Skip to content

Commit ea46a8d

Browse files
chore(AlgebraicGeometry): remove use of clear*- from isClosedMap_iff_specializingMap (leanprover-community#36961)
In the previous proof of isClosedMap_iff_specializingMap the tactic clearExcept (clear*-) is used to clear the auxDecl which is created by wlog since there are two wlog in the proof. This is undesirable because it requires knowledge of the unexpected behaviour of clearExcept to understand the proof. Marking the lemma as `nonrec` means that clearExcept can be removed from the proof.
1 parent 9b50fb6 commit ea46a8d

1 file changed

Lines changed: 1 addition & 2 deletions

File tree

Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean

Lines changed: 1 addition & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -224,7 +224,7 @@ lemma isCompact_iff_exists {U : X.Opens} :
224224
rwa [← Set.range_comp, ← TopCat.coe_comp, ← Scheme.Hom.comp_base, IsOpenImmersion.lift_fac]
225225

226226
@[stacks 01K9]
227-
lemma isClosedMap_iff_specializingMap (f : X ⟶ Y) [QuasiCompact f] :
227+
nonrec lemma isClosedMap_iff_specializingMap (f : X ⟶ Y) [QuasiCompact f] :
228228
IsClosedMap f ↔ SpecializingMap f := by
229229
refine ⟨fun h ↦ h.specializingMap, fun H ↦ ?_⟩
230230
wlog hY : ∃ R, Y = Spec R
@@ -236,7 +236,6 @@ lemma isClosedMap_iff_specializingMap (f : X ⟶ Y) [QuasiCompact f] :
236236
exact IsZariskiLocalAtTarget.of_isPullback
237237
(P := topologically @SpecializingMap) (.of_hasPullback _ _) H
238238
obtain ⟨S, rfl⟩ := hY
239-
clear * - H
240239
intro Z hZ
241240
replace H := hZ.stableUnderSpecialization.image H
242241
wlog hX : ∃ R, X = Spec R

0 commit comments

Comments
 (0)