algebra.order.nonneg.floor ⟷ Mathlib.Algebra.Order.Nonneg.Floor

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

@@ -46,10 +46,10 @@ instance floorSemiring [OrderedSemiring α] [FloorSemiring α] : FloorSemiring {
   gc_floor a n ha :=
     by
     refine' (FloorSemiring.gc_floor (show 0 ≤ (a : α) from ha)).trans _
-    rw [← Subtype.coe_le_coe, Nonneg.coe_nat_cast]
+    rw [← Subtype.coe_le_coe, Nonneg.coe_natCast]
   gc_ceil a n := by
     refine' (FloorSemiring.gc_ceil (a : α) n).trans _
-    rw [← Subtype.coe_le_coe, Nonneg.coe_nat_cast]
+    rw [← Subtype.coe_le_coe, Nonneg.coe_natCast]
 #align nonneg.floor_semiring Nonneg.floorSemiring
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 -/
-import Mathbin.Algebra.Order.Nonneg.Ring
-import Mathbin.Algebra.Order.Archimedean
+import Algebra.Order.Nonneg.Ring
+import Algebra.Order.Archimedean
 
 #align_import algebra.order.nonneg.floor from "leanprover-community/mathlib"@"b3f4f007a962e3787aa0f3b5c7942a1317f7d88e"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
-
-! This file was ported from Lean 3 source module algebra.order.nonneg.floor
-! leanprover-community/mathlib commit b3f4f007a962e3787aa0f3b5c7942a1317f7d88e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Nonneg.Ring
 import Mathbin.Algebra.Order.Archimedean
 
+#align_import algebra.order.nonneg.floor from "leanprover-community/mathlib"@"b3f4f007a962e3787aa0f3b5c7942a1317f7d88e"
+
 /-!
 # Nonnegative elements are archimedean
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -32,12 +32,15 @@ namespace Nonneg
 
 variable {α : Type _}
 
+#print Nonneg.archimedean /-
 instance archimedean [OrderedAddCommMonoid α] [Archimedean α] : Archimedean { x : α // 0 ≤ x } :=
   ⟨fun x y hy =>
     let ⟨n, hr⟩ := Archimedean.arch (x : α) (hy : (0 : α) < y)
     ⟨n, show (x : α) ≤ (n • y : { x : α // 0 ≤ x }) by simp [*, -nsmul_eq_mul, nsmul_coe]⟩⟩
 #align nonneg.archimedean Nonneg.archimedean
+-/
 
+#print Nonneg.floorSemiring /-
 instance floorSemiring [OrderedSemiring α] [FloorSemiring α] : FloorSemiring { r : α // 0 ≤ r }
     where
   floor a := ⌊(a : α)⌋₊
@@ -51,18 +54,23 @@ instance floorSemiring [OrderedSemiring α] [FloorSemiring α] : FloorSemiring {
     refine' (FloorSemiring.gc_ceil (a : α) n).trans _
     rw [← Subtype.coe_le_coe, Nonneg.coe_nat_cast]
 #align nonneg.floor_semiring Nonneg.floorSemiring
+-/
 
+#print Nonneg.nat_floor_coe /-
 @[norm_cast]
 theorem nat_floor_coe [OrderedSemiring α] [FloorSemiring α] (a : { r : α // 0 ≤ r }) :
     ⌊(a : α)⌋₊ = ⌊a⌋₊ :=
   rfl
 #align nonneg.nat_floor_coe Nonneg.nat_floor_coe
+-/
 
+#print Nonneg.nat_ceil_coe /-
 @[norm_cast]
 theorem nat_ceil_coe [OrderedSemiring α] [FloorSemiring α] (a : { r : α // 0 ≤ r }) :
     ⌈(a : α)⌉₊ = ⌈a⌉₊ :=
   rfl
 #align nonneg.nat_ceil_coe Nonneg.nat_ceil_coe
+-/
 
 end Nonneg
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -32,24 +32,12 @@ namespace Nonneg
 
 variable {α : Type _}
 
-/- warning: nonneg.archimedean -> Nonneg.archimedean is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nonneg.archimedean Nonneg.archimedeanₓ'. -/
 instance archimedean [OrderedAddCommMonoid α] [Archimedean α] : Archimedean { x : α // 0 ≤ x } :=
   ⟨fun x y hy =>
     let ⟨n, hr⟩ := Archimedean.arch (x : α) (hy : (0 : α) < y)
     ⟨n, show (x : α) ≤ (n • y : { x : α // 0 ≤ x }) by simp [*, -nsmul_eq_mul, nsmul_coe]⟩⟩
 #align nonneg.archimedean Nonneg.archimedean
 
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-Case conversion may be inaccurate. Consider using '#align nonneg.floor_semiring Nonneg.floorSemiringₓ'. -/
 instance floorSemiring [OrderedSemiring α] [FloorSemiring α] : FloorSemiring { r : α // 0 ≤ r }
     where
   floor a := ⌊(a : α)⌋₊
@@ -64,24 +52,12 @@ instance floorSemiring [OrderedSemiring α] [FloorSemiring α] : FloorSemiring {
     rw [← Subtype.coe_le_coe, Nonneg.coe_nat_cast]
 #align nonneg.floor_semiring Nonneg.floorSemiring
 
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 @[norm_cast]
 theorem nat_floor_coe [OrderedSemiring α] [FloorSemiring α] (a : { r : α // 0 ≤ r }) :
     ⌊(a : α)⌋₊ = ⌊a⌋₊ :=
   rfl
 #align nonneg.nat_floor_coe Nonneg.nat_floor_coe
 
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 @[norm_cast]
 theorem nat_ceil_coe [OrderedSemiring α] [FloorSemiring α] (a : { r : α // 0 ≤ r }) :
     ⌈(a : α)⌉₊ = ⌈a⌉₊ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -34,7 +34,7 @@ variable {α : Type _}
 
 /- warning: nonneg.archimedean -> Nonneg.archimedean is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} α] [_inst_2 : Archimedean.{u1} α _inst_1], Archimedean.{u1} (Subtype.{succ u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddCommMonoid.toAddMonoid.{u1} α (OrderedAddCommMonoid.toAddCommMonoid.{u1} α _inst_1))))))) x)) (Nonneg.orderedAddCommMonoid.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} α] [_inst_2 : Archimedean.{u1} α _inst_1], Archimedean.{u1} (Subtype.{succ u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (AddCommMonoid.toAddMonoid.{u1} α (OrderedAddCommMonoid.toAddCommMonoid.{u1} α _inst_1))))))) x)) (Nonneg.orderedAddCommMonoid.{u1} α _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : OrderedAddCommMonoid.{u1} α] [_inst_2 : Archimedean.{u1} α _inst_1], Archimedean.{u1} (Subtype.{succ u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (AddMonoid.toZero.{u1} α (AddCommMonoid.toAddMonoid.{u1} α (OrderedAddCommMonoid.toAddCommMonoid.{u1} α _inst_1))))) x)) (Nonneg.orderedAddCommMonoid.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align nonneg.archimedean Nonneg.archimedeanₓ'. -/
@@ -46,7 +46,7 @@ instance archimedean [OrderedAddCommMonoid α] [Archimedean α] : Archimedean {
 
 /- warning: nonneg.floor_semiring -> Nonneg.floorSemiring is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1], FloorSemiring.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1], FloorSemiring.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1], FloorSemiring.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align nonneg.floor_semiring Nonneg.floorSemiringₓ'. -/
@@ -66,7 +66,7 @@ instance floorSemiring [OrderedSemiring α] [FloorSemiring α] : FloorSemiring {
 
 /- warning: nonneg.nat_floor_coe -> Nonneg.nat_floor_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1] (a : Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)), Eq.{1} Nat (Nat.floor.{u1} α _inst_1 _inst_2 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeSubtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r))))) a)) (Nat.floor.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1) (Nonneg.floorSemiring.{u1} α _inst_1 _inst_2) a)
+  forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1] (a : Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)), Eq.{1} Nat (Nat.floor.{u1} α _inst_1 _inst_2 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeSubtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r))))) a)) (Nat.floor.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1) (Nonneg.floorSemiring.{u1} α _inst_1 _inst_2) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1] (a : Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r)), Eq.{1} Nat (Nat.floor.{u1} α _inst_1 _inst_2 (Subtype.val.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r) a)) (Nat.floor.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1) (Nonneg.floorSemiring.{u1} α _inst_1 _inst_2) a)
 Case conversion may be inaccurate. Consider using '#align nonneg.nat_floor_coe Nonneg.nat_floor_coeₓ'. -/
@@ -78,7 +78,7 @@ theorem nat_floor_coe [OrderedSemiring α] [FloorSemiring α] (a : { r : α // 0
 
 /- warning: nonneg.nat_ceil_coe -> Nonneg.nat_ceil_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1] (a : Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)), Eq.{1} Nat (Nat.ceil.{u1} α _inst_1 _inst_2 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeSubtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r))))) a)) (Nat.ceil.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1) (Nonneg.floorSemiring.{u1} α _inst_1 _inst_2) a)
+  forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1] (a : Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)), Eq.{1} Nat (Nat.ceil.{u1} α _inst_1 _inst_2 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (HasLiftT.mk.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (CoeTCₓ.coe.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeBase.{succ u1, succ u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) α (coeSubtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r))))) a)) (Nat.ceil.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommMonoid.toPartialOrder.{u1} α (OrderedSemiring.toOrderedAddCommMonoid.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1)))))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1) (Nonneg.floorSemiring.{u1} α _inst_1 _inst_2) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : OrderedSemiring.{u1} α] [_inst_2 : FloorSemiring.{u1} α _inst_1] (a : Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r)), Eq.{1} Nat (Nat.ceil.{u1} α _inst_1 _inst_2 (Subtype.val.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r) a)) (Nat.ceil.{u1} (Subtype.{succ u1} α (fun (r : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedSemiring.toPartialOrder.{u1} α _inst_1))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α (OrderedSemiring.toSemiring.{u1} α _inst_1))))) r)) (Nonneg.orderedSemiring.{u1} α _inst_1) (Nonneg.floorSemiring.{u1} α _inst_1 _inst_2) a)
 Case conversion may be inaccurate. Consider using '#align nonneg.nat_ceil_coe Nonneg.nat_ceil_coeₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

We already have the instances for ℕ, ℤ, and ℚ in this file, so adding NNRat doesn't feel that out of place, as it completes this {negation,division} lattice.

Follows on from #9917. These changes knock off 132 dependencies from NNRat, though adds more to Archimedean. I think this is acceptable; we need NNRat to be super early if we want to be able to use it in norm_num, and the depth of Archimedean will reduce with NNRat as I work towards this.

@@ -3,8 +3,8 @@ Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 -/
+import Mathlib.Algebra.Order.Floor
 import Mathlib.Algebra.Order.Nonneg.Ring
-import Mathlib.Algebra.Order.Archimedean
 
 #align_import algebra.order.nonneg.floor from "leanprover-community/mathlib"@"b3f4f007a962e3787aa0f3b5c7942a1317f7d88e"
 
@@ -25,12 +25,6 @@ namespace Nonneg
 
 variable {α : Type*}
 
-instance archimedean [OrderedAddCommMonoid α] [Archimedean α] : Archimedean { x : α // 0 ≤ x } :=
-  ⟨fun x y hy =>
-    let ⟨n, hr⟩ := Archimedean.arch (x : α) (hy : (0 : α) < y)
-    ⟨n, show (x : α) ≤ (n • y : { x : α // 0 ≤ x }) by simp [*, -nsmul_eq_mul, nsmul_coe]⟩⟩
-#align nonneg.archimedean Nonneg.archimedean
-
 instance floorSemiring [OrderedSemiring α] [FloorSemiring α] :
     FloorSemiring { r : α // 0 ≤ r } where
   floor a := ⌊(a : α)⌋₊

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

This has nice performance benefits.

@@ -23,7 +23,7 @@ This is used to derive algebraic structures on `ℝ≥0` and `ℚ≥0` automatic
 
 namespace Nonneg
 
-variable {α : Type _}
+variable {α : Type*}
 
 instance archimedean [OrderedAddCommMonoid α] [Archimedean α] : Archimedean { x : α // 0 ≤ x } :=
   ⟨fun x y hy =>

• 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) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
-
-! This file was ported from Lean 3 source module algebra.order.nonneg.floor
-! leanprover-community/mathlib commit b3f4f007a962e3787aa0f3b5c7942a1317f7d88e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Order.Nonneg.Ring
 import Mathlib.Algebra.Order.Archimedean
 
+#align_import algebra.order.nonneg.floor from "leanprover-community/mathlib"@"b3f4f007a962e3787aa0f3b5c7942a1317f7d88e"
+
 /-!
 # Nonnegative elements are archimedean
 

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -21,7 +21,7 @@ This is used to derive algebraic structures on `ℝ≥0` and `ℚ≥0` automatic
 
 ## Main declarations
 
-* `{x : α // 0 ≤ x}` is a `floor_semiring` if `α` is.
+* `{x : α // 0 ≤ x}` is a `FloorSemiring` if `α` is.
 -/
 
 namespace Nonneg

Match https://github.com/leanprover-community/mathlib/pull/18590 and https://github.com/leanprover-community/mathlib/pull/18596

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