linear_algebra.affine_space.midpoint_zero ⟷ Mathlib.LinearAlgebra.AffineSpace.MidpointZero

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Algebra.CharP.Invertible
-import Mathbin.LinearAlgebra.AffineSpace.Midpoint
+import Algebra.CharP.Invertible
+import LinearAlgebra.AffineSpace.Midpoint
 
 #align_import linear_algebra.affine_space.midpoint_zero from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.midpoint_zero
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.CharP.Invertible
 import Mathbin.LinearAlgebra.AffineSpace.Midpoint
 
+#align_import linear_algebra.affine_space.midpoint_zero from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Midpoint of a segment for characteristic zero
 

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

@@ -27,32 +27,43 @@ midpoint
 
 open AffineMap AffineEquiv
 
+#print lineMap_inv_two /-
 theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (2⁻¹ : R) = midpoint R a b :=
   rfl
 #align line_map_inv_two lineMap_inv_two
+-/
 
+#print lineMap_one_half /-
 theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (1 / 2 : R) = midpoint R a b := by
   rw [one_div, lineMap_inv_two]
 #align line_map_one_half lineMap_one_half
+-/
 
+#print homothety_invOf_two /-
 theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible (2 : R)]
     [AddCommGroup V] [Module R V] [AddTorsor V P] (a b : P) :
     homothety a (⅟ 2 : R) b = midpoint R a b :=
   rfl
 #align homothety_inv_of_two homothety_invOf_two
+-/
 
+#print homothety_inv_two /-
 theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (2⁻¹ : k) b = midpoint k a b :=
   rfl
 #align homothety_inv_two homothety_inv_two
+-/
 
+#print homothety_one_half /-
 theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (1 / 2 : k) b = midpoint k a b := by
   rw [one_div, homothety_inv_two]
 #align homothety_one_half homothety_one_half
+-/
 
+#print pi_midpoint_apply /-
 @[simp]
 theorem pi_midpoint_apply {k ι : Type _} {V : ∀ i : ι, Type _} {P : ∀ i : ι, Type _} [Field k]
     [Invertible (2 : k)] [∀ i, AddCommGroup (V i)] [∀ i, Module k (V i)]
@@ -60,4 +71,5 @@ theorem pi_midpoint_apply {k ι : Type _} {V : ∀ i : ι, Type _} {P : ∀ i :
     midpoint k f g i = midpoint k (f i) (g i) :=
   rfl
 #align pi_midpoint_apply pi_midpoint_apply
+-/
 

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

@@ -27,68 +27,32 @@ midpoint
 
 open AffineMap AffineEquiv
 
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 theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (2⁻¹ : R) = midpoint R a b :=
   rfl
 #align line_map_inv_two lineMap_inv_two
 
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 theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (1 / 2 : R) = midpoint R a b := by
   rw [one_div, lineMap_inv_two]
 #align line_map_one_half lineMap_one_half
 
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 theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible (2 : R)]
     [AddCommGroup V] [Module R V] [AddTorsor V P] (a b : P) :
     homothety a (⅟ 2 : R) b = midpoint R a b :=
   rfl
 #align homothety_inv_of_two homothety_invOf_two
 
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 theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (2⁻¹ : k) b = midpoint k a b :=
   rfl
 #align homothety_inv_two homothety_inv_two
 
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 theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (1 / 2 : k) b = midpoint k a b := by
   rw [one_div, homothety_inv_two]
 #align homothety_one_half homothety_one_half
 
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-  forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (Semiring.toOne.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.instAddTorsorForAllForAllAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
-Case conversion may be inaccurate. Consider using '#align pi_midpoint_apply pi_midpoint_applyₓ'. -/
 @[simp]
 theorem pi_midpoint_apply {k ι : Type _} {V : ∀ i : ι, Type _} {P : ∀ i : ι, Type _} [Field k]
     [Invertible (2 : k)] [∀ i, AddCommGroup (V i)] [∀ i, Module k (V i)]

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

@@ -31,7 +31,7 @@ open AffineMap AffineEquiv
 lean 3 declaration is
   forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : R) => P) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align line_map_inv_two lineMap_inv_twoₓ'. -/
 theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (2⁻¹ : R) = midpoint R a b :=
@@ -42,7 +42,7 @@ theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R
 lean 3 declaration is
   forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : R) => P) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align line_map_one_half lineMap_one_halfₓ'. -/
 theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (1 / 2 : R) = midpoint R a b := by
@@ -53,7 +53,7 @@ theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero
 lean 3 declaration is
   forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Invertible.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) _inst_2)) b) (midpoint.{u1, u2, u3} R V P (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : Invertible.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) _inst_2)) b) (midpoint.{u3, u2, u1} R V P (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : Invertible.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) _inst_2)) b) (midpoint.{u3, u2, u1} R V P (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_inv_of_two homothety_invOf_twoₓ'. -/
 theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible (2 : R)]
     [AddCommGroup V] [Module R V] [AddTorsor V P] (a b : P) :
@@ -65,7 +65,7 @@ theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u3} k (Field.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u3} k (Field.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_inv_two homothety_inv_twoₓ'. -/
 theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (2⁻¹ : k) b = midpoint k a b :=
@@ -76,7 +76,7 @@ theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [Ad
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u1, u1, u1} k k k (instHDiv.{u1} k (DivInvMonoid.toHasDiv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u3, u3, u3} k k k (instHDiv.{u3} k (Field.toDiv.{u3} k _inst_1)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u3, u3, u3} k k k (instHDiv.{u3} k (Field.toDiv.{u3} k _inst_1)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_one_half homothety_one_halfₓ'. -/
 theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (1 / 2 : k) b = midpoint k a b := by
@@ -87,7 +87,7 @@ theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [A
 lean 3 declaration is
   forall {k : Type.{u1}} {ι : Type.{u2}} {V : ι -> Type.{u3}} {P : ι -> Type.{u4}} [_inst_1 : Field.{u1} k] [_inst_2 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))] [_inst_3 : forall (i : ι), AddCommGroup.{u3} (V i)] [_inst_4 : forall (i : ι), Module.{u1, u3} k (V i) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u3, u4} (V i) (P i) (AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u4} (P i) (midpoint.{u1, max u2 u3, max u2 u4} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.addTorsor.{u2, u3, u4} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u1, u3, u4} k (V i) (P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
 but is expected to have type
-  forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (Semiring.toOne.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => P i) (fun (i : ι) => _inst_3 i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
+  forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (Semiring.toOne.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.instAddTorsorForAllForAllAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
 Case conversion may be inaccurate. Consider using '#align pi_midpoint_apply pi_midpoint_applyₓ'. -/
 @[simp]
 theorem pi_midpoint_apply {k ι : Type _} {V : ∀ i : ι, Type _} {P : ∀ i : ι, Type _} [Field k]

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -31,7 +31,7 @@ open AffineMap AffineEquiv
 lean 3 declaration is
   forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align line_map_inv_two lineMap_inv_twoₓ'. -/
 theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (2⁻¹ : R) = midpoint R a b :=
@@ -42,7 +42,7 @@ theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R
 lean 3 declaration is
   forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (Semiring.toOne.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align line_map_one_half lineMap_one_halfₓ'. -/
 theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (1 / 2 : R) = midpoint R a b := by
@@ -53,7 +53,7 @@ theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero
 lean 3 declaration is
   forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Invertible.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) _inst_2)) b) (midpoint.{u1, u2, u3} R V P (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : Invertible.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) _inst_2)) b) (midpoint.{u3, u2, u1} R V P (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : Invertible.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (Semiring.toNatCast.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) _inst_2)) b) (midpoint.{u3, u2, u1} R V P (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_inv_of_two homothety_invOf_twoₓ'. -/
 theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible (2 : R)]
     [AddCommGroup V] [Module R V] [AddTorsor V P] (a b : P) :
@@ -65,7 +65,7 @@ theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u3} k (Field.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u3} k (Field.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_inv_two homothety_inv_twoₓ'. -/
 theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (2⁻¹ : k) b = midpoint k a b :=
@@ -76,7 +76,7 @@ theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [Ad
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u1, u1, u1} k k k (instHDiv.{u1} k (DivInvMonoid.toHasDiv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u3, u3, u3} k k k (instHDiv.{u3} k (Field.toDiv.{u3} k _inst_1)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u3, u3, u3} k k k (instHDiv.{u3} k (Field.toDiv.{u3} k _inst_1)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (Semiring.toNatCast.{u3} k (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_one_half homothety_one_halfₓ'. -/
 theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (1 / 2 : k) b = midpoint k a b := by
@@ -87,7 +87,7 @@ theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [A
 lean 3 declaration is
   forall {k : Type.{u1}} {ι : Type.{u2}} {V : ι -> Type.{u3}} {P : ι -> Type.{u4}} [_inst_1 : Field.{u1} k] [_inst_2 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))] [_inst_3 : forall (i : ι), AddCommGroup.{u3} (V i)] [_inst_4 : forall (i : ι), Module.{u1, u3} k (V i) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u3, u4} (V i) (P i) (AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u4} (P i) (midpoint.{u1, max u2 u3, max u2 u4} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.addTorsor.{u2, u3, u4} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u1, u3, u4} k (V i) (P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
 but is expected to have type
-  forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (NonAssocRing.toNatCast.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => P i) (fun (i : ι) => _inst_3 i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
+  forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (Semiring.toOne.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => P i) (fun (i : ι) => _inst_3 i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
 Case conversion may be inaccurate. Consider using '#align pi_midpoint_apply pi_midpoint_applyₓ'. -/
 @[simp]
 theorem pi_midpoint_apply {k ι : Type _} {V : ∀ i : ι, Type _} {P : ∀ i : ι, Type _} [Field k]

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.midpoint_zero
-! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.AffineSpace.Midpoint
 /-!
 # Midpoint of a segment for characteristic zero
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We collect lemmas that require that the underlying ring has characteristic zero.
 
 ## Tags

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -26,7 +26,7 @@ open AffineMap AffineEquiv
 
 /- warning: line_map_inv_two -> lineMap_inv_two is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
   forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align line_map_inv_two lineMap_inv_twoₓ'. -/
@@ -37,7 +37,7 @@ theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R
 
 /- warning: line_map_one_half -> lineMap_one_half is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
   forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u3, u3, u3} R R R (instHDiv.{u3} R (DivisionRing.toDiv.{u3} R _inst_1)) (OfNat.ofNat.{u3} R 1 (One.toOfNat1.{u3} R (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align line_map_one_half lineMap_one_halfₓ'. -/
@@ -48,7 +48,7 @@ theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero
 
 /- warning: homothety_inv_of_two -> homothety_invOf_two is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Invertible.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) _inst_2)) b) (midpoint.{u1, u2, u3} R V P (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
+  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Invertible.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} R V P V P (CommRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) _inst_2)) b) (midpoint.{u1, u2, u3} R V P (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
   forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : Invertible.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} R V P V P (CommRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} R V P _inst_1 _inst_3 _inst_5 _inst_4 a (Invertible.invOf.{u3} R (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) _inst_2)) b) (midpoint.{u3, u2, u1} R V P (CommRing.toRing.{u3} R _inst_1) _inst_2 _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_inv_of_two homothety_invOf_twoₓ'. -/
@@ -60,7 +60,7 @@ theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible
 
 /- warning: homothety_inv_two -> homothety_inv_two is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u1} k (DivInvMonoid.toHasInv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (Inv.inv.{u3} k (Field.toInv.{u3} k _inst_1) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_inv_two homothety_inv_twoₓ'. -/
@@ -71,7 +71,7 @@ theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [Ad
 
 /- warning: homothety_one_half -> homothety_one_half is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u1, u1, u1} k k k (instHDiv.{u1} k (DivInvMonoid.toHasDiv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u1, u1, u1} k k k (instHDiv.{u1} k (DivInvMonoid.toHasDiv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u3, u3, u3} k k k (instHDiv.{u3} k (Field.toDiv.{u3} k _inst_1)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
 Case conversion may be inaccurate. Consider using '#align homothety_one_half homothety_one_halfₓ'. -/
@@ -82,7 +82,7 @@ theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [A
 
 /- warning: pi_midpoint_apply -> pi_midpoint_apply is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {ι : Type.{u2}} {V : ι -> Type.{u3}} {P : ι -> Type.{u4}} [_inst_1 : Field.{u1} k] [_inst_2 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))] [_inst_3 : forall (i : ι), AddCommGroup.{u3} (V i)] [_inst_4 : forall (i : ι), Module.{u1, u3} k (V i) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u3, u4} (V i) (P i) (AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u4} (P i) (midpoint.{u1, max u2 u3, max u2 u4} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.addTorsor.{u2, u3, u4} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u1, u3, u4} k (V i) (P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
+  forall {k : Type.{u1}} {ι : Type.{u2}} {V : ι -> Type.{u3}} {P : ι -> Type.{u4}} [_inst_1 : Field.{u1} k] [_inst_2 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))] [_inst_3 : forall (i : ι), AddCommGroup.{u3} (V i)] [_inst_4 : forall (i : ι), Module.{u1, u3} k (V i) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u3, u4} (V i) (P i) (AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u4} (P i) (midpoint.{u1, max u2 u3, max u2 u4} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.addTorsor.{u2, u3, u4} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u1, u3, u4} k (V i) (P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
 but is expected to have type
   forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (NonAssocRing.toNatCast.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => P i) (fun (i : ι) => _inst_3 i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
 Case conversion may be inaccurate. Consider using '#align pi_midpoint_apply pi_midpoint_applyₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -24,32 +24,68 @@ midpoint
 
 open AffineMap AffineEquiv
 
+/- warning: line_map_inv_two -> lineMap_inv_two is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+but is expected to have type
+  forall {R : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} R] [_inst_2 : CharZero.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} R V (DivisionSemiring.toSemiring.{u3} R (DivisionRing.toDivisionSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) R (fun (_x : R) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : R) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} R R R V P (DivisionRing.toRing.{u3} R _inst_1) (Ring.toAddCommGroup.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1)) (addGroupIsAddTorsor.{u3} R (AddGroupWithOne.toAddGroup.{u3} R (Ring.toAddGroupWithOne.{u3} R (DivisionRing.toRing.{u3} R _inst_1)))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (Inv.inv.{u3} R (DivisionRing.toInv.{u3} R _inst_1) (OfNat.ofNat.{u3} R 2 (instOfNat.{u3} R 2 (NonAssocRing.toNatCast.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R _inst_1))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (midpoint.{u3, u2, u1} R V P (DivisionRing.toRing.{u3} R _inst_1) (invertibleTwo.{u3} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+Case conversion may be inaccurate. Consider using '#align line_map_inv_two lineMap_inv_twoₓ'. -/
 theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (2⁻¹ : R) = midpoint R a b :=
   rfl
 #align line_map_inv_two lineMap_inv_two
 
+/- warning: line_map_one_half -> lineMap_one_half is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : CharZero.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} R V (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) => R -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} R R R V P (DivisionRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (addGroupIsAddTorsor.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))) _inst_3 _inst_4 _inst_5) (AffineMap.lineMap.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) _inst_3 _inst_4 _inst_5 a b) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))))))))))) (midpoint.{u1, u2, u3} R V P (DivisionRing.toRing.{u1} R _inst_1) (invertibleTwo.{u1} R _inst_1 _inst_2) _inst_3 _inst_4 _inst_5 a b)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align line_map_one_half lineMap_one_halfₓ'. -/
 theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (1 / 2 : R) = midpoint R a b := by
   rw [one_div, lineMap_inv_two]
 #align line_map_one_half lineMap_one_half
 
+/- warning: homothety_inv_of_two -> homothety_invOf_two is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align homothety_inv_of_two homothety_invOf_twoₓ'. -/
 theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible (2 : R)]
     [AddCommGroup V] [Module R V] [AddTorsor V P] (a b : P) :
     homothety a (⅟ 2 : R) b = midpoint R a b :=
   rfl
 #align homothety_inv_of_two homothety_invOf_two
 
+/- warning: homothety_inv_two -> homothety_inv_two is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align homothety_inv_two homothety_inv_twoₓ'. -/
 theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (2⁻¹ : k) b = midpoint k a b :=
   rfl
 #align homothety_inv_two homothety_inv_two
 
+/- warning: homothety_one_half -> homothety_one_half is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Field.{u1} k] [_inst_2 : CharZero.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) => P -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k V P V P (CommRing.toRing.{u1} k (Field.toCommRing.{u1} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u1, u2, u3} k V P (Field.toCommRing.{u1} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u1, u1, u1} k k k (instHDiv.{u1} k (DivInvMonoid.toHasDiv.{u1} k (DivisionRing.toDivInvMonoid.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))))))))) b) (midpoint.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Field.{u3} k] [_inst_2 : CharZero.{u3} k (AddGroupWithOne.toAddMonoidWithOne.{u3} k (Ring.toAddGroupWithOne.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1))))] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (Semifield.toDivisionSemiring.{u3} k (Field.toSemifield.{u3} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_3)] (a : P) (b : P), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) b) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k V P V P (CommRing.toRing.{u3} k (Field.toCommRing.{u3} k _inst_1)) _inst_3 _inst_4 _inst_5 _inst_3 _inst_4 _inst_5) (AffineMap.homothety.{u3, u2, u1} k V P (Field.toCommRing.{u3} k _inst_1) _inst_3 _inst_5 _inst_4 a (HDiv.hDiv.{u3, u3, u3} k k k (instHDiv.{u3} k (Field.toDiv.{u3} k _inst_1)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))))) (OfNat.ofNat.{u3} k 2 (instOfNat.{u3} k 2 (NonAssocRing.toNatCast.{u3} k (Ring.toNonAssocRing.{u3} k (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) b) (midpoint.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k (Field.toDivisionRing.{u3} k _inst_1)) (invertibleTwo.{u3} k (Field.toDivisionRing.{u3} k _inst_1) _inst_2) _inst_3 _inst_4 _inst_5 a b)
+Case conversion may be inaccurate. Consider using '#align homothety_one_half homothety_one_halfₓ'. -/
 theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (1 / 2 : k) b = midpoint k a b := by
   rw [one_div, homothety_inv_two]
 #align homothety_one_half homothety_one_half
 
+/- warning: pi_midpoint_apply -> pi_midpoint_apply is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {ι : Type.{u2}} {V : ι -> Type.{u3}} {P : ι -> Type.{u4}} [_inst_1 : Field.{u1} k] [_inst_2 : Invertible.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))))) (OfNat.ofNat.{u1} k 2 (OfNat.mk.{u1} k 2 (bit0.{u1} k (Distrib.toHasAdd.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)))) (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (NonAssocRing.toAddGroupWithOne.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))))))))))] [_inst_3 : forall (i : ι), AddCommGroup.{u3} (V i)] [_inst_4 : forall (i : ι), Module.{u1, u3} k (V i) (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u3, u4} (V i) (P i) (AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u4} (P i) (midpoint.{u1, max u2 u3, max u2 u4} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (Pi.addCommGroup.{u2, u3} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (Pi.addTorsor.{u2, u3, u4} ι (fun (i : ι) => V i) (fun (i : ι) => AddCommGroup.toAddGroup.{u3} (V i) (_inst_3 i)) (fun (i : ι) => P i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u1, u3, u4} k (V i) (P i) (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
+but is expected to have type
+  forall {k : Type.{u4}} {ι : Type.{u3}} {V : ι -> Type.{u2}} {P : ι -> Type.{u1}} [_inst_1 : Field.{u4} k] [_inst_2 : Invertible.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))))) (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 2 (instOfNat.{u4} k 2 (NonAssocRing.toNatCast.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] [_inst_3 : forall (i : ι), AddCommGroup.{u2} (V i)] [_inst_4 : forall (i : ι), Module.{u4, u2} k (V i) (DivisionSemiring.toSemiring.{u4} k (Semifield.toDivisionSemiring.{u4} k (Field.toSemifield.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i))] [_inst_5 : forall (i : ι), AddTorsor.{u2, u1} (V i) (P i) (AddCommGroup.toAddGroup.{u2} (V i) (_inst_3 i))] (f : forall (i : ι), P i) (g : forall (i : ι), P i) (i : ι), Eq.{succ u1} (P i) (midpoint.{u4, max u3 u2, max u3 u1} k (forall (i : ι), V i) (forall (i : ι), P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (Pi.addCommGroup.{u3, u2} ι (fun (i : ι) => V i) (fun (i : ι) => _inst_3 i)) (Pi.module.{u3, u2, u4} ι (fun (i : ι) => V i) k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (V i) (_inst_3 i)) (fun (i : ι) => _inst_4 i)) (AffineMap.instAddTorsorForAllForAllAddGroupToAddGroup.{u3, u2, u1} ι (fun (i : ι) => V i) (fun (i : ι) => P i) (fun (i : ι) => _inst_3 i) (fun (i : ι) => _inst_5 i)) f g i) (midpoint.{u4, u2, u1} k (V i) (P i) (DivisionRing.toRing.{u4} k (Field.toDivisionRing.{u4} k _inst_1)) _inst_2 (_inst_3 i) (_inst_4 i) (_inst_5 i) (f i) (g i))
+Case conversion may be inaccurate. Consider using '#align pi_midpoint_apply pi_midpoint_applyₓ'. -/
 @[simp]
 theorem pi_midpoint_apply {k ι : Type _} {V : ∀ i : ι, Type _} {P : ∀ i : ι, Type _} [Field k]
     [Invertible (2 : k)] [∀ i, AddCommGroup (V i)] [∀ i, Module k (V i)]

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -48,7 +48,7 @@ theorem homothety_one_half {k : Type*} {V P : Type*} [Field k] [CharZero k] [Add
 #align homothety_one_half homothety_one_half
 
 @[simp]
-theorem pi_midpoint_apply {k ι : Type*} {V : ∀ _ : ι, Type*} {P : ∀ _ : ι, Type*} [Field k]
+theorem pi_midpoint_apply {k ι : Type*} {V : ι → Type*} {P : ι → Type*} [Field k]
     [Invertible (2 : k)] [∀ i, AddCommGroup (V i)] [∀ i, Module k (V i)]
     [∀ i, AddTorsor (V i) (P i)] (f g : ∀ i, P i) (i : ι) :
     midpoint k f g i = midpoint k (f i) (g i) :=

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

This has nice performance benefits.

@@ -21,34 +21,34 @@ midpoint
 
 open AffineMap AffineEquiv
 
-theorem lineMap_inv_two {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
+theorem lineMap_inv_two {R : Type*} {V P : Type*} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (2⁻¹ : R) = midpoint R a b :=
   rfl
 #align line_map_inv_two lineMap_inv_two
 
-theorem lineMap_one_half {R : Type _} {V P : Type _} [DivisionRing R] [CharZero R] [AddCommGroup V]
+theorem lineMap_one_half {R : Type*} {V P : Type*} [DivisionRing R] [CharZero R] [AddCommGroup V]
     [Module R V] [AddTorsor V P] (a b : P) : lineMap a b (1 / 2 : R) = midpoint R a b := by
   rw [one_div, lineMap_inv_two]
 #align line_map_one_half lineMap_one_half
 
-theorem homothety_invOf_two {R : Type _} {V P : Type _} [CommRing R] [Invertible (2 : R)]
+theorem homothety_invOf_two {R : Type*} {V P : Type*} [CommRing R] [Invertible (2 : R)]
     [AddCommGroup V] [Module R V] [AddTorsor V P] (a b : P) :
     homothety a (⅟ 2 : R) b = midpoint R a b :=
   rfl
 #align homothety_inv_of_two homothety_invOf_two
 
-theorem homothety_inv_two {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
+theorem homothety_inv_two {k : Type*} {V P : Type*} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (2⁻¹ : k) b = midpoint k a b :=
   rfl
 #align homothety_inv_two homothety_inv_two
 
-theorem homothety_one_half {k : Type _} {V P : Type _} [Field k] [CharZero k] [AddCommGroup V]
+theorem homothety_one_half {k : Type*} {V P : Type*} [Field k] [CharZero k] [AddCommGroup V]
     [Module k V] [AddTorsor V P] (a b : P) : homothety a (1 / 2 : k) b = midpoint k a b := by
   rw [one_div, homothety_inv_two]
 #align homothety_one_half homothety_one_half
 
 @[simp]
-theorem pi_midpoint_apply {k ι : Type _} {V : ∀ _ : ι, Type _} {P : ∀ _ : ι, Type _} [Field k]
+theorem pi_midpoint_apply {k ι : Type*} {V : ∀ _ : ι, Type*} {P : ∀ _ : ι, Type*} [Field k]
     [Invertible (2 : k)] [∀ i, AddCommGroup (V i)] [∀ i, Module k (V i)]
     [∀ i, AddTorsor (V i) (P i)] (f g : ∀ i, P i) (i : ι) :
     midpoint k f g i = midpoint k (f i) (g i) :=

• 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) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.midpoint_zero
-! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.CharP.Invertible
 import Mathlib.LinearAlgebra.AffineSpace.Midpoint
 
+#align_import linear_algebra.affine_space.midpoint_zero from "leanprover-community/mathlib"@"78261225eb5cedc61c5c74ecb44e5b385d13b733"
+
 /-!
 # Midpoint of a segment for characteristic zero
 

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>