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artie2000 committed Jan 7, 2025
1 parent fc38474 commit 652511a
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3 changes: 1 addition & 2 deletions RealClosedField/RealClosedField/RingOrdering/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -317,7 +317,7 @@ variable {A B C : Type*} [CommRing A] [CommRing B] [CommRing C]
/-- The preimage of a preordering along a ring homomorphism is a preordering. -/
def comap (f : A →+* B) (P : RingPreordering B) : RingPreordering A where
__ := P.toSubsemiring.comap f
isSquare_mem' := by aesop (add unsafe apply IsSquare.map) /- TODO : automate? -/
isSquare_mem' := by aesop (add unsafe apply IsSquare.map) /- TODO : automate -/
minus_one_not_mem' := by aesop

@[simp]
Expand Down Expand Up @@ -371,7 +371,6 @@ def map {f : A →+* B} {P : RingPreordering A} (hf : Function.Surjective f)
isSquare_mem' hx := by
rcases hx with ⟨y, rfl⟩
rcases hf y with ⟨y', rfl⟩ /- TODO : generalise? ie Surjective f → IsSquare x → ∃ y, f y = x ∧ IsSquare y -/
simp_all
aesop
minus_one_not_mem' := fun ⟨x', hx', _⟩ => by
have : -(x' + 1) + x' ∈ P := add_mem (hsupp (show f (x' + 1) = 0 by simp_all)).2 hx'
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3 changes: 2 additions & 1 deletion RealClosedField/RealClosedField/Semireal/Field.lean
Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@ import RealClosedField.RealClosedField.FormallyReal
import RealClosedField.RealClosedField.RingOrdering.Order
import RealClosedField.RealClosedField.RingOrdering.Adjoin

variable (F : Type*) [Field F]
variable {F : Type*} [Field F]

instance : RingConeClass (RingPreordering F) F where
eq_zero_of_mem_of_neg_mem {P} {a} ha hna := by
Expand All @@ -26,6 +26,7 @@ instance IsSemireal.instIsFormallyReal [IsSemireal F] : IsFormallyReal F where

variable [IsSemireal F]

variable (F) in
open Classical RingPreordering in
noncomputable def LinearOrderedField.mkOfIsSemireal [IsSemireal F] : LinearOrderedField F where
__ := have := (choose_spec <| exists_le_isPrimeOrdering (⊥ : RingPreordering F)).2
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