field_theory.finite.trace ⟷ Mathlib.FieldTheory.Finite.Trace

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

@@ -32,7 +32,7 @@ theorem trace_to_zmod_nondegenerate (F : Type _) [Field F] [Finite F]
   by
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩
   have htr := traceForm_nondegenerate (ZMod (ringChar F)) F a
-  simp_rw [Algebra.traceForm_apply] at htr 
+  simp_rw [Algebra.traceForm_apply] at htr
   by_contra! hf
   exact ha (htr hf)
 #align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zmod_nondegenerate

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

@@ -33,7 +33,7 @@ theorem trace_to_zmod_nondegenerate (F : Type _) [Field F] [Finite F]
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩
   have htr := traceForm_nondegenerate (ZMod (ringChar F)) F a
   simp_rw [Algebra.traceForm_apply] at htr 
-  by_contra' hf
+  by_contra! hf
   exact ha (htr hf)
 #align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zmod_nondegenerate
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Michael Stoll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 -/
-import Mathbin.RingTheory.Trace
-import Mathbin.FieldTheory.Finite.GaloisField
+import RingTheory.Trace
+import FieldTheory.Finite.GaloisField
 
 #align_import field_theory.finite.trace from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Michael Stoll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
-
-! This file was ported from Lean 3 source module field_theory.finite.trace
-! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Trace
 import Mathbin.FieldTheory.Finite.GaloisField
 
+#align_import field_theory.finite.trace from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
+
 /-!
 # The trace map for finite fields
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -27,9 +27,9 @@ finite field, trace
 
 namespace FiniteField
 
-#print FiniteField.trace_to_zMod_nondegenerate /-
+#print FiniteField.trace_to_zmod_nondegenerate /-
 /-- The trace map from a finite field to its prime field is nongedenerate. -/
-theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
+theorem trace_to_zmod_nondegenerate (F : Type _) [Field F] [Finite F]
     [Algebra (ZMod (ringChar F)) F] {a : F} (ha : a ≠ 0) :
     ∃ b : F, Algebra.trace (ZMod (ringChar F)) F (a * b) ≠ 0 :=
   by
@@ -38,7 +38,7 @@ theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
   simp_rw [Algebra.traceForm_apply] at htr 
   by_contra' hf
   exact ha (htr hf)
-#align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zMod_nondegenerate
+#align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zmod_nondegenerate
 -/
 
 end FiniteField

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 
 ! This file was ported from Lean 3 source module field_theory.finite.trace
-! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
+! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.FieldTheory.Finite.GaloisField
 /-!
 # The trace map for finite fields
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We state the fact that the trace map from a finite field of
 characteristic `p` to `zmod p` is nondegenerate.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -24,6 +24,7 @@ finite field, trace
 
 namespace FiniteField
 
+#print FiniteField.trace_to_zMod_nondegenerate /-
 /-- The trace map from a finite field to its prime field is nongedenerate. -/
 theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
     [Algebra (ZMod (ringChar F)) F] {a : F} (ha : a ≠ 0) :
@@ -35,6 +36,7 @@ theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
   by_contra' hf
   exact ha (htr hf)
 #align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zMod_nondegenerate
+-/
 
 end FiniteField
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 
 ! This file was ported from Lean 3 source module field_theory.finite.trace
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -25,7 +25,8 @@ finite field, trace
 namespace FiniteField
 
 /-- The trace map from a finite field to its prime field is nongedenerate. -/
-theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F] {a : F} (ha : a ≠ 0) :
+theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
+    [Algebra (ZMod (ringChar F)) F] {a : F} (ha : a ≠ 0) :
     ∃ b : F, Algebra.trace (ZMod (ringChar F)) F (a * b) ≠ 0 :=
   by
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -30,7 +30,7 @@ theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F] {a : F} (h
   by
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩
   have htr := traceForm_nondegenerate (ZMod (ringChar F)) F a
-  simp_rw [Algebra.traceForm_apply] at htr
+  simp_rw [Algebra.traceForm_apply] at htr 
   by_contra' hf
   exact ha (htr hf)
 #align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zMod_nondegenerate

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -29,7 +29,7 @@ theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F] {a : F} (h
     ∃ b : F, Algebra.trace (ZMod (ringChar F)) F (a * b) ≠ 0 :=
   by
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩
-  have htr := traceFormNondegenerate (ZMod (ringChar F)) F a
+  have htr := traceForm_nondegenerate (ZMod (ringChar F)) F a
   simp_rw [Algebra.traceForm_apply] at htr
   by_contra' hf
   exact ha (htr hf)

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

To fit with the "please try harder" convention of ! tactics.

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

@@ -28,7 +28,7 @@ theorem trace_to_zmod_nondegenerate (F : Type*) [Field F] [Finite F]
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩
   have htr := traceForm_nondegenerate (ZMod (ringChar F)) F a
   simp_rw [Algebra.traceForm_apply] at htr
-  by_contra' hf
+  by_contra! hf
   exact ha (htr hf)
 #align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zmod_nondegenerate
 

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

This has nice performance benefits.

@@ -22,7 +22,7 @@ finite field, trace
 namespace FiniteField
 
 /-- The trace map from a finite field to its prime field is nongedenerate. -/
-theorem trace_to_zmod_nondegenerate (F : Type _) [Field F] [Finite F]
+theorem trace_to_zmod_nondegenerate (F : Type*) [Field F] [Finite F]
     [Algebra (ZMod (ringChar F)) F] {a : F} (ha : a ≠ 0) :
     ∃ b : F, Algebra.trace (ZMod (ringChar F)) F (a * b) ≠ 0 := by
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩

• 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) 2022 Michael Stoll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
-
-! This file was ported from Lean 3 source module field_theory.finite.trace
-! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Trace
 import Mathlib.FieldTheory.Finite.GaloisField
 
+#align_import field_theory.finite.trace from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
+
 /-!
 # The trace map for finite fields
 

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -25,7 +25,7 @@ finite field, trace
 namespace FiniteField
 
 /-- The trace map from a finite field to its prime field is nongedenerate. -/
-theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
+theorem trace_to_zmod_nondegenerate (F : Type _) [Field F] [Finite F]
     [Algebra (ZMod (ringChar F)) F] {a : F} (ha : a ≠ 0) :
     ∃ b : F, Algebra.trace (ZMod (ringChar F)) F (a * b) ≠ 0 := by
   haveI : Fact (ringChar F).Prime := ⟨CharP.char_is_prime F _⟩
@@ -33,6 +33,6 @@ theorem trace_to_zMod_nondegenerate (F : Type _) [Field F] [Finite F]
   simp_rw [Algebra.traceForm_apply] at htr
   by_contra' hf
   exact ha (htr hf)
-#align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zMod_nondegenerate
+#align finite_field.trace_to_zmod_nondegenerate FiniteField.trace_to_zmod_nondegenerate
 
 end FiniteField