime.ofDual⟩ := infPrime_ofDual
 #align sup_prime.of_dual SupPrime.ofDual
 
 end SemilatticeInf
@@ -316,10 +316,10 @@ theorem infPrime_iff_infIrred : InfPrime a ↔ InfIrred a :=
     And.imp_right fun h b c => by simp_rw [← sup_eq_left, sup_inf_left]; exact @h _ _⟩
 #align inf_prime_iff_inf_irred infPrime_iff_infIrred
 
-alias supPrime_iff_supIrred ↔ _ SupIrred.supPrime
+alias ⟨_, SupIrred.supPrime⟩ := supPrime_iff_supIrred
 #align sup_irred.sup_prime SupIrred.supPrime
 
-alias infPrime_iff_infIrred ↔ _ InfIrred.infPrime
+alias ⟨_, InfIrred.infPrime⟩ := infPrime_iff_infIrred
 #align inf_irred.inf_prime InfIrred.infPrime
 
 -- porting note: was attribute [protected] SupIrred.supPrime InfIrred.infPrime
@@ -351,4 +351,3 @@ theorem infIrred_iff_not_isMax : InfIrred a ↔ ¬IsMax a :=
 #align inf_irred_iff_not_is_max infIrred_iff_not_isMax
 
 end LinearOrder
-

@@ -113,7 +113,7 @@ theorem SupIrred.finset_sup_eq (ha : SupIrred a) (h : s.sup f = a) : ∃ i ∈ s
   induction' s using Finset.induction with i s _ ih
   · simpa [ha.ne_bot] using h.symm
   simp only [exists_prop, exists_mem_insert] at ih ⊢
-  rw [sup_insert] at h 
+  rw [sup_insert] at h
   exact (ha.2 h).imp_right ih
 #align sup_irred.finset_sup_eq SupIrred.finset_sup_eq
 
@@ -136,7 +136,7 @@ theorem exists_supIrred_decomposition (a : α) :
   rintro a ih
   by_cases ha : SupIrred a
   · exact ⟨{a}, by simp [ha]⟩
-  rw [not_supIrred] at ha 
+  rw [not_supIrred] at ha
   obtain ha | ⟨b, c, rfl, hb, hc⟩ := ha
   · exact ⟨∅, by simp [ha.eq_bot]⟩
   obtain ⟨s, rfl, hs⟩ := ih _ hb

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -34,7 +34,7 @@ Both hold for all (non-minimal) elements in a linear order.
 
 open Finset OrderDual
 
-variable {ι α : Type _}
+variable {ι α : Type*}
 
 /-! ### Irreducible and prime elements -/
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module order.irreducible
-! leanprover-community/mathlib commit bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Finset.Lattice
 import Mathlib.Data.Fintype.Card
 
+#align_import order.irreducible from "leanprover-community/mathlib"@"bf2428c9486c407ca38b5b3fb10b87dad0bc99fa"
+
 /-!
 # Irreducible and prime elements in an order
 

Co-authored-by: Scott Morrison <scott@tqft.net>