data.rat.star ⟷ Mathlib.Data.Rat.Star

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

@@ -30,7 +30,7 @@ instance : StarRing ℚ where
 instance : TrivialStar ℚ where star_trivial _ := rfl
 
 instance : StarOrderedRing ℚ :=
-  StarOrderedRing.ofNonnegIff (fun _ _ => add_le_add_left) fun x =>
+  StarOrderedRing.of_nonneg_iff (fun _ _ => add_le_add_left) fun x =>
     by
     refine'
       ⟨fun hx => _, fun hx =>
@@ -52,7 +52,7 @@ instance : StarOrderedRing ℚ :=
     simp only [Int.cast_mul, Int.cast_natCast, coe_int_eq_mk, coe_nat_eq_mk]
     rw [mul_assoc, ← mul_assoc (mk (x.denom : ℤ) 1), mk_mul_mk_cancel one_ne_zero, ←
       one_mul (x.denom : ℤ), div_mk_div_cancel_left (by simpa using x.pos.ne' : (x.denom : ℤ) ≠ 0),
-      one_mul, mk_one_one, one_mul, mk_mul_mk_cancel one_ne_zero, Rat.num_den]
+      one_mul, mk_one_one, one_mul, mk_mul_mk_cancel one_ne_zero, Rat.num_divInt_den]
 
 end Rat
 

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

@@ -47,9 +47,9 @@ instance : StarOrderedRing ℚ :=
         x
       by exact this ▸ sum_mem fun n hn => AddSubmonoid.subset_closure ⟨_, rfl⟩
     simp only [Function.const_apply, Finset.sum_const, Finset.card_range, nsmul_eq_mul, mk_pnat_eq]
-    rw [← Int.cast_ofNat, Int.ofNat_mul, Int.natCast_natAbs,
-      abs_of_nonneg (num_nonneg_iff_zero_le.mpr hx), Int.cast_mul, Int.cast_ofNat]
-    simp only [Int.cast_mul, Int.cast_ofNat, coe_int_eq_mk, coe_nat_eq_mk]
+    rw [← Int.cast_natCast, Int.ofNat_mul, Int.natCast_natAbs,
+      abs_of_nonneg (num_nonneg_iff_zero_le.mpr hx), Int.cast_mul, Int.cast_natCast]
+    simp only [Int.cast_mul, Int.cast_natCast, coe_int_eq_mk, coe_nat_eq_mk]
     rw [mul_assoc, ← mul_assoc (mk (x.denom : ℤ) 1), mk_mul_mk_cancel one_ne_zero, ←
       one_mul (x.denom : ℤ), div_mk_div_cancel_left (by simpa using x.pos.ne' : (x.denom : ℤ) ≠ 0),
       one_mul, mk_one_one, one_mul, mk_mul_mk_cancel one_ne_zero, Rat.num_den]

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

@@ -47,7 +47,7 @@ instance : StarOrderedRing ℚ :=
         x
       by exact this ▸ sum_mem fun n hn => AddSubmonoid.subset_closure ⟨_, rfl⟩
     simp only [Function.const_apply, Finset.sum_const, Finset.card_range, nsmul_eq_mul, mk_pnat_eq]
-    rw [← Int.cast_ofNat, Int.ofNat_mul, Int.coe_natAbs,
+    rw [← Int.cast_ofNat, Int.ofNat_mul, Int.natCast_natAbs,
       abs_of_nonneg (num_nonneg_iff_zero_le.mpr hx), Int.cast_mul, Int.cast_ofNat]
     simp only [Int.cast_mul, Int.cast_ofNat, coe_int_eq_mk, coe_nat_eq_mk]
     rw [mul_assoc, ← mul_assoc (mk (x.denom : ℤ) 1), mk_mul_mk_cancel one_ne_zero, ←

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

@@ -34,7 +34,7 @@ instance : StarOrderedRing ℚ :=
     by
     refine'
       ⟨fun hx => _, fun hx =>
-        AddSubmonoid.closure_induction hx (by rintro - ⟨s, rfl⟩; exact mul_self_nonneg s) le_rfl
+        AddSubmonoid.closure_induction hx (by rintro - ⟨s, rfl⟩; exact hMul_self_nonneg s) le_rfl
           fun _ _ => add_nonneg⟩
     /- If `x = p / q`, then, since `0 ≤ x`, we have `p q : ℕ`, and `p / q` is the sum of `p * q`
       copies of `(1 / q) ^ 2`, and so `x` lies in the `add_submonoid` generated by square elements.

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

@@ -3,9 +3,9 @@ Copyright (c) 2023 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Mathbin.Algebra.Star.Order
-import Mathbin.Data.Rat.Lemmas
-import Mathbin.GroupTheory.Submonoid.Membership
+import Algebra.Star.Order
+import Data.Rat.Lemmas
+import GroupTheory.Submonoid.Membership
 
 #align_import data.rat.star from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
 

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

@@ -24,7 +24,7 @@ namespace Rat
 instance : StarRing ℚ where
   unit := id
   star_involutive _ := rfl
-  star_mul _ _ := mul_comm _ _
+  star_hMul _ _ := mul_comm _ _
   star_add _ _ := rfl
 
 instance : TrivialStar ℚ where star_trivial _ := rfl

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module data.rat.star
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Star.Order
 import Mathbin.Data.Rat.Lemmas
 import Mathbin.GroupTheory.Submonoid.Membership
 
+#align_import data.rat.star from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-! # Star order structure on ℚ
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module data.rat.star
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.GroupTheory.Submonoid.Membership
 
 /-! # Star order structure on ℚ
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Here we put the trivial `star` operation on `ℚ` for convenience and show that it is a
 `star_ordered_ring`. In particular, this means that every element of `ℚ` is a sum of squares.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

Also golf the existing instance for ℚ and rename Rat.num_nonneg_iff_zero_le to Rat.num_nonneg, Rat.num_pos_iff_pos to Rat.num_pos.

From LeanAPAP

@@ -1,52 +1,64 @@
 /-
 Copyright (c) 2023 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Jireh Loreaux
+Authors: Jireh Loreaux, Yaël Dillies
 -/
+import Mathlib.Algebra.GroupWithZero.Power
+import Mathlib.Algebra.Parity
 import Mathlib.Algebra.Star.Order
-import Mathlib.Data.Rat.Lemmas
-import Mathlib.Data.Rat.Order
-import Mathlib.GroupTheory.Submonoid.Membership
+import Mathlib.Data.NNRat.Lemmas
+import Mathlib.GroupTheory.Submonoid.Order
+import Mathlib.Tactic.FieldSimp
 
 #align_import data.rat.star from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
 
-/-! # Star order structure on ℚ
+/-!
+# Star ordered ring structures on `ℚ` and `ℚ≥0`
 
-Here we put the trivial `star` operation on `ℚ` for convenience and show that it is a
-`StarOrderedRing`. In particular, this means that every element of `ℚ` is a sum of squares.
+This file shows that `ℚ` and `ℚ≥0` are `StarOrderedRing`s. In particular, this means that every
+nonnegative rational number is a sum of squares.
 -/
 
+open AddSubmonoid Set
+open scoped NNRat
+
+namespace NNRat
+
+@[simp] lemma addSubmonoid_closure_range_pow {n : ℕ} (hn₀ : n ≠ 0) :
+    closure (range fun x : ℚ≥0 ↦ x ^ n) = ⊤ := by
+  refine (eq_top_iff' _).2 fun x ↦ ?_
+  suffices x = (x.num * x.den ^ (n - 1)) • (x.den : ℚ≥0)⁻¹ ^ n by
+    rw [this]
+    exact nsmul_mem (subset_closure <| mem_range_self _) _
+  rw [nsmul_eq_mul]
+  push_cast
+  rw [mul_assoc, pow_sub₀, pow_one, mul_right_comm, ← mul_pow, mul_inv_cancel, one_pow, one_mul,
+    ← div_eq_mul_inv, num_div_den]
+  all_goals simp [x.den_pos.ne', Nat.one_le_iff_ne_zero, *]
+
+@[simp] lemma addSubmonoid_closure_range_mul_self : closure (range fun x : ℚ≥0 ↦ x * x) = ⊤ := by
+  simpa only [sq] using addSubmonoid_closure_range_pow two_ne_zero
+
+instance instStarOrderedRing : StarOrderedRing ℚ≥0 where
+  le_iff a b := by simp [le_iff_exists_nonneg_add a b]
+
+end NNRat
 
 namespace Rat
 
-instance : StarRing ℚ where
-  star := id
-  star_involutive _ := rfl
-  star_mul _ _ := mul_comm _ _
-  star_add _ _ := rfl
-
-instance : TrivialStar ℚ where star_trivial _ := rfl
-
-instance : StarOrderedRing ℚ :=
-  StarOrderedRing.ofNonnegIff (fun {_ _} => add_le_add_left) fun x => by
-    refine'
-      ⟨fun hx => _, fun hx =>
-        AddSubmonoid.closure_induction hx (by rintro - ⟨s, rfl⟩; exact mul_self_nonneg s) le_rfl
-          fun _ _ => add_nonneg⟩
-    /- If `x = p / q`, then, since `0 ≤ x`, we have `p q : ℕ`, and `p / q` is the sum of `p * q`
-      copies of `(1 / q) ^ 2`, and so `x` lies in the `AddSubmonoid` generated by square elements.
-
-      Note: it's possible to rephrase this argument as `x = (p * q) • (1 / q) ^ 2`, but this would
-      be somewhat challenging without increasing import requirements. -/
-    -- Porting note: rewrote proof to avoid removed constructor rat.mk_pnat
-    suffices
-      (Finset.range (x.num.natAbs * x.den)).sum
-          (Function.const ℕ ((1 : ℚ) / x.den * ((1 : ℚ) / x.den))) =
-        x
-      by exact this ▸ sum_mem fun n _ => AddSubmonoid.subset_closure ⟨_, rfl⟩
-    simp only [Function.const_apply, Finset.sum_const, Finset.card_range, nsmul_eq_mul]
-    rw [← Int.cast_ofNat, Int.ofNat_mul, Int.coe_natAbs,
-      abs_of_nonneg (num_nonneg.mpr hx), Int.cast_mul, Int.cast_ofNat]
-    rw [← mul_assoc, mul_assoc (x.num : ℚ), mul_one_div_cancel (Nat.cast_ne_zero.mpr x.pos.ne'),
-      mul_one, mul_one_div, Rat.num_div_den]
+@[simp] lemma addSubmonoid_closure_range_pow {n : ℕ} (hn₀ : n ≠ 0) (hn : Even n) :
+    closure (range fun x : ℚ ↦ x ^ n) = nonneg _ := by
+  convert (AddMonoidHom.map_mclosure NNRat.coeHom <| range fun x ↦ x ^ n).symm
+  · have (x : ℚ) : ∃ y : ℚ≥0, y ^ n = x ^ n := ⟨x.nnabs, by simp [hn.pow_abs]⟩
+    simp [subset_antisymm_iff, range_subset_iff, this]
+  · ext
+    simp [NNRat.addSubmonoid_closure_range_pow hn₀, NNRat.exists]
+
+@[simp]
+lemma addSubmonoid_closure_range_mul_self : closure (range fun x : ℚ ↦ x * x) = nonneg _ := by
+  simpa only [sq] using addSubmonoid_closure_range_pow two_ne_zero even_two
+
+instance instStarOrderedRing : StarOrderedRing ℚ where
+  le_iff a b := by simp [le_iff_exists_nonneg_add a b]
+
 end Rat

and rename num_nonneg_iff_zero_le to num_nonneg, num_pos_iff_pos to num_pos

From LeanAPAP

@@ -46,7 +46,7 @@ instance : StarOrderedRing ℚ :=
       by exact this ▸ sum_mem fun n _ => AddSubmonoid.subset_closure ⟨_, rfl⟩
     simp only [Function.const_apply, Finset.sum_const, Finset.card_range, nsmul_eq_mul]
     rw [← Int.cast_ofNat, Int.ofNat_mul, Int.coe_natAbs,
-      abs_of_nonneg (num_nonneg_iff_zero_le.mpr hx), Int.cast_mul, Int.cast_ofNat]
+      abs_of_nonneg (num_nonneg.mpr hx), Int.cast_mul, Int.cast_ofNat]
     rw [← mul_assoc, mul_assoc (x.num : ℚ), mul_one_div_cancel (Nat.cast_ne_zero.mpr x.pos.ne'),
       mul_one, mul_one_div, Rat.num_div_den]
 end Rat

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -5,6 +5,7 @@ Authors: Jireh Loreaux
 -/
 import Mathlib.Algebra.Star.Order
 import Mathlib.Data.Rat.Lemmas
+import Mathlib.Data.Rat.Order
 import Mathlib.GroupTheory.Submonoid.Membership
 
 #align_import data.rat.star from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -46,7 +46,6 @@ instance : StarOrderedRing ℚ :=
     simp only [Function.const_apply, Finset.sum_const, Finset.card_range, nsmul_eq_mul]
     rw [← Int.cast_ofNat, Int.ofNat_mul, Int.coe_natAbs,
       abs_of_nonneg (num_nonneg_iff_zero_le.mpr hx), Int.cast_mul, Int.cast_ofNat]
-    simp only [Int.cast_mul, Int.cast_ofNat]
     rw [← mul_assoc, mul_assoc (x.num : ℚ), mul_one_div_cancel (Nat.cast_ne_zero.mpr x.pos.ne'),
       mul_one, mul_one_div, Rat.num_div_den]
 end Rat

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module data.rat.star
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Star.Order
 import Mathlib.Data.Rat.Lemmas
 import Mathlib.GroupTheory.Submonoid.Membership
 
+#align_import data.rat.star from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-! # Star order structure on ℚ
 
 Here we put the trivial `star` operation on `ℚ` for convenience and show that it is a