data.polynomial.lifts | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

63417e01

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

10bf4f82

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Data.Polynomial.AlgebraMap
-import Data.Polynomial.Monic
+import Algebra.Polynomial.AlgebraMap
+import Algebra.Polynomial.Monic
 
 #align_import data.polynomial.lifts from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -172,19 +172,18 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   · use 0
     simp only [hzero, degree_zero, eq_self_iff_true, and_self_iff, monomial_zero_right,
       Polynomial.map_zero]
-  rw [lifts_iff_set_range] at hl 
+  rw [lifts_iff_set_range] at hl
   obtain ⟨q, hq⟩ := hl
   replace hq := (ext_iff.1 hq) n
-  have hcoeff : f (q.coeff n) = s :=
-    by
-    simp [coeff_monomial] at hq 
+  have hcoeff : f (q.coeff n) = s := by
+    simp [coeff_monomial] at hq
     exact hq
   use monomial n (q.coeff n)
   constructor
   · simp only [hcoeff, map_monomial]
   have hqzero : q.coeff n ≠ 0 := by
     intro habs
-    simp only [habs, RingHom.map_zero] at hcoeff 
+    simp only [habs, RingHom.map_zero] at hcoeff
     exact hzero hcoeff.symm
   repeat' rw [← C_mul_X_pow_eq_monomial]
   simp only [hzero, hqzero, Ne.def, not_false_iff, degree_C_mul_X_pow]
@@ -209,7 +208,7 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
   have pzero : p ≠ 0 := by
     intro habs
     exfalso
-    rw [habs, erase_lead_zero, eq_self_iff_true, not_true] at erase_zero 
+    rw [habs, erase_lead_zero, eq_self_iff_true, not_true] at erase_zero
     exact erase_zero
   have lead_zero : p.coeff p.nat_degree ≠ 0 := by
     rw [← leading_coeff, Ne.def, leading_coeff_eq_zero] <;> exact pzero
@@ -218,7 +217,7 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
       (monomial_mem_lifts p.nat_degree ((lifts_iff_coeff_lifts p).1 hlifts p.nat_degree))
   have deg_lead : lead.degree = p.nat_degree := by
     rw [hlead.2, ← C_mul_X_pow_eq_monomial, degree_C_mul_X_pow p.nat_degree lead_zero]
-  rw [hdeg] at deg_erase 
+  rw [hdeg] at deg_erase
   obtain ⟨erase, herase⟩ :=
     hn p.erase_lead.nat_degree deg_erase (erase_mem_lifts p.nat_degree hlifts)
       (refl p.erase_lead.nat_degree)
@@ -226,9 +225,9 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
   constructor
   · simp only [hlead, herase, Polynomial.map_add]
     nth_rw 1 [erase_lead_add_monomial_nat_degree_leading_coeff p]
-  rw [← hdeg, erase_lead] at deg_erase 
+  rw [← hdeg, erase_lead] at deg_erase
   replace deg_erase := lt_of_le_of_lt degree_le_nat_degree (WithBot.coe_lt_coe.2 deg_erase)
-  rw [← deg_lead, ← herase.2] at deg_erase 
+  rw [← deg_lead, ← herase.2] at deg_erase
   rw [degree_add_eq_right_of_degree_lt deg_erase, deg_lead, degree_eq_nat_degree pzero]
 #align polynomial.mem_lifts_and_degree_eq Polynomial.mem_lifts_and_degree_eq
 -/

10bf4f82

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.Polynomial.Monic
+import Data.Polynomial.AlgebraMap
+import Data.Polynomial.Monic
 
 #align_import data.polynomial.lifts from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module data.polynomial.lifts
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.Data.Polynomial.Monic
 
+#align_import data.polynomial.lifts from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Polynomials that lift

10bf4f82

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -66,29 +66,40 @@ def lifts (f : R →+* S) : Subsemiring S[X] :=
 #align polynomial.lifts Polynomial.lifts
 -/
 
+#print Polynomial.mem_lifts /-
 theorem mem_lifts (p : S[X]) : p ∈ lifts f ↔ ∃ q : R[X], map f q = p := by
   simp only [coe_map_ring_hom, lifts, RingHom.mem_rangeS]
 #align polynomial.mem_lifts Polynomial.mem_lifts
+-/
 
+#print Polynomial.lifts_iff_set_range /-
 theorem lifts_iff_set_range (p : S[X]) : p ∈ lifts f ↔ p ∈ Set.range (map f) := by
   simp only [coe_map_ring_hom, lifts, Set.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_set_range Polynomial.lifts_iff_set_range
+-/
 
+#print Polynomial.lifts_iff_ringHom_rangeS /-
 theorem lifts_iff_ringHom_rangeS (p : S[X]) : p ∈ lifts f ↔ p ∈ (mapRingHom f).srange := by
   simp only [coe_map_ring_hom, lifts, Set.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_ring_hom_srange Polynomial.lifts_iff_ringHom_rangeS
+-/
 
+#print Polynomial.lifts_iff_coeff_lifts /-
 theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coeff n ∈ Set.range f := by
   rw [lifts_iff_ring_hom_srange, mem_map_srange f]; rfl
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
+-/
 
+#print Polynomial.C_mem_lifts /-
 /-- If `(r : R)`, then `C (f r)` lifts. -/
 theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
   ⟨C r, by
     simp only [coe_map_ring_hom, map_C, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       and_self_iff]⟩
 #align polynomial.C_mem_lifts Polynomial.C_mem_lifts
+-/
 
+#print Polynomial.C'_mem_lifts /-
 /-- If `(s : S)` is in the image of `f`, then `C s` lifts. -/
 theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ lifts f :=
   by
@@ -97,21 +108,27 @@ theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ l
   simp only [coe_map_ring_hom, map_C, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
     and_self_iff]
 #align polynomial.C'_mem_lifts Polynomial.C'_mem_lifts
+-/
 
+#print Polynomial.X_mem_lifts /-
 /-- The polynomial `X` lifts. -/
 theorem X_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
   ⟨X, by
     simp only [coe_map_ring_hom, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true, map_X,
       and_self_iff]⟩
 #align polynomial.X_mem_lifts Polynomial.X_mem_lifts
+-/
 
+#print Polynomial.X_pow_mem_lifts /-
 /-- The polynomial `X ^ n` lifts. -/
 theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
   ⟨X ^ n, by
     simp only [coe_map_ring_hom, map_pow, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       map_X, and_self_iff]⟩
 #align polynomial.X_pow_mem_lifts Polynomial.X_pow_mem_lifts
+-/
 
+#print Polynomial.base_mul_mem_lifts /-
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
   by
@@ -120,7 +137,9 @@ theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p
   use C r * p₁
   simp only [coe_map_ring_hom, map_C, map_mul]
 #align polynomial.base_mul_mem_lifts Polynomial.base_mul_mem_lifts
+-/
 
+#print Polynomial.monomial_mem_lifts /-
 /-- If `(s : S)` is in the image of `f`, then `monomial n s` lifts. -/
 theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial n s ∈ lifts f :=
   by
@@ -129,7 +148,9 @@ theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial
   simp only [coe_map_ring_hom, Set.mem_univ, map_monomial, Subsemiring.coe_top, eq_self_iff_true,
     and_self_iff]
 #align polynomial.monomial_mem_lifts Polynomial.monomial_mem_lifts
+-/
 
+#print Polynomial.erase_mem_lifts /-
 /-- If `p` lifts then `p.erase n` lifts. -/
 theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n ∈ lifts f :=
   by
@@ -142,9 +163,11 @@ theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n
   use i
   simp only [hi, hk, erase_ne, Ne.def, not_false_iff]
 #align polynomial.erase_mem_lifts Polynomial.erase_mem_lifts
+-/
 
 section LiftDeg
 
+#print Polynomial.monomial_mem_lifts_and_degree_eq /-
 theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s ∈ lifts f) :
     ∃ q : R[X], map f q = monomial n s ∧ q.degree = (monomial n s).degree :=
   by
@@ -169,7 +192,9 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   repeat' rw [← C_mul_X_pow_eq_monomial]
   simp only [hzero, hqzero, Ne.def, not_false_iff, degree_C_mul_X_pow]
 #align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eq
+-/
 
+#print Polynomial.mem_lifts_and_degree_eq /-
 /-- A polynomial lifts if and only if it can be lifted to a polynomial of the same degree. -/
 theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
     ∃ q : R[X], map f q = p ∧ q.degree = p.degree :=
@@ -209,11 +234,13 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
   rw [← deg_lead, ← herase.2] at deg_erase 
   rw [degree_add_eq_right_of_degree_lt deg_erase, deg_lead, degree_eq_nat_degree pzero]
 #align polynomial.mem_lifts_and_degree_eq Polynomial.mem_lifts_and_degree_eq
+-/
 
 end LiftDeg
 
 section Monic
 
+#print Polynomial.lifts_and_degree_eq_and_monic /-
 /-- A monic polynomial lifts if and only if it can be lifted to a monic polynomial
 of the same degree. -/
 theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈ lifts f)
@@ -238,7 +265,9 @@ theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈
   · rw [Polynomial.map_add, hq.1, Polynomial.map_pow, map_X, H]
   · rw [degree_add_eq_right_of_degree_lt hdeg, degree_X_pow, degree_eq_nat_degree hp.ne_zero]
 #align polynomial.lifts_and_degree_eq_and_monic Polynomial.lifts_and_degree_eq_and_monic
+-/
 
+#print Polynomial.lifts_and_natDegree_eq_and_monic /-
 theorem lifts_and_natDegree_eq_and_monic {p : S[X]} (hlifts : p ∈ lifts f) (hp : p.Monic) :
     ∃ q : R[X], map f q = p ∧ q.natDegree = p.natDegree ∧ q.Monic :=
   by
@@ -248,6 +277,7 @@ theorem lifts_and_natDegree_eq_and_monic {p : S[X]} (hlifts : p ∈ lifts f) (hp
   obtain ⟨p', h₁, h₂, h₃⟩ := lifts_and_degree_eq_and_monic hlifts hp
   exact ⟨p', h₁, nat_degree_eq_of_degree_eq h₂, h₃⟩
 #align polynomial.lifts_and_nat_degree_eq_and_monic Polynomial.lifts_and_natDegree_eq_and_monic
+-/
 
 end Monic
 
@@ -264,11 +294,13 @@ def liftsRing (f : R →+* S) : Subring S[X] :=
 #align polynomial.lifts_ring Polynomial.liftsRing
 -/
 
+#print Polynomial.lifts_iff_liftsRing /-
 /-- If `R` and `S` are rings, `p` is in the subring of polynomials that lift if and only if it is in
 the subsemiring of polynomials that lift. -/
 theorem lifts_iff_liftsRing (p : S[X]) : p ∈ lifts f ↔ p ∈ liftsRing f := by
   simp only [lifts, lifts_ring, RingHom.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_lifts_ring Polynomial.lifts_iff_liftsRing
+-/
 
 end Ring
 
@@ -284,22 +316,28 @@ def mapAlg (R : Type u) [CommSemiring R] (S : Type v) [Semiring S] [Algebra R S]
 #align polynomial.map_alg Polynomial.mapAlg
 -/
 
+#print Polynomial.mapAlg_eq_map /-
 /-- `map_alg` is the morphism induced by `R → S`. -/
 theorem mapAlg_eq_map (p : R[X]) : mapAlg R S p = map (algebraMap R S) p := by
   simp only [map_alg, aeval_def, eval₂, map, algebraMap_apply, RingHom.coe_comp]
 #align polynomial.map_alg_eq_map Polynomial.mapAlg_eq_map
+-/
 
+#print Polynomial.mem_lifts_iff_mem_alg /-
 /-- A polynomial `p` lifts if and only if it is in the image of `map_alg`. -/
 theorem mem_lifts_iff_mem_alg (R : Type u) [CommSemiring R] {S : Type v} [Semiring S] [Algebra R S]
     (p : S[X]) : p ∈ lifts (algebraMap R S) ↔ p ∈ AlgHom.range (@mapAlg R _ S _ _) := by
   simp only [coe_map_ring_hom, lifts, map_alg_eq_map, AlgHom.mem_range, RingHom.mem_rangeS]
 #align polynomial.mem_lifts_iff_mem_alg Polynomial.mem_lifts_iff_mem_alg
+-/
 
+#print Polynomial.smul_mem_lifts /-
 /-- If `p` lifts and `(r : R)` then `r • p` lifts. -/
 theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
     r • p ∈ lifts (algebraMap R S) := by rw [mem_lifts_iff_mem_alg] at hp ⊢;
   exact Subalgebra.smul_mem (map_alg R S).range hp r
 #align polynomial.smul_mem_lifts Polynomial.smul_mem_lifts
+-/
 
 end Algebra

10bf4f82

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -115,7 +115,7 @@ theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
   by
-  simp only [lifts, RingHom.mem_rangeS] at hp⊢
+  simp only [lifts, RingHom.mem_rangeS] at hp ⊢
   obtain ⟨p₁, rfl⟩ := hp
   use C r * p₁
   simp only [coe_map_ring_hom, map_C, map_mul]
@@ -133,7 +133,7 @@ theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial
 /-- If `p` lifts then `p.erase n` lifts. -/
 theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n ∈ lifts f :=
   by
-  rw [lifts_iff_ring_hom_srange, mem_map_srange] at h⊢
+  rw [lifts_iff_ring_hom_srange, mem_map_srange] at h ⊢
   intro k
   by_cases hk : k = n
   · use 0
@@ -152,18 +152,19 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   · use 0
     simp only [hzero, degree_zero, eq_self_iff_true, and_self_iff, monomial_zero_right,
       Polynomial.map_zero]
-  rw [lifts_iff_set_range] at hl
+  rw [lifts_iff_set_range] at hl 
   obtain ⟨q, hq⟩ := hl
   replace hq := (ext_iff.1 hq) n
-  have hcoeff : f (q.coeff n) = s := by
-    simp [coeff_monomial] at hq
+  have hcoeff : f (q.coeff n) = s :=
+    by
+    simp [coeff_monomial] at hq 
     exact hq
   use monomial n (q.coeff n)
   constructor
   · simp only [hcoeff, map_monomial]
   have hqzero : q.coeff n ≠ 0 := by
     intro habs
-    simp only [habs, RingHom.map_zero] at hcoeff
+    simp only [habs, RingHom.map_zero] at hcoeff 
     exact hzero hcoeff.symm
   repeat' rw [← C_mul_X_pow_eq_monomial]
   simp only [hzero, hqzero, Ne.def, not_false_iff, degree_C_mul_X_pow]
@@ -186,7 +187,7 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
   have pzero : p ≠ 0 := by
     intro habs
     exfalso
-    rw [habs, erase_lead_zero, eq_self_iff_true, not_true] at erase_zero
+    rw [habs, erase_lead_zero, eq_self_iff_true, not_true] at erase_zero 
     exact erase_zero
   have lead_zero : p.coeff p.nat_degree ≠ 0 := by
     rw [← leading_coeff, Ne.def, leading_coeff_eq_zero] <;> exact pzero
@@ -195,7 +196,7 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
       (monomial_mem_lifts p.nat_degree ((lifts_iff_coeff_lifts p).1 hlifts p.nat_degree))
   have deg_lead : lead.degree = p.nat_degree := by
     rw [hlead.2, ← C_mul_X_pow_eq_monomial, degree_C_mul_X_pow p.nat_degree lead_zero]
-  rw [hdeg] at deg_erase
+  rw [hdeg] at deg_erase 
   obtain ⟨erase, herase⟩ :=
     hn p.erase_lead.nat_degree deg_erase (erase_mem_lifts p.nat_degree hlifts)
       (refl p.erase_lead.nat_degree)
@@ -203,9 +204,9 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
   constructor
   · simp only [hlead, herase, Polynomial.map_add]
     nth_rw 1 [erase_lead_add_monomial_nat_degree_leading_coeff p]
-  rw [← hdeg, erase_lead] at deg_erase
+  rw [← hdeg, erase_lead] at deg_erase 
   replace deg_erase := lt_of_le_of_lt degree_le_nat_degree (WithBot.coe_lt_coe.2 deg_erase)
-  rw [← deg_lead, ← herase.2] at deg_erase
+  rw [← deg_lead, ← herase.2] at deg_erase 
   rw [degree_add_eq_right_of_degree_lt deg_erase, deg_lead, degree_eq_nat_degree pzero]
 #align polynomial.mem_lifts_and_degree_eq Polynomial.mem_lifts_and_degree_eq
 
@@ -296,7 +297,7 @@ theorem mem_lifts_iff_mem_alg (R : Type u) [CommSemiring R] {S : Type v} [Semiri
 
 /-- If `p` lifts and `(r : R)` then `r • p` lifts. -/
 theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
-    r • p ∈ lifts (algebraMap R S) := by rw [mem_lifts_iff_mem_alg] at hp⊢;
+    r • p ∈ lifts (algebraMap R S) := by rw [mem_lifts_iff_mem_alg] at hp ⊢;
   exact Subalgebra.smul_mem (map_alg R S).range hp r
 #align polynomial.smul_mem_lifts Polynomial.smul_mem_lifts

10bf4f82

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -283,12 +283,10 @@ def mapAlg (R : Type u) [CommSemiring R] (S : Type v) [Semiring S] [Algebra R S]
 #align polynomial.map_alg Polynomial.mapAlg
 -/
 
-#print Polynomial.mapAlg_eq_map /-
 /-- `map_alg` is the morphism induced by `R → S`. -/
 theorem mapAlg_eq_map (p : R[X]) : mapAlg R S p = map (algebraMap R S) p := by
   simp only [map_alg, aeval_def, eval₂, map, algebraMap_apply, RingHom.coe_comp]
 #align polynomial.map_alg_eq_map Polynomial.mapAlg_eq_map
--/
 
 /-- A polynomial `p` lifts if and only if it is in the image of `map_alg`. -/
 theorem mem_lifts_iff_mem_alg (R : Type u) [CommSemiring R] {S : Type v} [Semiring S] [Algebra R S]

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -47,7 +47,7 @@ that lift is a subalgebra. (By `lift_iff` this is true if `R` is commutative.)
 -/
 
 
-open Classical BigOperators Polynomial
+open scoped Classical BigOperators Polynomial
 
 noncomputable section

10bf4f82

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -66,49 +66,22 @@ def lifts (f : R →+* S) : Subsemiring S[X] :=
 #align polynomial.lifts Polynomial.lifts
 -/
 
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 theorem mem_lifts (p : S[X]) : p ∈ lifts f ↔ ∃ q : R[X], map f q = p := by
   simp only [coe_map_ring_hom, lifts, RingHom.mem_rangeS]
 #align polynomial.mem_lifts Polynomial.mem_lifts
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_set_range Polynomial.lifts_iff_set_rangeₓ'. -/
 theorem lifts_iff_set_range (p : S[X]) : p ∈ lifts f ↔ p ∈ Set.range (map f) := by
   simp only [coe_map_ring_hom, lifts, Set.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_set_range Polynomial.lifts_iff_set_range
 
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 theorem lifts_iff_ringHom_rangeS (p : S[X]) : p ∈ lifts f ↔ p ∈ (mapRingHom f).srange := by
   simp only [coe_map_ring_hom, lifts, Set.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_ring_hom_srange Polynomial.lifts_iff_ringHom_rangeS
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_liftsₓ'. -/
 theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coeff n ∈ Set.range f := by
   rw [lifts_iff_ring_hom_srange, mem_map_srange f]; rfl
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
-/- warning: polynomial.C_mem_lifts -> Polynomial.C_mem_lifts is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.C_mem_lifts Polynomial.C_mem_liftsₓ'. -/
 /-- If `(r : R)`, then `C (f r)` lifts. -/
 theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
   ⟨C r, by
@@ -116,12 +89,6 @@ theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
       and_self_iff]⟩
 #align polynomial.C_mem_lifts Polynomial.C_mem_lifts
 
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 /-- If `(s : S)` is in the image of `f`, then `C s` lifts. -/
 theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ lifts f :=
   by
@@ -131,12 +98,6 @@ theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ l
     and_self_iff]
 #align polynomial.C'_mem_lifts Polynomial.C'_mem_lifts
 
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 /-- The polynomial `X` lifts. -/
 theorem X_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
   ⟨X, by
@@ -144,12 +105,6 @@ theorem X_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
       and_self_iff]⟩
 #align polynomial.X_mem_lifts Polynomial.X_mem_lifts
 
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 /-- The polynomial `X ^ n` lifts. -/
 theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
   ⟨X ^ n, by
@@ -157,9 +112,6 @@ theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :
       map_X, and_self_iff]⟩
 #align polynomial.X_pow_mem_lifts Polynomial.X_pow_mem_lifts
 
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 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
   by
@@ -169,12 +121,6 @@ theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p
   simp only [coe_map_ring_hom, map_C, map_mul]
 #align polynomial.base_mul_mem_lifts Polynomial.base_mul_mem_lifts
 
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 /-- If `(s : S)` is in the image of `f`, then `monomial n s` lifts. -/
 theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial n s ∈ lifts f :=
   by
@@ -184,12 +130,6 @@ theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial
     and_self_iff]
 #align polynomial.monomial_mem_lifts Polynomial.monomial_mem_lifts
 
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 /-- If `p` lifts then `p.erase n` lifts. -/
 theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n ∈ lifts f :=
   by
@@ -205,9 +145,6 @@ theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n
 
 section LiftDeg
 
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-<too large>
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 theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s ∈ lifts f) :
     ∃ q : R[X], map f q = monomial n s ∧ q.degree = (monomial n s).degree :=
   by
@@ -232,12 +169,6 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   simp only [hzero, hqzero, Ne.def, not_false_iff, degree_C_mul_X_pow]
 #align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eq
 
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 /-- A polynomial lifts if and only if it can be lifted to a polynomial of the same degree. -/
 theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
     ∃ q : R[X], map f q = p ∧ q.degree = p.degree :=
@@ -282,12 +213,6 @@ end LiftDeg
 
 section Monic
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.lifts_and_degree_eq_and_monic Polynomial.lifts_and_degree_eq_and_monicₓ'. -/
 /-- A monic polynomial lifts if and only if it can be lifted to a monic polynomial
 of the same degree. -/
 theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈ lifts f)
@@ -313,12 +238,6 @@ theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈
   · rw [degree_add_eq_right_of_degree_lt hdeg, degree_X_pow, degree_eq_nat_degree hp.ne_zero]
 #align polynomial.lifts_and_degree_eq_and_monic Polynomial.lifts_and_degree_eq_and_monic
 
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 theorem lifts_and_natDegree_eq_and_monic {p : S[X]} (hlifts : p ∈ lifts f) (hp : p.Monic) :
     ∃ q : R[X], map f q = p ∧ q.natDegree = p.natDegree ∧ q.Monic :=
   by
@@ -344,12 +263,6 @@ def liftsRing (f : R →+* S) : Subring S[X] :=
 #align polynomial.lifts_ring Polynomial.liftsRing
 -/
 
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 /-- If `R` and `S` are rings, `p` is in the subring of polynomials that lift if and only if it is in
 the subsemiring of polynomials that lift. -/
 theorem lifts_iff_liftsRing (p : S[X]) : p ∈ lifts f ↔ p ∈ liftsRing f := by
@@ -377,24 +290,12 @@ theorem mapAlg_eq_map (p : R[X]) : mapAlg R S p = map (algebraMap R S) p := by
 #align polynomial.map_alg_eq_map Polynomial.mapAlg_eq_map
 -/
 
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 /-- A polynomial `p` lifts if and only if it is in the image of `map_alg`. -/
 theorem mem_lifts_iff_mem_alg (R : Type u) [CommSemiring R] {S : Type v} [Semiring S] [Algebra R S]
     (p : S[X]) : p ∈ lifts (algebraMap R S) ↔ p ∈ AlgHom.range (@mapAlg R _ S _ _) := by
   simp only [coe_map_ring_hom, lifts, map_alg_eq_map, AlgHom.mem_range, RingHom.mem_rangeS]
 #align polynomial.mem_lifts_iff_mem_alg Polynomial.mem_lifts_iff_mem_alg
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.smul_mem_lifts Polynomial.smul_mem_liftsₓ'. -/
 /-- If `p` lifts and `(r : R)` then `r • p` lifts. -/
 theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
     r • p ∈ lifts (algebraMap R S) := by rw [mem_lifts_iff_mem_alg] at hp⊢;

10bf4f82

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -102,10 +102,8 @@ lean 3 declaration is
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_liftsₓ'. -/
-theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coeff n ∈ Set.range f :=
-  by
-  rw [lifts_iff_ring_hom_srange, mem_map_srange f]
-  rfl
+theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coeff n ∈ Set.range f := by
+  rw [lifts_iff_ring_hom_srange, mem_map_srange f]; rfl
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
 /- warning: polynomial.C_mem_lifts -> Polynomial.C_mem_lifts is a dubious translation:
@@ -399,9 +397,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align polynomial.smul_mem_lifts Polynomial.smul_mem_liftsₓ'. -/
 /-- If `p` lifts and `(r : R)` then `r • p` lifts. -/
 theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
-    r • p ∈ lifts (algebraMap R S) :=
-  by
-  rw [mem_lifts_iff_mem_alg] at hp⊢
+    r • p ∈ lifts (algebraMap R S) := by rw [mem_lifts_iff_mem_alg] at hp⊢;
   exact Subalgebra.smul_mem (map_alg R S).range hp r
 #align polynomial.smul_mem_lifts Polynomial.smul_mem_lifts

10bf4f82

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -109,10 +109,7 @@ theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coef
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mem_lifts Polynomial.C_mem_liftsₓ'. -/
 /-- If `(r : R)`, then `C (f r)` lifts. -/
 theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
@@ -163,10 +160,7 @@ theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :
 #align polynomial.X_pow_mem_lifts Polynomial.X_pow_mem_lifts
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.base_mul_mem_lifts Polynomial.base_mul_mem_liftsₓ'. -/
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
@@ -214,10 +208,7 @@ theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n
 section LiftDeg
 
 /- warning: polynomial.monomial_mem_lifts_and_degree_eq -> Polynomial.monomial_mem_lifts_and_degree_eq is a dubious translation:
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n) s)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eqₓ'. -/
 theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s ∈ lifts f) :
     ∃ q : R[X], map f q = monomial n s ∧ q.degree = (monomial n s).degree :=

10bf4f82

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -181,7 +181,7 @@ theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts Polynomial.monomial_mem_liftsₓ'. -/
 /-- If `(s : S)` is in the image of `f`, then `monomial n s` lifts. -/
 theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial n s ∈ lifts f :=
@@ -217,7 +217,7 @@ section LiftDeg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} {n : Nat}, (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} {n : Nat}, (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} {n : Nat}, (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eqₓ'. -/
 theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s ∈ lifts f) :
     ∃ q : R[X], map f q = monomial n s ∧ q.degree = (monomial n s).degree :=

10bf4f82

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -100,7 +100,7 @@ theorem lifts_iff_ringHom_rangeS (p : S[X]) : p ∈ lifts f ↔ p ∈ (mapRingHo
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (forall (n : Nat), Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) (Polynomial.coeff.{u2} S _inst_2 p n) (Set.range.{u2, succ u1} S R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (forall (n : Nat), Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) (Polynomial.coeff.{u2} S _inst_2 p n) (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (forall (n : Nat), Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) (Polynomial.coeff.{u2} S _inst_2 p n) (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_liftsₓ'. -/
 theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coeff n ∈ Set.range f :=
   by
@@ -112,7 +112,7 @@ theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coef
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f r)) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align polynomial.C_mem_lifts Polynomial.C_mem_liftsₓ'. -/
 /-- If `(r : R)`, then `C (f r)` lifts. -/
 theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
@@ -125,7 +125,7 @@ theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S}, (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) s (Set.range.{u2, succ u1} S R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f))) -> (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S}, (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.C.{u2} S _inst_2) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S}, (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u2} S _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) (Polynomial.C.{u2} S _inst_2) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.C'_mem_lifts Polynomial.C'_mem_liftsₓ'. -/
 /-- If `(s : S)` is in the image of `f`, then `C s` lifts. -/
 theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ lifts f :=
@@ -166,7 +166,7 @@ theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {p : Polynomial.{u2} S _inst_2} (r : R), (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHMul.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.mul'.{u2} S _inst_2)) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f r)) p) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) p) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {p : Polynomial.{u2} S _inst_2} (r : R), (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Polynomial.{u2} S _inst_2) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (instHMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Polynomial.mul'.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) p) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.base_mul_mem_lifts Polynomial.base_mul_mem_liftsₓ'. -/
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
@@ -181,7 +181,7 @@ theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) s (Set.range.{u2, succ u1} S R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f))) -> (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts Polynomial.monomial_mem_liftsₓ'. -/
 /-- If `(s : S)` is in the image of `f`, then `monomial n s` lifts. -/
 theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial n s ∈ lifts f :=

10bf4f82

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -181,7 +181,7 @@ theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) s (Set.range.{u2, succ u1} S R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f))) -> (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} (n : Nat), (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) s (Set.range.{u2, succ u1} S R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f))) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts Polynomial.monomial_mem_liftsₓ'. -/
 /-- If `(s : S)` is in the image of `f`, then `monomial n s` lifts. -/
 theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial n s ∈ lifts f :=
@@ -217,7 +217,7 @@ section LiftDeg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} {n : Nat}, (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} {n : Nat}, (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {s : S} {n : Nat}, (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) s) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) S (Polynomial.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : S) => Polynomial.{u2} S _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, u2} S S S (Polynomial.{u2} S _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S _inst_2) (Polynomial.module.{u2, u2} S _inst_2 S _inst_2 (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Polynomial.monomial.{u2} S _inst_2 n) s)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eqₓ'. -/
 theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s ∈ lifts f) :
     ∃ q : R[X], map f q = monomial n s ∧ q.degree = (monomial n s).degree :=

10bf4f82

bump to nightly-2023-05-09-00

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

a5be454e

Diff

@@ -384,7 +384,7 @@ def mapAlg (R : Type u) [CommSemiring R] (S : Type v) [Semiring S] [Algebra R S]
 #print Polynomial.mapAlg_eq_map /-
 /-- `map_alg` is the morphism induced by `R → S`. -/
 theorem mapAlg_eq_map (p : R[X]) : mapAlg R S p = map (algebraMap R S) p := by
-  simp only [map_alg, aeval_def, eval₂, map, algebra_map_apply, RingHom.coe_comp]
+  simp only [map_alg, aeval_def, eval₂, map, algebraMap_apply, RingHom.coe_comp]
 #align polynomial.map_alg_eq_map Polynomial.mapAlg_eq_map
 -/

10bf4f82

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -359,7 +359,7 @@ def liftsRing (f : R →+* S) : Subring S[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (p : Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.setLike.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) p (Polynomial.lifts.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S _inst_2) f)) (Membership.Mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.setLike.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2))) p (Polynomial.liftsRing.{u1, u2} R _inst_1 S _inst_2 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (p : Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) p (Polynomial.lifts.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S _inst_2) f)) (Membership.mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (SetLike.instMembership.{u2, u2} (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.instSetLikeSubring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2))) p (Polynomial.liftsRing.{u1, u2} R _inst_1 S _inst_2 f))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (p : Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) p (Polynomial.lifts.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S _inst_2) f)) (Membership.mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (SetLike.instMembership.{u2, u2} (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.instSetLikeSubring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2))) p (Polynomial.liftsRing.{u1, u2} R _inst_1 S _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_lifts_ring Polynomial.lifts_iff_liftsRingₓ'. -/
 /-- If `R` and `S` are rings, `p` is in the subring of polynomials that lift if and only if it is in
 the subsemiring of polynomials that lift. -/

10bf4f82

bump to nightly-2023-03-17-16

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

624c906c

Diff

@@ -108,18 +108,18 @@ theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coef
   rfl
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
-/- warning: polynomial.C_mem_lifts -> Polynomial.c_mem_lifts is a dubious translation:
+/- warning: polynomial.C_mem_lifts -> Polynomial.C_mem_lifts is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (fun (_x : RingHom.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) => S -> (Polynomial.{u2} S _inst_2)) (RingHom.hasCoeToFun.{u2, u2} S (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.C.{u2} S _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f r)) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) => Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (Polynomial.semiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))))) (Polynomial.C.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) f r)) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align polynomial.C_mem_lifts Polynomial.c_mem_liftsₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.C_mem_lifts Polynomial.C_mem_liftsₓ'. -/
 /-- If `(r : R)`, then `C (f r)` lifts. -/
-theorem c_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
+theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
   ⟨C r, by
     simp only [coe_map_ring_hom, map_C, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       and_self_iff]⟩
-#align polynomial.C_mem_lifts Polynomial.c_mem_lifts
+#align polynomial.C_mem_lifts Polynomial.C_mem_lifts
 
 /- warning: polynomial.C'_mem_lifts -> Polynomial.C'_mem_lifts is a dubious translation:
 lean 3 declaration is
@@ -136,31 +136,31 @@ theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ l
     and_self_iff]
 #align polynomial.C'_mem_lifts Polynomial.C'_mem_lifts
 
-/- warning: polynomial.X_mem_lifts -> Polynomial.x_mem_lifts is a dubious translation:
+/- warning: polynomial.X_mem_lifts -> Polynomial.X_mem_lifts is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Polynomial.X.{u2} S _inst_2) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Polynomial.X.{u2} S _inst_2) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align polynomial.X_mem_lifts Polynomial.x_mem_liftsₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.X_mem_lifts Polynomial.X_mem_liftsₓ'. -/
 /-- The polynomial `X` lifts. -/
-theorem x_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
+theorem X_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
   ⟨X, by
     simp only [coe_map_ring_hom, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true, map_X,
       and_self_iff]⟩
-#align polynomial.X_mem_lifts Polynomial.x_mem_lifts
+#align polynomial.X_mem_lifts Polynomial.X_mem_lifts
 
-/- warning: polynomial.X_pow_mem_lifts -> Polynomial.x_pow_mem_lifts is a dubious translation:
+/- warning: polynomial.X_pow_mem_lifts -> Polynomial.X_pow_mem_lifts is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (HPow.hPow.{u2, 0, u2} (Polynomial.{u2} S _inst_2) Nat (Polynomial.{u2} S _inst_2) (instHPow.{u2, 0} (Polynomial.{u2} S _inst_2) Nat (Monoid.Pow.{u2} (Polynomial.{u2} S _inst_2) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))) (Polynomial.X.{u2} S _inst_2) n) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (n : Nat), Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (HPow.hPow.{u2, 0, u2} (Polynomial.{u2} S _inst_2) Nat (Polynomial.{u2} S _inst_2) (instHPow.{u2, 0} (Polynomial.{u2} S _inst_2) Nat (Monoid.Pow.{u2} (Polynomial.{u2} S _inst_2) (MonoidWithZero.toMonoid.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toMonoidWithZero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))) (Polynomial.X.{u2} S _inst_2) n) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align polynomial.X_pow_mem_lifts Polynomial.x_pow_mem_liftsₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.X_pow_mem_lifts Polynomial.X_pow_mem_liftsₓ'. -/
 /-- The polynomial `X ^ n` lifts. -/
-theorem x_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
+theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
   ⟨X ^ n, by
     simp only [coe_map_ring_hom, map_pow, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       map_X, and_self_iff]⟩
-#align polynomial.X_pow_mem_lifts Polynomial.x_pow_mem_lifts
+#align polynomial.X_pow_mem_lifts Polynomial.X_pow_mem_lifts
 
 /- warning: polynomial.base_mul_mem_lifts -> Polynomial.base_mul_mem_lifts is a dubious translation:
 lean 3 declaration is

10bf4f82

bump to nightly-2023-03-16-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module data.polynomial.lifts
-! leanprover-community/mathlib commit 63417e01fbc711beaf25fa73b6edb395c0cfddd0
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Polynomial.Monic
 /-!
 # Polynomials that lift
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given semirings `R` and `S` with a morphism `f : R →+* S`, we define a subsemiring `lifts` of
 `S[X]` by the image of `ring_hom.of (map f)`.
 Then, we prove that a polynomial that lifts can always be lifted to a polynomial of the same degree

63417e01

bump to nightly-2023-03-13-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

a0c9db6f

Diff

@@ -56,29 +56,61 @@ section Semiring
 
 variable {R : Type u} [Semiring R] {S : Type v} [Semiring S] {f : R →+* S}
 
+#print Polynomial.lifts /-
 /-- We define the subsemiring of polynomials that lifts as the image of `ring_hom.of (map f)`. -/
 def lifts (f : R →+* S) : Subsemiring S[X] :=
   RingHom.rangeS (mapRingHom f)
 #align polynomial.lifts Polynomial.lifts
+-/
 
+/- warning: polynomial.mem_lifts -> Polynomial.mem_lifts is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_lifts Polynomial.mem_liftsₓ'. -/
 theorem mem_lifts (p : S[X]) : p ∈ lifts f ↔ ∃ q : R[X], map f q = p := by
   simp only [coe_map_ring_hom, lifts, RingHom.mem_rangeS]
 #align polynomial.mem_lifts Polynomial.mem_lifts
 
+/- warning: polynomial.lifts_iff_set_range -> Polynomial.lifts_iff_set_range is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Set.{u2} (Polynomial.{u2} S _inst_2)) (Set.hasMem.{u2} (Polynomial.{u2} S _inst_2)) p (Set.range.{u2, succ u1} (Polynomial.{u2} S _inst_2) (Polynomial.{u1} R _inst_1) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} (p : Polynomial.{u2} S _inst_2), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Set.{u2} (Polynomial.{u2} S _inst_2)) (Set.instMembershipSet.{u2} (Polynomial.{u2} S _inst_2)) p (Set.range.{u2, succ u1} (Polynomial.{u2} S _inst_2) (Polynomial.{u1} R _inst_1) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f)))
+Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_set_range Polynomial.lifts_iff_set_rangeₓ'. -/
 theorem lifts_iff_set_range (p : S[X]) : p ∈ lifts f ↔ p ∈ Set.range (map f) := by
   simp only [coe_map_ring_hom, lifts, Set.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_set_range Polynomial.lifts_iff_set_range
 
+/- warning: polynomial.lifts_iff_ring_hom_srange -> Polynomial.lifts_iff_ringHom_rangeS is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_ring_hom_srange Polynomial.lifts_iff_ringHom_rangeSₓ'. -/
 theorem lifts_iff_ringHom_rangeS (p : S[X]) : p ∈ lifts f ↔ p ∈ (mapRingHom f).srange := by
   simp only [coe_map_ring_hom, lifts, Set.mem_range, RingHom.mem_rangeS]
 #align polynomial.lifts_iff_ring_hom_srange Polynomial.lifts_iff_ringHom_rangeS
 
+/- warning: polynomial.lifts_iff_coeff_lifts -> Polynomial.lifts_iff_coeff_lifts is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_liftsₓ'. -/
 theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coeff n ∈ Set.range f :=
   by
   rw [lifts_iff_ring_hom_srange, mem_map_srange f]
   rfl
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.C_mem_lifts Polynomial.c_mem_liftsₓ'. -/
 /-- If `(r : R)`, then `C (f r)` lifts. -/
 theorem c_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
   ⟨C r, by
@@ -86,6 +118,12 @@ theorem c_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
       and_self_iff]⟩
 #align polynomial.C_mem_lifts Polynomial.c_mem_lifts
 
+/- warning: polynomial.C'_mem_lifts -> Polynomial.C'_mem_lifts is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.C'_mem_lifts Polynomial.C'_mem_liftsₓ'. -/
 /-- If `(s : S)` is in the image of `f`, then `C s` lifts. -/
 theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ lifts f :=
   by
@@ -95,6 +133,12 @@ theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ l
     and_self_iff]
 #align polynomial.C'_mem_lifts Polynomial.C'_mem_lifts
 
+/- warning: polynomial.X_mem_lifts -> Polynomial.x_mem_lifts is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Polynomial.X.{u2} S _inst_2) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (Polynomial.X.{u2} S _inst_2) (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align polynomial.X_mem_lifts Polynomial.x_mem_liftsₓ'. -/
 /-- The polynomial `X` lifts. -/
 theorem x_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
   ⟨X, by
@@ -102,6 +146,12 @@ theorem x_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
       and_self_iff]⟩
 #align polynomial.X_mem_lifts Polynomial.x_mem_lifts
 
+/- warning: polynomial.X_pow_mem_lifts -> Polynomial.x_pow_mem_lifts is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.X_pow_mem_lifts Polynomial.x_pow_mem_liftsₓ'. -/
 /-- The polynomial `X ^ n` lifts. -/
 theorem x_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
   ⟨X ^ n, by
@@ -109,6 +159,12 @@ theorem x_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :
       map_X, and_self_iff]⟩
 #align polynomial.X_pow_mem_lifts Polynomial.x_pow_mem_lifts
 
+/- warning: polynomial.base_mul_mem_lifts -> Polynomial.base_mul_mem_lifts is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.base_mul_mem_lifts Polynomial.base_mul_mem_liftsₓ'. -/
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
   by
@@ -118,6 +174,12 @@ theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p
   simp only [coe_map_ring_hom, map_C, map_mul]
 #align polynomial.base_mul_mem_lifts Polynomial.base_mul_mem_lifts
 
+/- warning: polynomial.monomial_mem_lifts -> Polynomial.monomial_mem_lifts is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts Polynomial.monomial_mem_liftsₓ'. -/
 /-- If `(s : S)` is in the image of `f`, then `monomial n s` lifts. -/
 theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial n s ∈ lifts f :=
   by
@@ -127,6 +189,12 @@ theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial
     and_self_iff]
 #align polynomial.monomial_mem_lifts Polynomial.monomial_mem_lifts
 
+/- warning: polynomial.erase_mem_lifts -> Polynomial.erase_mem_lifts is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_mem_lifts Polynomial.erase_mem_liftsₓ'. -/
 /-- If `p` lifts then `p.erase n` lifts. -/
 theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n ∈ lifts f :=
   by
@@ -142,6 +210,12 @@ theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.eraseₓ n
 
 section LiftDeg
 
+/- warning: polynomial.monomial_mem_lifts_and_degree_eq -> Polynomial.monomial_mem_lifts_and_degree_eq is a dubious translation:
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n) s)))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eqₓ'. -/
 theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s ∈ lifts f) :
     ∃ q : R[X], map f q = monomial n s ∧ q.degree = (monomial n s).degree :=
   by
@@ -166,6 +240,12 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   simp only [hzero, hqzero, Ne.def, not_false_iff, degree_C_mul_X_pow]
 #align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eq
 
+/- warning: polynomial.mem_lifts_and_degree_eq -> Polynomial.mem_lifts_and_degree_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {p : Polynomial.{u2} S _inst_2}, (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 p))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {p : Polynomial.{u2} S _inst_2}, (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p) (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_lifts_and_degree_eq Polynomial.mem_lifts_and_degree_eqₓ'. -/
 /-- A polynomial lifts if and only if it can be lifted to a polynomial of the same degree. -/
 theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
     ∃ q : R[X], map f q = p ∧ q.degree = p.degree :=
@@ -210,6 +290,12 @@ end LiftDeg
 
 section Monic
 
+/- warning: polynomial.lifts_and_degree_eq_and_monic -> Polynomial.lifts_and_degree_eq_and_monic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} [_inst_3 : Nontrivial.{u2} S] {p : Polynomial.{u2} S _inst_2}, (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Polynomial.Monic.{u2} S _inst_2 p) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p) (And (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 p)) (Polynomial.Monic.{u1} R _inst_1 q))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} [_inst_3 : Nontrivial.{u2} S] {p : Polynomial.{u2} S _inst_2}, (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Polynomial.Monic.{u2} S _inst_2 p) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p) (And (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 q) (Polynomial.degree.{u2} S _inst_2 p)) (Polynomial.Monic.{u1} R _inst_1 q))))
+Case conversion may be inaccurate. Consider using '#align polynomial.lifts_and_degree_eq_and_monic Polynomial.lifts_and_degree_eq_and_monicₓ'. -/
 /-- A monic polynomial lifts if and only if it can be lifted to a monic polynomial
 of the same degree. -/
 theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈ lifts f)
@@ -235,6 +321,12 @@ theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈
   · rw [degree_add_eq_right_of_degree_lt hdeg, degree_X_pow, degree_eq_nat_degree hp.ne_zero]
 #align polynomial.lifts_and_degree_eq_and_monic Polynomial.lifts_and_degree_eq_and_monic
 
+/- warning: polynomial.lifts_and_nat_degree_eq_and_monic -> Polynomial.lifts_and_natDegree_eq_and_monic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {p : Polynomial.{u2} S _inst_2}, (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Polynomial.Monic.{u2} S _inst_2 p) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p) (And (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (Polynomial.natDegree.{u2} S _inst_2 p)) (Polynomial.Monic.{u1} R _inst_1 q))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {p : Polynomial.{u2} S _inst_2}, (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R _inst_1 S _inst_2 f)) -> (Polynomial.Monic.{u2} S _inst_2 p) -> (Exists.{succ u1} (Polynomial.{u1} R _inst_1) (fun (q : Polynomial.{u1} R _inst_1) => And (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (Polynomial.map.{u1, u2} R S _inst_1 _inst_2 f q) p) (And (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 q) (Polynomial.natDegree.{u2} S _inst_2 p)) (Polynomial.Monic.{u1} R _inst_1 q))))
+Case conversion may be inaccurate. Consider using '#align polynomial.lifts_and_nat_degree_eq_and_monic Polynomial.lifts_and_natDegree_eq_and_monicₓ'. -/
 theorem lifts_and_natDegree_eq_and_monic {p : S[X]} (hlifts : p ∈ lifts f) (hp : p.Monic) :
     ∃ q : R[X], map f q = p ∧ q.natDegree = p.natDegree ∧ q.Monic :=
   by
@@ -253,11 +345,19 @@ section Ring
 
 variable {R : Type u} [Ring R] {S : Type v} [Ring S] (f : R →+* S)
 
+#print Polynomial.liftsRing /-
 /-- The subring of polynomials that lift. -/
 def liftsRing (f : R →+* S) : Subring S[X] :=
   RingHom.range (mapRingHom f)
 #align polynomial.lifts_ring Polynomial.liftsRing
+-/
 
+/- warning: polynomial.lifts_iff_lifts_ring -> Polynomial.lifts_iff_liftsRing is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (p : Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.setLike.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) p (Polynomial.lifts.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S _inst_2) f)) (Membership.Mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.setLike.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2))) p (Polynomial.liftsRing.{u1, u2} R _inst_1 S _inst_2 f))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (p : Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.semiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) p (Polynomial.lifts.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) S (Ring.toSemiring.{u2} S _inst_2) f)) (Membership.mem.{u2, u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (SetLike.instMembership.{u2, u2} (Subring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2)) (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Subring.instSetLikeSubring.{u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Polynomial.ring.{u2} S _inst_2))) p (Polynomial.liftsRing.{u1, u2} R _inst_1 S _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align polynomial.lifts_iff_lifts_ring Polynomial.lifts_iff_liftsRingₓ'. -/
 /-- If `R` and `S` are rings, `p` is in the subring of polynomials that lift if and only if it is in
 the subsemiring of polynomials that lift. -/
 theorem lifts_iff_liftsRing (p : S[X]) : p ∈ lifts f ↔ p ∈ liftsRing f := by
@@ -270,23 +370,39 @@ section Algebra
 
 variable {R : Type u} [CommSemiring R] {S : Type v} [Semiring S] [Algebra R S]
 
+#print Polynomial.mapAlg /-
 /-- The map `R[X] → S[X]` as an algebra homomorphism. -/
 def mapAlg (R : Type u) [CommSemiring R] (S : Type v) [Semiring S] [Algebra R S] :
     R[X] →ₐ[R] S[X] :=
   @aeval _ S[X] _ _ _ (X : S[X])
 #align polynomial.map_alg Polynomial.mapAlg
+-/
 
+#print Polynomial.mapAlg_eq_map /-
 /-- `map_alg` is the morphism induced by `R → S`. -/
 theorem mapAlg_eq_map (p : R[X]) : mapAlg R S p = map (algebraMap R S) p := by
   simp only [map_alg, aeval_def, eval₂, map, algebra_map_apply, RingHom.coe_comp]
 #align polynomial.map_alg_eq_map Polynomial.mapAlg_eq_map
+-/
 
+/- warning: polynomial.mem_lifts_iff_mem_alg -> Polynomial.mem_lifts_iff_mem_alg is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_4 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_5 : Semiring.{u2} S] [_inst_6 : Algebra.{u1, u2} R S _inst_4 _inst_5] (p : Polynomial.{u2} S _inst_5), Iff (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_5) (Subsemiring.{u2} (Polynomial.{u2} S _inst_5) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_5) (Polynomial.semiring.{u2} S _inst_5))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_5) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_5) (Polynomial.semiring.{u2} S _inst_5))) (Polynomial.{u2} S _inst_5) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_5) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_5) (Polynomial.semiring.{u2} S _inst_5)))) p (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_4) S _inst_5 (algebraMap.{u1, u2} R S _inst_4 _inst_5 _inst_6))) (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_5) (Subalgebra.{u1, u2} R (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6)) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6)) (Polynomial.{u2} S _inst_5) (Subalgebra.setLike.{u1, u2} R (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6))) p (AlgHom.range.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_4 (CommSemiring.toSemiring.{u1} R _inst_4) (Algebra.id.{u1} R _inst_4)) (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6) (Polynomial.mapAlg.{u1, u2} R _inst_4 S _inst_5 _inst_6)))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_4 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_5 : Semiring.{u2} S] [_inst_6 : Algebra.{u1, u2} R S _inst_4 _inst_5] (p : Polynomial.{u2} S _inst_5), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_5) (Subsemiring.{u2} (Polynomial.{u2} S _inst_5) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_5) (Polynomial.semiring.{u2} S _inst_5))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_5) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_5) (Polynomial.semiring.{u2} S _inst_5))) (Polynomial.{u2} S _inst_5) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_5) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_5) (Polynomial.semiring.{u2} S _inst_5)))) p (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_4) S _inst_5 (algebraMap.{u1, u2} R S _inst_4 _inst_5 _inst_6))) (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_5) (Subalgebra.{u1, u2} R (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6)) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6)) (Polynomial.{u2} S _inst_5) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6))) p (AlgHom.range.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Polynomial.{u2} S _inst_5) _inst_4 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_4 (CommSemiring.toSemiring.{u1} R _inst_4) (Algebra.id.{u1} R _inst_4)) (Polynomial.semiring.{u2} S _inst_5) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_4 _inst_5 _inst_6) (Polynomial.mapAlg.{u1, u2} R _inst_4 S _inst_5 _inst_6)))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_lifts_iff_mem_alg Polynomial.mem_lifts_iff_mem_algₓ'. -/
 /-- A polynomial `p` lifts if and only if it is in the image of `map_alg`. -/
 theorem mem_lifts_iff_mem_alg (R : Type u) [CommSemiring R] {S : Type v} [Semiring S] [Algebra R S]
     (p : S[X]) : p ∈ lifts (algebraMap R S) ↔ p ∈ AlgHom.range (@mapAlg R _ S _ _) := by
   simp only [coe_map_ring_hom, lifts, map_alg_eq_map, AlgHom.mem_range, RingHom.mem_rangeS]
 #align polynomial.mem_lifts_iff_mem_alg Polynomial.mem_lifts_iff_mem_alg
 
+/- warning: polynomial.smul_mem_lifts -> Polynomial.smul_mem_lifts is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 _inst_2] {p : Polynomial.{u2} S _inst_2} (r : R), (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_1) S _inst_2 (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_3))) -> (Membership.Mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.setLike.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (SMul.smul.{u1, u2} R (Polynomial.{u2} S _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} R (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2) (Polynomial.smulZeroClass.{u2, u1} S _inst_2 R (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_3)))))) r p) (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_1) S _inst_2 (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_3)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_2 : Semiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 _inst_2] {p : Polynomial.{u2} S _inst_2} (r : R), (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) p (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_1) S _inst_2 (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_3))) -> (Membership.mem.{u2, u2} (Polynomial.{u2} S _inst_2) (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.{u2} S _inst_2) (Subsemiring.instSetLikeSubsemiring.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R (Polynomial.{u2} S _inst_2) (Polynomial.{u2} S _inst_2) (instHSMul.{u1, u2} R (Polynomial.{u2} S _inst_2) (Algebra.toSMul.{u1, u2} R (Polynomial.{u2} S _inst_2) _inst_1 (Polynomial.semiring.{u2} S _inst_2) (Polynomial.algebraOfAlgebra.{u1, u2} R S _inst_1 _inst_2 _inst_3))) r p) (Polynomial.lifts.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_1) S _inst_2 (algebraMap.{u1, u2} R S _inst_1 _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align polynomial.smul_mem_lifts Polynomial.smul_mem_liftsₓ'. -/
 /-- If `p` lifts and `(r : R)` then `r • p` lifts. -/
 theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
     r • p ∈ lifts (algebraMap R S) :=

63417e01

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -80,14 +80,14 @@ theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coef
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
 /-- If `(r : R)`, then `C (f r)` lifts. -/
-theorem c_mem_lifts (f : R →+* S) (r : R) : c (f r) ∈ lifts f :=
-  ⟨c r, by
+theorem c_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
+  ⟨C r, by
     simp only [coe_map_ring_hom, map_C, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       and_self_iff]⟩
 #align polynomial.C_mem_lifts Polynomial.c_mem_lifts
 
 /-- If `(s : S)` is in the image of `f`, then `C s` lifts. -/
-theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : c s ∈ lifts f :=
+theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ lifts f :=
   by
   obtain ⟨r, rfl⟩ := Set.mem_range.1 h
   use C r
@@ -96,21 +96,21 @@ theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : c s ∈ l
 #align polynomial.C'_mem_lifts Polynomial.C'_mem_lifts
 
 /-- The polynomial `X` lifts. -/
-theorem x_mem_lifts (f : R →+* S) : (x : S[X]) ∈ lifts f :=
-  ⟨x, by
+theorem x_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
+  ⟨X, by
     simp only [coe_map_ring_hom, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true, map_X,
       and_self_iff]⟩
 #align polynomial.X_mem_lifts Polynomial.x_mem_lifts
 
 /-- The polynomial `X ^ n` lifts. -/
-theorem x_pow_mem_lifts (f : R →+* S) (n : ℕ) : (x ^ n : S[X]) ∈ lifts f :=
-  ⟨x ^ n, by
+theorem x_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
+  ⟨X ^ n, by
     simp only [coe_map_ring_hom, map_pow, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       map_X, and_self_iff]⟩
 #align polynomial.X_pow_mem_lifts Polynomial.x_pow_mem_lifts
 
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
-theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : c (f r) * p ∈ lifts f :=
+theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f :=
   by
   simp only [lifts, RingHom.mem_rangeS] at hp⊢
   obtain ⟨p₁, rfl⟩ := hp
@@ -273,7 +273,7 @@ variable {R : Type u} [CommSemiring R] {S : Type v} [Semiring S] [Algebra R S]
 /-- The map `R[X] → S[X]` as an algebra homomorphism. -/
 def mapAlg (R : Type u) [CommSemiring R] (S : Type v) [Semiring S] [Algebra R S] :
     R[X] →ₐ[R] S[X] :=
-  @aeval _ S[X] _ _ _ (x : S[X])
+  @aeval _ S[X] _ _ _ (X : S[X])
 #align polynomial.map_alg Polynomial.mapAlg
 
 /-- `map_alg` is the morphism induced by `R → S`. -/

63417e01

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

63417e01

move(Polynomial): Move out of Data (#11751)

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

56e439ec

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.Polynomial.Monic
+import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.Monic
 
 #align_import data.polynomial.lifts from "leanprover-community/mathlib"@"63417e01fbc711beaf25fa73b6edb395c0cfddd0"

63417e01

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -133,7 +133,7 @@ theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.erase n ∈
     simp only [hk, RingHom.map_zero, erase_same]
   obtain ⟨i, hi⟩ := h k
   use i
-  simp only [hi, hk, erase_ne, Ne.def, not_false_iff]
+  simp only [hi, hk, erase_ne, Ne, not_false_iff]
 #align polynomial.erase_mem_lifts Polynomial.erase_mem_lifts
 
 section LiftDeg
@@ -159,7 +159,7 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
     exact hzero hcoeff.symm
   rw [← C_mul_X_pow_eq_monomial]
   rw [← C_mul_X_pow_eq_monomial]
-  simp only [hzero, hqzero, Ne.def, not_false_iff, degree_C_mul_X_pow]
+  simp only [hzero, hqzero, Ne, not_false_iff, degree_C_mul_X_pow]
 #align polynomial.monomial_mem_lifts_and_degree_eq Polynomial.monomial_mem_lifts_and_degree_eq
 
 /-- A polynomial lifts if and only if it can be lifted to a polynomial of the same degree. -/
@@ -181,7 +181,7 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
     rw [habs, eraseLead_zero, eq_self_iff_true, not_true] at erase_zero
     exact erase_zero
   have lead_zero : p.coeff p.natDegree ≠ 0 := by
-    rw [← leadingCoeff, Ne.def, leadingCoeff_eq_zero]; exact pzero
+    rw [← leadingCoeff, Ne, leadingCoeff_eq_zero]; exact pzero
   obtain ⟨lead, hlead⟩ :=
     monomial_mem_lifts_and_degree_eq
       (monomial_mem_lifts p.natDegree ((lifts_iff_coeff_lifts p).1 hlifts p.natDegree))

63417e01

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -234,7 +234,7 @@ theorem lifts_and_natDegree_eq_and_monic {p : S[X]} (hlifts : p ∈ lifts f) (hp
     ∃ q : R[X], map f q = p ∧ q.natDegree = p.natDegree ∧ q.Monic := by
   cases' subsingleton_or_nontrivial S with hR hR
   · obtain rfl : p = 1 := Subsingleton.elim _ _
-    refine' ⟨1, Subsingleton.elim _ _, by simp, by simp⟩
+    exact ⟨1, Subsingleton.elim _ _, by simp, by simp⟩
   obtain ⟨p', h₁, h₂, h₃⟩ := lifts_and_degree_eq_and_monic hlifts hp
   exact ⟨p', h₁, natDegree_eq_of_degree_eq h₂, h₃⟩
 #align polynomial.lifts_and_nat_degree_eq_and_monic Polynomial.lifts_and_natDegree_eq_and_monic

63417e01

chore: move to v4.6.0-rc1, merging adaptations from bump/v4.6.0 (#10176)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

490d2d48

Diff

@@ -148,8 +148,7 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   obtain ⟨q, hq⟩ := hl
   replace hq := (ext_iff.1 hq) n
   have hcoeff : f (q.coeff n) = s := by
-    simp? [coeff_monomial] at hq says
-      simp only [coeff_map, coeff_monomial, ite_true] at hq
+    simp? [coeff_monomial] at hq says simp only [coeff_map, coeff_monomial, ↓reduceIte] at hq
     exact hq
   use monomial n (q.coeff n)
   constructor

63417e01

chore: Remove nonterminal simp at (#7795)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

4160b2aa

Diff

@@ -148,7 +148,8 @@ theorem monomial_mem_lifts_and_degree_eq {s : S} {n : ℕ} (hl : monomial n s 
   obtain ⟨q, hq⟩ := hl
   replace hq := (ext_iff.1 hq) n
   have hcoeff : f (q.coeff n) = s := by
-    simp [coeff_monomial] at hq
+    simp? [coeff_monomial] at hq says
+      simp only [coeff_map, coeff_monomial, ite_true] at hq
     exact hq
   use monomial n (q.coeff n)
   constructor

63417e01

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -194,11 +194,11 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
   use erase + lead
   constructor
   · simp only [hlead, herase, Polynomial.map_add]
-    rw [←eraseLead, ←leadingCoeff]
+    rw [← eraseLead, ← leadingCoeff]
     rw [eraseLead_add_monomial_natDegree_leadingCoeff p]
-  rw [degree_eq_natDegree pzero, ←deg_lead]
+  rw [degree_eq_natDegree pzero, ← deg_lead]
   apply degree_add_eq_right_of_degree_lt
-  rw [herase.2, deg_lead, ←degree_eq_natDegree pzero]
+  rw [herase.2, deg_lead, ← degree_eq_natDegree pzero]
   exact degree_erase_lt pzero
 #align polynomial.mem_lifts_and_degree_eq Polynomial.mem_lifts_and_degree_eq
 
@@ -223,7 +223,7 @@ theorem lifts_and_degree_eq_and_monic [Nontrivial S] {p : S[X]} (hlifts : p ∈
   obtain ⟨q, hq⟩ := mem_lifts_and_degree_eq (erase_mem_lifts p.natDegree hlifts)
   have p_neq_0 : p ≠ 0 := by intro hp; apply h0; rw [hp]; simp only [natDegree_zero, erase_zero]
   have hdeg : q.degree < (X ^ p.natDegree).degree := by
-    rw [@degree_X_pow R, hq.2, ←degree_eq_natDegree p_neq_0]
+    rw [@degree_X_pow R, hq.2, ← degree_eq_natDegree p_neq_0]
     exact degree_erase_lt p_neq_0
   refine' ⟨q + X ^ p.natDegree, _, _, (monic_X_pow _).add_of_right hdeg⟩
   · rw [Polynomial.map_add, hq.1, Polynomial.map_pow, map_X, H]

63417e01

refactor(Data/Polynomial): remove open Classical (#7706)

This doesn't change any polynomial operations, but:

Makes some Decidable values computable (otherwise, they're pointless!)
Add a few missing arguments to lemmas here and there to make them more general

This is exhaustive, within the directories it touches.

Once again, the use of letI := Classical.decEq R instead of classical here is because of the weird style of proofs in these files, where if is preferred to by_cases.

4a7ff0e3

Diff

@@ -41,7 +41,7 @@ that lift is a subalgebra. (By `lift_iff` this is true if `R` is commutative.)
 -/
 
 
-open Classical BigOperators Polynomial
+open BigOperators Polynomial
 
 noncomputable section

63417e01

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module data.polynomial.lifts
-! leanprover-community/mathlib commit 63417e01fbc711beaf25fa73b6edb395c0cfddd0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.Polynomial.Monic
 
+#align_import data.polynomial.lifts from "leanprover-community/mathlib"@"63417e01fbc711beaf25fa73b6edb395c0cfddd0"
+
 /-!
 # Polynomials that lift

63417e01

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -184,7 +184,7 @@ theorem mem_lifts_and_degree_eq {p : S[X]} (hlifts : p ∈ lifts f) :
     rw [habs, eraseLead_zero, eq_self_iff_true, not_true] at erase_zero
     exact erase_zero
   have lead_zero : p.coeff p.natDegree ≠ 0 := by
-    rw [← leadingCoeff, Ne.def, leadingCoeff_eq_zero] ; exact pzero
+    rw [← leadingCoeff, Ne.def, leadingCoeff_eq_zero]; exact pzero
   obtain ⟨lead, hlead⟩ :=
     monomial_mem_lifts_and_degree_eq
       (monomial_mem_lifts p.natDegree ((lifts_iff_coeff_lifts p).1 hlifts p.natDegree))

63417e01

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -113,7 +113,7 @@ set_option linter.uppercaseLean3 false in
 
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f := by
-  simp only [lifts, RingHom.mem_rangeS] at hp⊢
+  simp only [lifts, RingHom.mem_rangeS] at hp ⊢
   obtain ⟨p₁, rfl⟩ := hp
   use C r * p₁
   simp only [coe_mapRingHom, map_C, map_mul]
@@ -129,7 +129,7 @@ theorem monomial_mem_lifts {s : S} (n : ℕ) (h : s ∈ Set.range f) : monomial
 
 /-- If `p` lifts then `p.erase n` lifts. -/
 theorem erase_mem_lifts {p : S[X]} (n : ℕ) (h : p ∈ lifts f) : p.erase n ∈ lifts f := by
-  rw [lifts_iff_ringHom_rangeS, mem_map_rangeS] at h⊢
+  rw [lifts_iff_ringHom_rangeS, mem_map_rangeS] at h ⊢
   intro k
   by_cases hk : k = n
   · use 0
@@ -288,7 +288,7 @@ theorem mem_lifts_iff_mem_alg (R : Type u) [CommSemiring R] {S : Type v} [Semiri
 /-- If `p` lifts and `(r : R)` then `r • p` lifts. -/
 theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
     r • p ∈ lifts (algebraMap R S) := by
-  rw [mem_lifts_iff_mem_alg] at hp⊢
+  rw [mem_lifts_iff_mem_alg] at hp ⊢
   exact Subalgebra.smul_mem (mapAlg R S).range hp r
 #align polynomial.smul_mem_lifts Polynomial.smul_mem_lifts

63417e01

chore: tidy various files (#2950)

f03c405e

Diff

@@ -79,12 +79,12 @@ theorem lifts_iff_coeff_lifts (p : S[X]) : p ∈ lifts f ↔ ∀ n : ℕ, p.coef
 #align polynomial.lifts_iff_coeff_lifts Polynomial.lifts_iff_coeff_lifts
 
 /-- If `(r : R)`, then `C (f r)` lifts. -/
-theorem c_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
+theorem C_mem_lifts (f : R →+* S) (r : R) : C (f r) ∈ lifts f :=
   ⟨C r, by
     simp only [coe_mapRingHom, map_C, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       and_self_iff]⟩
 set_option linter.uppercaseLean3 false in
-#align polynomial.C_mem_lifts Polynomial.c_mem_lifts
+#align polynomial.C_mem_lifts Polynomial.C_mem_lifts
 
 /-- If `(s : S)` is in the image of `f`, then `C s` lifts. -/
 theorem C'_mem_lifts {f : R →+* S} {s : S} (h : s ∈ Set.range f) : C s ∈ lifts f := by
@@ -96,20 +96,20 @@ set_option linter.uppercaseLean3 false in
 #align polynomial.C'_mem_lifts Polynomial.C'_mem_lifts
 
 /-- The polynomial `X` lifts. -/
-theorem x_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
+theorem X_mem_lifts (f : R →+* S) : (X : S[X]) ∈ lifts f :=
   ⟨X, by
     simp only [coe_mapRingHom, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true, map_X,
       and_self_iff]⟩
 set_option linter.uppercaseLean3 false in
-#align polynomial.X_mem_lifts Polynomial.x_mem_lifts
+#align polynomial.X_mem_lifts Polynomial.X_mem_lifts
 
 /-- The polynomial `X ^ n` lifts. -/
-theorem x_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
+theorem X_pow_mem_lifts (f : R →+* S) (n : ℕ) : (X ^ n : S[X]) ∈ lifts f :=
   ⟨X ^ n, by
     simp only [coe_mapRingHom, map_pow, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,
       map_X, and_self_iff]⟩
 set_option linter.uppercaseLean3 false in
-#align polynomial.X_pow_mem_lifts Polynomial.x_pow_mem_lifts
+#align polynomial.X_pow_mem_lifts Polynomial.X_pow_mem_lifts
 
 /-- If `p` lifts and `(r : R)` then `r * p` lifts. -/
 theorem base_mul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts f) : C (f r) * p ∈ lifts f := by
@@ -295,4 +295,3 @@ theorem smul_mem_lifts {p : S[X]} (r : R) (hp : p ∈ lifts (algebraMap R S)) :
 end Algebra
 
 end Polynomial
-

63417e01

feat: Port Data.Polynomial.Lifts (#2835)

f5400954

`data.polynomial.lifts` ⟷ `Mathlib.Data.Polynomial.Lifts`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 471

data.polynomial.lifts ⟷ Mathlib.Data.Polynomial.Lifts

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 471

`data.polynomial.lifts` ⟷ `Mathlib.Data.Polynomial.Lifts`