module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Data.List.ToFinsupp | {
"line": 98,
"column": 2
} | {
"line": 108,
"column": 54
} | [
{
"pp": "R : Type u_2\ninst✝³ : AddZeroClass R\nl₁ l₂ : List R\ninst✝² : DecidablePred fun x ↦ (l₁ ++ l₂).getD x 0 ≠ 0\ninst✝¹ : DecidablePred fun x ↦ l₁.getD x 0 ≠ 0\ninst✝ : DecidablePred fun x ↦ l₂.getD x 0 ≠ 0\n⊢ (l₁ ++ l₂).toFinsupp = l₁.toFinsupp + Finsupp.embDomain (addLeftEmbedding l₁.length) l₂.toFinsu... | ext n
simp only [toFinsupp_apply, Finsupp.add_apply]
cases lt_or_ge n l₁.length with
| inl h =>
rw [getD_append _ _ _ _ h, Finsupp.embDomain_notin_range, add_zero]
rintro ⟨k, rfl : length l₁ + k = n⟩
lia
| inr h =>
rcases Nat.exists_eq_add_of_le h with ⟨k, rfl⟩
rw [getD_append_right _ _ _ _ ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 36
} | {
"line": 132,
"column": 44
} | [
{
"pp": "α : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ ∀ b ∈ s, b ≠ a → (Pi.single a n b)! = 1",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"eq_false",
"Monoid.toMulOneClass",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 36
} | {
"line": 132,
"column": 44
} | [
{
"pp": "α : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ ∀ b ∈ s, b ≠ a → (Pi.single a n b)! = 1",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"eq_false",
"Monoid.toMulOneClass",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 36
} | {
"line": 132,
"column": 44
} | [
{
"pp": "α : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ ∀ b ∈ s, b ≠ a → (Pi.single a n b)! = 1",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"eq_false",
"Monoid.toMulOneClass",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 50
} | {
"line": 132,
"column": 58
} | [
{
"pp": "α : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ a ∉ s → (Pi.single a n a)! = 1",
"usedConstants": [
"Nat.factorial_eq_one._simp_1",
"CommMonoidWithZero.toCommMonoid",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Monoid.toMulOne... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 50
} | {
"line": 132,
"column": 58
} | [
{
"pp": "α : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ a ∉ s → (Pi.single a n a)! = 1",
"usedConstants": [
"Nat.factorial_eq_one._simp_1",
"CommMonoidWithZero.toCommMonoid",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Monoid.toMulOne... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 50
} | {
"line": 132,
"column": 58
} | [
{
"pp": "α : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ a ∉ s → (Pi.single a n a)! = 1",
"usedConstants": [
"Nat.factorial_eq_one._simp_1",
"CommMonoidWithZero.toCommMonoid",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Monoid.toMulOne... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 355,
"column": 4
} | {
"line": 355,
"column": 55
} | [
{
"pp": "case inr.succ\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\np✝ q✝ : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\nn✝ : σ →₀ ℕ\nhR : Nontrivial R\nd : ℕ\nhd :\n ∀ (n : σ →₀ ℕ),\n Finsupp.degree n = d →\n ∀ (p q : MvPolynomial σ R), p ∣ (monomial n) 1 * q ↔ ∃ m r, m ≤ n ∧ r ∣ q ∧ p = (monomia... | refine ⟨fun hp ↦ ?_, fun ⟨m, r, hmn, hrq, hp⟩ ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 459,
"column": 2
} | {
"line": 459,
"column": 18
} | [
{
"pp": "case swap\nm : Multiset ℕ\nl✝ l' : List ℕ\nx y : ℕ\nl : List ℕ\n⊢ (y :: x :: l).multinomial = (x :: y :: l).multinomial",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Nat.instOrderedSub",
"Semigroup.toMul",
"Nat.choose_mul",
"Nat.choose",
"Nat.inst... | | @swap x y l => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.MvPolynomial.Expand | {
"line": 177,
"column": 2
} | {
"line": 180,
"column": 22
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommSemiring R\np : ℕ\nφ : MvPolynomial σ R\nm : σ →₀ ℕ\ni : σ\nh : ¬p ∣ m i\n⊢ coeff m ((expand p) φ) = 0",
"usedConstants": [
"Finsupp.instFunLike",
"Mathlib.Tactic.Contrapose.contrapose₂",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semir... | contrapose! h
grw [← mem_support_iff, support_expand_subset, Finset.mem_image] at h
rcases h with ⟨a, -, rfl⟩
exact ⟨a i, by simp⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MvPolynomial.Expand | {
"line": 177,
"column": 2
} | {
"line": 180,
"column": 22
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommSemiring R\np : ℕ\nφ : MvPolynomial σ R\nm : σ →₀ ℕ\ni : σ\nh : ¬p ∣ m i\n⊢ coeff m ((expand p) φ) = 0",
"usedConstants": [
"Finsupp.instFunLike",
"Mathlib.Tactic.Contrapose.contrapose₂",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semir... | contrapose! h
grw [← mem_support_iff, support_expand_subset, Finset.mem_image] at h
rcases h with ⟨a, -, rfl⟩
exact ⟨a i, by simp⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.GameAdd | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 14
} | [
{
"pp": "case mpr\nα : Type u_1\nβ : Type u_2\nrα : α → α → Prop\nrβ : β → β → Prop\nx y : α × β\n⊢ rα x.1 y.1 ∧ x.2 = y.2 ∨ rβ x.2 y.2 ∧ x.1 = y.1 → GameAdd rα rβ x y",
"usedConstants": []
}
] | revert x y | Lean.Elab.Tactic.evalRevert | Lean.Parser.Tactic.revert |
Mathlib.Order.GameAdd | {
"line": 83,
"column": 22
} | {
"line": 85,
"column": 96
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nrα : α → α → Prop\nrβ : β → β → Prop\nx✝¹ x✝ : α × β\nh : RProd rα rβ x✝¹ x✝\n⊢ ∀ {a₁ : α} {b₁ : β} {a₂ : α} {b₂ : β}, rα a₁ a₂ → rβ b₁ b₂ → Relation.TransGen (GameAdd rα rβ) (a₁, b₁) (a₂, b₂)",
"usedConstants": [
"Prod.GameAdd",
"Prod.mk",
"Prod.GameAd... | by
intro _ _ _ _ hα hβ
exact Relation.TransGen.tail (Relation.TransGen.single <| GameAdd.fst hα) (GameAdd.snd hβ) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finsupp.MonomialOrder.DegLex | {
"line": 149,
"column": 29
} | {
"line": 151,
"column": 41
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : DegLex (α →₀ ℕ)\nh : a ≤ b\nc : DegLex (α →₀ ℕ)\n⊢ a + c ≤ b + c",
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
... | by
rw [le_iff] at h ⊢
simpa [ofDegLex_add, map_add] using h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.Tuple.Finset | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 43
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Type u_1\np : Fin (n + 1)\nx_pivot : α p\nx_remove : (i : Fin n) → α (p.succAbove i)\ns_pivot : Finset (α p)\ns_remove : (i : Fin n) → Finset (α (p.succAbove i))\n⊢ p.insertNth x_pivot x_remove ∈ piFinset (p.insertNth s_pivot s_remove) ↔\n x_pivot ∈ s_pivot ∧ x_remove ∈ piFi... | simp [mem_piFinset_iff_pivot_removeNth p] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Fin.Tuple.Finset | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 43
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Type u_1\np : Fin (n + 1)\nx_pivot : α p\nx_remove : (i : Fin n) → α (p.succAbove i)\ns_pivot : Finset (α p)\ns_remove : (i : Fin n) → Finset (α (p.succAbove i))\n⊢ p.insertNth x_pivot x_remove ∈ piFinset (p.insertNth s_pivot s_remove) ↔\n x_pivot ∈ s_pivot ∧ x_remove ∈ piFi... | simp [mem_piFinset_iff_pivot_removeNth p] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Finset | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 43
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Type u_1\np : Fin (n + 1)\nx_pivot : α p\nx_remove : (i : Fin n) → α (p.succAbove i)\ns_pivot : Finset (α p)\ns_remove : (i : Fin n) → Finset (α (p.succAbove i))\n⊢ p.insertNth x_pivot x_remove ∈ piFinset (p.insertNth s_pivot s_remove) ↔\n x_pivot ∈ s_pivot ∧ x_remove ∈ piFi... | simp [mem_piFinset_iff_pivot_removeNth p] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.Finset | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 57
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Type u_1\nS : (i : Fin (n + 1)) → Finset (α i)\nP : ((i : Fin n) → α i.succ) → Prop\ninst✝ : DecidablePred P\n⊢ map (consEquiv α).symm.toEmbedding ({r ∈ piFinset S | P (tail r)}) = S 0 ×ˢ {r ∈ piFinset (tail S) | P r}",
"usedConstants": [
"instNeZeroNatHAdd_1",
... | unfold tail; ext; simp [Fin.forall_iff_succ, and_assoc] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Finset | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 57
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Type u_1\nS : (i : Fin (n + 1)) → Finset (α i)\nP : ((i : Fin n) → α i.succ) → Prop\ninst✝ : DecidablePred P\n⊢ map (consEquiv α).symm.toEmbedding ({r ∈ piFinset S | P (tail r)}) = S 0 ×ˢ {r ∈ piFinset (tail S) | P r}",
"usedConstants": [
"instNeZeroNatHAdd_1",
... | unfold tail; ext; simp [Fin.forall_iff_succ, and_assoc] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 131,
"column": 6
} | {
"line": 131,
"column": 34
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\np : MvPolynomial σ R\n⊢ C (m.leadingCoeff p) * (monomial (m.degree p)) 1 = m.leadingTerm p",
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.inst... | MvPolynomial.C_mul_monomial, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 240,
"column": 25
} | {
"line": 242,
"column": 57
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\nd : σ →₀ ℕ\nhd : d ∈ f.support\n⊢ m.toSyn d ≤ m.toSyn (m.degree f)",
"usedConstants": [
"Nat.instMulZeroClass",
"Lattice.toSemilatticeSup",
"congrArg",
"MonomialOrder.syn",
"... | by
unfold degree
simp only [AddEquiv.apply_symm_apply, Finset.le_sup hd] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Squarefree | {
"line": 70,
"column": 6
} | {
"line": 70,
"column": 31
} | [
{
"pp": "n : ℕ\nhn : n ≠ 0\nhn' : ∀ (p : ℕ), n.factorization p ≤ 1\na : ℕ\n⊢ List.count a n.primeFactorsList ≤ 1",
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Nat.instMulZeroClass",
"congrArg",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"instBE... | primeFactorsList_count_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 294,
"column": 2
} | {
"line": 294,
"column": 30
} | [
{
"pp": "case h\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\nd : σ →₀ ℕ\n⊢ d ∈ f.support → m.toSyn d ≤ m.toSyn 0 ↔ d ∈ f.support → ∀ (x : σ), d x = 0",
"usedConstants": [
"Finsupp.instAddZeroClass",
"Finsupp.instFunLike",
"Nat.instMulZeroC... | apply imp_congr (rfl.to_iff) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.Nat.Squarefree | {
"line": 327,
"column": 80
} | {
"line": 327,
"column": 88
} | [
{
"pp": "n : ℕ\nS : Finset ℕ := {s ∈ range (n + 1) | s ∣ n ∧ ∃ x, s = x ^ 2}\nhSne : S.Nonempty\ns : ℕ := S.max' hSne\na b : ℕ\nhn : 0 < b ^ 2 * a\nhsa : n = b ^ 2 * a\nhsb : s = b ^ 2\nhlts : 0 < b ^ 2\nhlta : 0 < a\nx y : ℕ\nhy : a = x * x * y\nhx : ¬x = 1\nh : x = 0\n⊢ False",
"usedConstants": [
"F... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.Squarefree | {
"line": 327,
"column": 80
} | {
"line": 327,
"column": 88
} | [
{
"pp": "n : ℕ\nS : Finset ℕ := {s ∈ range (n + 1) | s ∣ n ∧ ∃ x, s = x ^ 2}\nhSne : S.Nonempty\ns : ℕ := S.max' hSne\na b : ℕ\nhn : 0 < b ^ 2 * a\nhsa : n = b ^ 2 * a\nhsb : s = b ^ 2\nhlts : 0 < b ^ 2\nhlta : 0 < a\nx y : ℕ\nhy : a = x * x * y\nhx : ¬x = 1\nh : x = 0\n⊢ False",
"usedConstants": [
"F... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Squarefree | {
"line": 327,
"column": 80
} | {
"line": 327,
"column": 88
} | [
{
"pp": "n : ℕ\nS : Finset ℕ := {s ∈ range (n + 1) | s ∣ n ∧ ∃ x, s = x ^ 2}\nhSne : S.Nonempty\ns : ℕ := S.max' hSne\na b : ℕ\nhn : 0 < b ^ 2 * a\nhsa : n = b ^ 2 * a\nhsb : s = b ^ 2\nhlts : 0 < b ^ 2\nhlta : 0 < a\nx y : ℕ\nhy : a = x * x * y\nhx : ¬x = 1\nh : x = 0\n⊢ False",
"usedConstants": [
"F... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Factorization.PrimePow | {
"line": 31,
"column": 4
} | {
"line": 31,
"column": 12
} | [
{
"pp": "case inl\nh : Nat.minFac 0 ^ (Nat.factorization 0) (Nat.minFac 0) = 0\nhn : 0 ≠ 1\n⊢ IsPrimePow 0",
"usedConstants": [
"Finsupp.instFunLike",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"False... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Nat.Factorization.PrimePow | {
"line": 31,
"column": 4
} | {
"line": 31,
"column": 12
} | [
{
"pp": "case inl\nh : Nat.minFac 0 ^ (Nat.factorization 0) (Nat.minFac 0) = 0\nhn : 0 ≠ 1\n⊢ IsPrimePow 0",
"usedConstants": [
"Finsupp.instFunLike",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"False... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Factorization.PrimePow | {
"line": 31,
"column": 4
} | {
"line": 31,
"column": 12
} | [
{
"pp": "case inl\nh : Nat.minFac 0 ^ (Nat.factorization 0) (Nat.minFac 0) = 0\nhn : 0 ≠ 1\n⊢ IsPrimePow 0",
"usedConstants": [
"Finsupp.instFunLike",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"False... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 698,
"column": 2
} | {
"line": 698,
"column": 42
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nP : ι → MvPolynomial σ R\ns : Finset ι\nH : ∀ i ∈ s, m.Monic (P i)\n⊢ m.Monic (∏ i ∈ s, P i)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
... | rw [Monic, leadingCoeff_prod_of_regular] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Antidiag.Nat | {
"line": 146,
"column": 6
} | {
"line": 146,
"column": 14
} | [
{
"pp": "case h\nd : ℕ\ni : Fin d\nhd : d ≠ 1\nk r : ℕ\nhn : ¬k * r = 0\nhs : Nontrivial (Fin d)\ni' : Fin d\nhi_ne : i' ≠ i\n⊢ (if i = i then k else if i = i' then r else 1) *\n ((if i' = i then k else if i' = i' then r else 1) *\n ∏ x ∈ (univ.erase i).erase i', if x = i then k else if x = i' t... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Antidiag.Nat | {
"line": 146,
"column": 6
} | {
"line": 146,
"column": 14
} | [
{
"pp": "case h\nd : ℕ\ni : Fin d\nhd : d ≠ 1\nk r : ℕ\nhn : ¬k * r = 0\nhs : Nontrivial (Fin d)\ni' : Fin d\nhi_ne : i' ≠ i\n⊢ (if i = i then k else if i = i' then r else 1) *\n ((if i' = i then k else if i' = i' then r else 1) *\n ∏ x ∈ (univ.erase i).erase i', if x = i then k else if x = i' t... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Antidiag.Nat | {
"line": 146,
"column": 6
} | {
"line": 146,
"column": 14
} | [
{
"pp": "case h\nd : ℕ\ni : Fin d\nhd : d ≠ 1\nk r : ℕ\nhn : ¬k * r = 0\nhs : Nontrivial (Fin d)\ni' : Fin d\nhi_ne : i' ≠ i\n⊢ (if i = i then k else if i = i' then r else 1) *\n ((if i' = i then k else if i' = i' then r else 1) *\n ∏ x ∈ (univ.erase i).erase i', if x = i then k else if x = i' t... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 403,
"column": 38
} | {
"line": 403,
"column": 46
} | [
{
"pp": "R : Type u_2\ninst✝ : Semiring R\nf g : ArithmeticFunction R\nN : ℕ\nx✝¹ : ℕ × ℕ\nx✝ : x✝¹ ∈ Ioc 0 N ×ˢ Ioc 0 N\n⊢ (∑ x ∈ Ioc 0 N, if x✝¹.1 * x✝¹.2 = x then f x✝¹.1 * g x✝¹.2 else 0) =\n if x✝¹.1 * x✝¹.2 ≤ N then f x✝¹.1 * g x✝¹.2 else 0",
"usedConstants": [
"Nat.instMulZeroClass",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 403,
"column": 38
} | {
"line": 403,
"column": 46
} | [
{
"pp": "R : Type u_2\ninst✝ : Semiring R\nf g : ArithmeticFunction R\nN : ℕ\nx✝¹ : ℕ × ℕ\nx✝ : x✝¹ ∈ Ioc 0 N ×ˢ Ioc 0 N\n⊢ (∑ x ∈ Ioc 0 N, if x✝¹.1 * x✝¹.2 = x then f x✝¹.1 * g x✝¹.2 else 0) =\n if x✝¹.1 * x✝¹.2 ≤ N then f x✝¹.1 * g x✝¹.2 else 0",
"usedConstants": [
"Nat.instMulZeroClass",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 403,
"column": 38
} | {
"line": 403,
"column": 46
} | [
{
"pp": "R : Type u_2\ninst✝ : Semiring R\nf g : ArithmeticFunction R\nN : ℕ\nx✝¹ : ℕ × ℕ\nx✝ : x✝¹ ∈ Ioc 0 N ×ˢ Ioc 0 N\n⊢ (∑ x ∈ Ioc 0 N, if x✝¹.1 * x✝¹.2 = x then f x✝¹.1 * g x✝¹.2 else 0) =\n if x✝¹.1 * x✝¹.2 ≤ N then f x✝¹.1 * g x✝¹.2 else 0",
"usedConstants": [
"Nat.instMulZeroClass",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 294,
"column": 6
} | {
"line": 294,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nx : ℕ\nx0 : ¬x = 0\nh : {(x, 1)} ⊆ x.divisorsAntidiagonal\ny₁ y₂ : ℕ\nymem : (y₁, y₂) ∈ x.divisorsAntidiagonal\nynotMem : (y₁, y₂) ∉ {(x, 1)}\ncon : y₂ = 1\n⊢ False",
"usedConstants": [
"False",
"HMul.hMul",
"Nat.divisors... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Archimedean.IndicatorCard | {
"line": 77,
"column": 78
} | {
"line": 77,
"column": 87
} | [
{
"pp": "case h\nα : Type u_1\nR : Type u_2\ninst✝⁴ : AddCommMonoid R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedAddMonoid R\ninst✝¹ : AddLeftStrictMono R\ninst✝ : Archimedean R\nr : R\nh : 0 < r\ns : ℕ → Set α\nω : α\n⊢ Tendsto (fun n ↦ ∑ k ∈ Finset.range n, {n | ω ∈ s n}.indicator (fun x ↦ r) k) atTop atTop ... | iff_eq_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 1069,
"column": 6
} | {
"line": 1069,
"column": 14
} | [
{
"pp": "case pos\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nd : m.syn\nι : Type u_3\ng : ι → MvPolynomial σ R\nb : ι\nB : Finset ι\nhb : b ∉ B\nh :\n (∀ b ∈ B, m.toSyn (m.degree (g b)) = d ∧ IsUnit (m.leadingCoeff (g b)) ∨ g b = 0) →\n m.toSyn (m.degree (∑ b ∈ B, g b)) < d →\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 1069,
"column": 6
} | {
"line": 1069,
"column": 14
} | [
{
"pp": "case pos\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nd : m.syn\nι : Type u_3\ng : ι → MvPolynomial σ R\nb : ι\nB : Finset ι\nhb : b ∉ B\nh :\n (∀ b ∈ B, m.toSyn (m.degree (g b)) = d ∧ IsUnit (m.leadingCoeff (g b)) ∨ g b = 0) →\n m.toSyn (m.degree (∑ b ∈ B, g b)) < d →\n ... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 1069,
"column": 6
} | {
"line": 1069,
"column": 14
} | [
{
"pp": "case pos\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nd : m.syn\nι : Type u_3\ng : ι → MvPolynomial σ R\nb : ι\nB : Finset ι\nhb : b ∉ B\nh :\n (∀ b ∈ B, m.toSyn (m.degree (g b)) = d ∧ IsUnit (m.leadingCoeff (g b)) ∨ g b = 0) →\n m.toSyn (m.degree (∑ b ∈ B, g b)) < d →\n ... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Chebyshev | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 57
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝³ : Semiring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : ExistsAddOfLE α\ns : Finset ι\nf : ι → α\n⊢ (∑ i ∈ s, f i) * ∑ i ∈ s, f i ≤ ↑(#s) * ∑ x ∈ s, f x * f x",
"usedConstants": [
"Finset",
"PartialOrder.toPreorder",
"monova... | exact (monovaryOn_self _ _).sum_mul_sum_le_card_mul_sum | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 302,
"column": 12
} | {
"line": 302,
"column": 20
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\n⊢ a = 1 → mk a = ⊤",
"usedConstants": [
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"PartialOrder.toPreorder",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 302,
"column": 12
} | {
"line": 302,
"column": 20
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\n⊢ a = 1 → mk a = ⊤",
"usedConstants": [
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"PartialOrder.toPreorder",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 302,
"column": 12
} | {
"line": 302,
"column": 20
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\n⊢ a = 1 → mk a = ⊤",
"usedConstants": [
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"PartialOrder.toPreorder",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 543,
"column": 29
} | {
"line": 543,
"column": 35
} | [
{
"pp": "case mk\nM : Type u_1\ninst✝⁵ : CommGroup M\ninst✝⁴ : LinearOrder M\ninst✝³ : IsOrderedMonoid M\nN : Type u_2\ninst✝² : CommGroup N\ninst✝¹ : LinearOrder N\ninst✝ : IsOrderedMonoid N\nf : M →*o N\nh : Function.Injective ⇑f\nb : MulArchimedeanClass M\na : M\n⊢ (orderHom f) (mk a) = (orderHom f) b → mk a... | | mk a
=> | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Order.Floor.Semifield | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 33
} | [
{
"pp": "case inr\nK : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsOrderedRing K\ninst✝ : FloorSemiring K\na b : K\nhb : 1 < b\nhba✝ : ↑⌈(b - 1)⁻¹⌉₊ / b ≤ a\nhba : ↑⌈(b - 1)⁻¹⌉₊ / b < a\n⊢ ↑⌈a⌉₊ ≤ b * a",
"usedConstants": [
"HMul.hMul",
"PartialOrder.toPreorder",
"AddGro... | exact (ceil_lt_mul hb hba).le | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Floor.Semifield | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 33
} | [
{
"pp": "case inr\nK : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsOrderedRing K\ninst✝ : FloorSemiring K\na b : K\nhb : 1 < b\nhba✝ : ↑⌈(b - 1)⁻¹⌉₊ / b ≤ a\nhba : ↑⌈(b - 1)⁻¹⌉₊ / b < a\n⊢ ↑⌈a⌉₊ ≤ b * a",
"usedConstants": [
"HMul.hMul",
"PartialOrder.toPreorder",
"AddGro... | exact (ceil_lt_mul hb hba).le | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Semifield | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 33
} | [
{
"pp": "case inr\nK : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsOrderedRing K\ninst✝ : FloorSemiring K\na b : K\nhb : 1 < b\nhba✝ : ↑⌈(b - 1)⁻¹⌉₊ / b ≤ a\nhba : ↑⌈(b - 1)⁻¹⌉₊ / b < a\n⊢ ↑⌈a⌉₊ ≤ b * a",
"usedConstants": [
"HMul.hMul",
"PartialOrder.toPreorder",
"AddGro... | exact (ceil_lt_mul hb hba).le | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 55,
"column": 21
} | {
"line": 58,
"column": 68
} | [
{
"pp": "M : Type u_1\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\nK : Type u_2\ninst✝⁵ : Ring K\ninst✝⁴ : LinearOrder K\ninst✝³ : IsOrderedRing K\ninst✝² : Archimedean K\ninst✝¹ : Module K M\ninst✝ : PosSMulMono K M\ns : UpperSet (ArchimedeanClass M)\nk : K\na : M\n⊢ a ∈ (ad... | by
obtain rfl | hs := eq_or_ne s ⊤
· aesop
simpa [mem_addSubgroup_iff hs] using s.upper (mk_le_mk_smul a k) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finset.MulAntidiagonal | {
"line": 42,
"column": 2
} | {
"line": 45,
"column": 53
} | [
{
"pp": "α : Type u_1\ns t : Set α\ninst✝² : CommMonoid α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedCancelMonoid α\nhs : s.IsWF\nht : t.IsWF\nhsn : s.Nonempty\nhtn : t.Nonempty\n⊢ ⋯.min ⋯ = hs.min hsn * ht.min htn",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"HMul.hMul",
"CommMonoid.toC... | refine le_antisymm (IsWF.min_le _ _ (mem_mul.2 ⟨_, hs.min_mem _, _, ht.min_mem _, rfl⟩)) ?_
rw [IsWF.le_min_iff]
rintro _ ⟨x, hx, y, hy, rfl⟩
exact mul_le_mul' (hs.min_le _ hx) (ht.min_le _ hy) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.MulAntidiagonal | {
"line": 42,
"column": 2
} | {
"line": 45,
"column": 53
} | [
{
"pp": "α : Type u_1\ns t : Set α\ninst✝² : CommMonoid α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedCancelMonoid α\nhs : s.IsWF\nht : t.IsWF\nhsn : s.Nonempty\nhtn : t.Nonempty\n⊢ ⋯.min ⋯ = hs.min hsn * ht.min htn",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"HMul.hMul",
"CommMonoid.toC... | refine le_antisymm (IsWF.min_le _ _ (mem_mul.2 ⟨_, hs.min_mem _, _, ht.min_mem _, rfl⟩)) ?_
rw [IsWF.le_min_iff]
rintro _ ⟨x, hx, y, hy, rfl⟩
exact mul_le_mul' (hs.min_le _ hx) (ht.min_le _ hy) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 163,
"column": 21
} | {
"line": 163,
"column": 92
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : PartialOrder Γ'\nx : R⟦Γ'⟧⟦Γ⟧\na : Γ\n⊢ {y | toLex (a, y) ∈ Function.support fun g ↦ (x.coeff g.1).coeff g.2}.IsPWO",
"usedConstants": [
"Set.IsPWO",
"Eq.mpr",
"Equiv.instEqu... | by simpa [Function.mem_support, ne_eq] using (x.coeff a).isPWO_support' | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 167,
"column": 55
} | {
"line": 167,
"column": 68
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝¹ : PartialOrder Γ\ninst✝ : Zero R\nf : Γ → R\nh : (Function.support f).IsPWO\n⊢ (∀ (x : Γ), f x = 0) ↔ ∀ (x : Γ), f x = 0 x",
"usedConstants": [
"iff_self",
"Iff",
"of_eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
]
}
] | Pi.zero_apply | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 203,
"column": 12
} | {
"line": 203,
"column": 57
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝¹ : PartialOrder Γ\ninst✝ : Zero R\na : Γ\nr : R\n⊢ ((single a) r).coeff a = r",
"usedConstants": [
"Classical.propDecidable",
"Pi.single_eq_same",
"Eq"
]
}
] | exact Pi.single_eq_same (M := fun _ => R) a r | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 203,
"column": 12
} | {
"line": 203,
"column": 57
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝¹ : PartialOrder Γ\ninst✝ : Zero R\na : Γ\nr : R\n⊢ ((single a) r).coeff a = r",
"usedConstants": [
"Classical.propDecidable",
"Pi.single_eq_same",
"Eq"
]
}
] | exact Pi.single_eq_same (M := fun _ => R) a r | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 203,
"column": 12
} | {
"line": 203,
"column": 57
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝¹ : PartialOrder Γ\ninst✝ : Zero R\na : Γ\nr : R\n⊢ ((single a) r).coeff a = r",
"usedConstants": [
"Classical.propDecidable",
"Pi.single_eq_same",
"Eq"
]
}
] | exact Pi.single_eq_same (M := fun _ => R) a r | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 413,
"column": 4
} | {
"line": 413,
"column": 12
} | [
{
"pp": "case pos\nΓ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : Zero Γ\nx : R⟦Γ⟧\nh : x = 0\n⊢ 0 ≤ x.orderTop ↔ 0 ≤ x.order",
"usedConstants": [
"HahnSeries.order",
"instReflLe",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"HahnS... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 413,
"column": 4
} | {
"line": 413,
"column": 12
} | [
{
"pp": "case pos\nΓ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : Zero Γ\nx : R⟦Γ⟧\nh : x = 0\n⊢ 0 ≤ x.orderTop ↔ 0 ≤ x.order",
"usedConstants": [
"HahnSeries.order",
"instReflLe",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"HahnS... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 413,
"column": 4
} | {
"line": 413,
"column": 12
} | [
{
"pp": "case pos\nΓ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : Zero Γ\nx : R⟦Γ⟧\nh : x = 0\n⊢ 0 ≤ x.orderTop ↔ 0 ≤ x.order",
"usedConstants": [
"HahnSeries.order",
"instReflLe",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"HahnS... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 509,
"column": 6
} | {
"line": 509,
"column": 57
} | [
{
"pp": "case inr\nΓ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\n⊢ (embDomain f x).orderTop = WithTop.map (⇑f) x.orderTop",
"usedConstants": [
"Eq.mpr",
"HahnSeries.embDomain",
"congrArg",
... | ← WithTop.coe_untop x.orderTop (by simpa using hx), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 532,
"column": 2
} | {
"line": 532,
"column": 10
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝¹ : Zero R\ninst✝ : LinearOrder Γ\nf : Γ → R\nn : Γ\nhn : ∀ m < n, f m = 0\nx✝ : Γ\n⊢ ¬n ≤ x✝ → x✝ ∉ Function.support f",
"usedConstants": [
"False",
"Preorder.toLT",
"Function.mem_support._simp_1",
"congrArg",
"PartialOrder.toPreorder"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 164,
"column": 2
} | {
"line": 165,
"column": 29
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝¹ : PartialOrder Γ\ninst✝ : AddMonoid R\nx : Rᵃᵒᵖ⟦Γ⟧\n⊢ (AddOpposite.unop (addOppositeEquiv x)).orderTop = x.orderTop",
"usedConstants": [
"HahnSeries.support",
"Eq.mpr",
"Set.IsWF.min.congr_simp",
"dite_congr",
"Preorder.toLT",
"... | simp only [orderTop,
addOppositeEquiv_support] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 393,
"column": 64
} | {
"line": 397,
"column": 45
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : AddGroup R\ninst✝ : Zero Γ\nf : R⟦Γ⟧\n⊢ (-f).order = f.order",
"usedConstants": [
"HahnSeries.support",
"AddGroup.toSubtractionMonoid",
"HahnSeries.order",
"Set.IsWF.min.congr_simp",
"dite_congr",
"Pre... | by
classical
by_cases hf : f = 0
· simp only [hf, neg_zero]
simp only [order, support_neg, neg_eq_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 56
} | [
{
"pp": "M : Type u_1\ninst✝⁴ : CancelCommMonoid M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedMonoid M\ninst✝¹ : LocallyFiniteOrder M\ninst✝ : ExistsMulOfLE M\na b : M\nha : 1 ≤ a\nhb : 1 ≤ b\n⊢ Ico 1 b ∪ Ico (1 * b) (a * b) = Ico 1 (a * b)",
"usedConstants": [
"instIsRightCancelMulOfMulRightReflectLE... | simp [Ico_union_Ico, ha, hb, Right.one_le_mul ha hb] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 131,
"column": 29
} | {
"line": 131,
"column": 37
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\nx : G\nhx : (orderAddMonoidHom G).toAddMonoidHom x = 1\na : ℤ\n⊢ (orderAddMonoidHom G) (a • x) = a",
"usedConstants": [
"Int.instAddCommGroup",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 131,
"column": 29
} | {
"line": 131,
"column": 37
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\nx : G\nhx : (orderAddMonoidHom G).toAddMonoidHom x = 1\na : ℤ\n⊢ (orderAddMonoidHom G) (a • x) = a",
"usedConstants": [
"Int.instAddCommGroup",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 131,
"column": 29
} | {
"line": 131,
"column": 37
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\nx : G\nhx : (orderAddMonoidHom G).toAddMonoidHom x = 1\na : ℤ\n⊢ (orderAddMonoidHom G) (a • x) = a",
"usedConstants": [
"Int.instAddCommGroup",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 103,
"column": 2
} | {
"line": 105,
"column": 45
} | [
{
"pp": "case mpr\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\nh : 0 ≤ x\n⊢ 0 ≤ (ofLex x).leadingCoeff",
"usedConstants": [
"Iff.mpr",
"LE.le.eq_or_lt",
"Preorder.toLT",
"Equiv.instEquivLike",
"instReflLe",
"co... | · obtain rfl | hlt := h.eq_or_lt
· simp
· exact (leadingCoeff_pos_iff.mpr hlt).le | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 12
} | [
{
"pp": "case inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex 0).orderTop\n⊢ (∃ n, |0| ≤ n • |x|) ↔ ∃ n, |(ofLex 0).leadingCoeff| ≤ n • |(ofLex x).leadingCoeff|",
"usedConsta... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 12
} | [
{
"pp": "case inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex 0).orderTop\n⊢ (∃ n, |0| ≤ n • |x|) ↔ ∃ n, |(ofLex 0).leadingCoeff| ≤ n • |(ofLex x).leadingCoeff|",
"usedConsta... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 12
} | [
{
"pp": "case inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex 0).orderTop\n⊢ (∃ n, |0| ≤ n • |x|) ↔ ∃ n, |(ofLex 0).leadingCoeff| ≤ n • |(ofLex x).leadingCoeff|",
"usedConsta... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 257,
"column": 6
} | {
"line": 257,
"column": 22
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\n⊢ ArchimedeanClass.mk x = ArchimedeanClass.mk y ↔\n (ofLex x).orderTop = (ofLex y).orderTop ∧\n ArchimedeanClass.mk (ofLex x).leadingCoeff = Archime... | le_antisymm_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 217,
"column": 19
} | {
"line": 217,
"column": 27
} | [
{
"pp": "case singleton\nR : Type u_1\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\nα : Type u_2\nβ : Type u_3\nF : Type u_4\ninst✝² : AddCommGroup α\ninst✝¹ : FunLike F α R\ninst✝ : AddGroupSeminormClass F α R\nf : F\nnonarch : IsNonarchimedean ⇑f\ns : Finset β\nl : β → α\na k : β\nhk : k ∈ {a}\nhmax : ∀ j ∈ {... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 217,
"column": 19
} | {
"line": 217,
"column": 27
} | [
{
"pp": "case singleton\nR : Type u_1\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\nα : Type u_2\nβ : Type u_3\nF : Type u_4\ninst✝² : AddCommGroup α\ninst✝¹ : FunLike F α R\ninst✝ : AddGroupSeminormClass F α R\nf : F\nnonarch : IsNonarchimedean ⇑f\ns : Finset β\nl : β → α\na k : β\nhk : k ∈ {a}\nhmax : ∀ j ∈ {... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 217,
"column": 19
} | {
"line": 217,
"column": 27
} | [
{
"pp": "case singleton\nR : Type u_1\ninst✝⁴ : Semiring R\ninst✝³ : LinearOrder R\nα : Type u_2\nβ : Type u_3\nF : Type u_4\ninst✝² : AddCommGroup α\ninst✝¹ : FunLike F α R\ninst✝ : AddGroupSeminormClass F α R\nf : F\nnonarch : IsNonarchimedean ⇑f\ns : Finset β\nl : β → α\na k : β\nhk : k ∈ {a}\nhmax : ∀ j ∈ {... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 362,
"column": 25
} | {
"line": 362,
"column": 33
} | [
{
"pp": "case pos\nR : Type u_3\nV : Type u_5\ninst✝⁷ : AddCommMonoid V\nΓ : Type u_6\nΓ' : Type u_7\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : LinearOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\ninst✝² : MulZeroClass R\ninst✝¹ : SMulWithZero R V\nx : R⟦Γ⟧\ninst✝ : VAdd (WithTop Γ) (WithTop Γ')\ny : H... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 362,
"column": 25
} | {
"line": 362,
"column": 33
} | [
{
"pp": "case pos\nR : Type u_3\nV : Type u_5\ninst✝⁷ : AddCommMonoid V\nΓ : Type u_6\nΓ' : Type u_7\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : LinearOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\ninst✝² : MulZeroClass R\ninst✝¹ : SMulWithZero R V\nx : R⟦Γ⟧\ninst✝ : VAdd (WithTop Γ) (WithTop Γ')\ny : H... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 362,
"column": 25
} | {
"line": 362,
"column": 33
} | [
{
"pp": "case pos\nR : Type u_3\nV : Type u_5\ninst✝⁷ : AddCommMonoid V\nΓ : Type u_6\nΓ' : Type u_7\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : LinearOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\ninst✝² : MulZeroClass R\ninst✝¹ : SMulWithZero R V\nx : R⟦Γ⟧\ninst✝ : VAdd (WithTop Γ) (WithTop Γ')\ny : H... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 363,
"column": 25
} | {
"line": 363,
"column": 33
} | [
{
"pp": "case pos\nR : Type u_3\nV : Type u_5\ninst✝⁷ : AddCommMonoid V\nΓ : Type u_6\nΓ' : Type u_7\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : LinearOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\ninst✝² : MulZeroClass R\ninst✝¹ : SMulWithZero R V\nx : R⟦Γ⟧\ninst✝ : VAdd (WithTop Γ) (WithTop Γ')\ny : H... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 363,
"column": 25
} | {
"line": 363,
"column": 33
} | [
{
"pp": "case pos\nR : Type u_3\nV : Type u_5\ninst✝⁷ : AddCommMonoid V\nΓ : Type u_6\nΓ' : Type u_7\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : LinearOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\ninst✝² : MulZeroClass R\ninst✝¹ : SMulWithZero R V\nx : R⟦Γ⟧\ninst✝ : VAdd (WithTop Γ) (WithTop Γ')\ny : H... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 363,
"column": 25
} | {
"line": 363,
"column": 33
} | [
{
"pp": "case pos\nR : Type u_3\nV : Type u_5\ninst✝⁷ : AddCommMonoid V\nΓ : Type u_6\nΓ' : Type u_7\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : LinearOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\ninst✝² : MulZeroClass R\ninst✝¹ : SMulWithZero R V\nx : R⟦Γ⟧\ninst✝ : VAdd (WithTop Γ) (WithTop Γ')\ny : H... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 146,
"column": 37
} | {
"line": 146,
"column": 45
} | [
{
"pp": "case mk.inl\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\n⊢ mk 0 = 0 ∨ mk 0 = ⊤",
"usedConstants": [
"False",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.instLinearOrder",
"PartialOrder.t... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 146,
"column": 37
} | {
"line": 146,
"column": 45
} | [
{
"pp": "case mk.inr\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nx : S\nh : x ≠ 0\n⊢ mk x = 0 ∨ mk x = ⊤",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.ins... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx y z : ArchimedeanClass R\nhx : x ≠ ⊤\nh : x + y = x + z\n⊢ y = z",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.instLinearOrd... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx y z : ArchimedeanClass R\nhx : x ≠ ⊤\nh : x + y = x + z\n⊢ y = z",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.instLinearOrd... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx y z : ArchimedeanClass R\nhx : x ≠ ⊤\nh : x + y = x + z\n⊢ y = z",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.instLinearOrd... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 245,
"column": 13
} | {
"line": 246,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx y z : ArchimedeanClass R\nhx : x ≠ ⊤\nh : x + y = x + z\n⊢ y = z",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.instLinearOrd... | by
simp_all | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 544,
"column": 2
} | {
"line": 544,
"column": 10
} | [
{
"pp": "case neg.h\nΓ : Type u_1\nR : Type u_3\ninst✝⁴ : AddCommMonoid Γ\ninst✝³ : LinearOrder Γ\ninst✝² : IsOrderedCancelAddMonoid Γ\ninst✝¹ : NonUnitalNonAssocSemiring R\nx y : R⟦Γ⟧\ninst✝ : NoZeroDivisors R\nhx : ¬x = 0\nhy : ¬y = 0\n⊢ x.leadingCoeff * y.leadingCoeff ≠ 0",
"usedConstants": [
"Fals... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 10
} | [
{
"pp": "case neg.h\nΓ : Type u_1\nR : Type u_3\ninst✝⁴ : AddCommMonoid Γ\ninst✝³ : LinearOrder Γ\ninst✝² : IsOrderedCancelAddMonoid Γ\ninst✝¹ : NonUnitalNonAssocSemiring R\nx y : R⟦Γ⟧\ninst✝ : NoZeroDivisors R\nhx : ¬x = 0\nhy : ¬y = 0\n⊢ x.leadingCoeff * y.leadingCoeff ≠ 0",
"usedConstants": [
"Fals... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 281,
"column": 6
} | {
"line": 281,
"column": 14
} | [
{
"pp": "case inl\nR : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\ny : R\nh : mk 0 = mk y\n⊢ (fun x ↦ mk x⁻¹) 0 = (fun x ↦ mk x⁻¹) y",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"DivisionCommMonoid.toDivisionMonoid"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 281,
"column": 6
} | {
"line": 281,
"column": 14
} | [
{
"pp": "case inl\nR : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\ny : R\nh : mk 0 = mk y\n⊢ (fun x ↦ mk x⁻¹) 0 = (fun x ↦ mk x⁻¹) y",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"DivisionCommMonoid.toDivisionMonoid"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 281,
"column": 6
} | {
"line": 281,
"column": 14
} | [
{
"pp": "case inl\nR : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\ny : R\nh : mk 0 = mk y\n⊢ (fun x ↦ mk x⁻¹) 0 = (fun x ↦ mk x⁻¹) y",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"DivisionCommMonoid.toDivisionMonoid"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 283,
"column": 6
} | {
"line": 283,
"column": 14
} | [
{
"pp": "case inr.inl\nR : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx : R\nhx : x ≠ 0\nh : mk x = mk 0\n⊢ (fun x ↦ mk x⁻¹) x = (fun x ↦ mk x⁻¹) 0",
"usedConstants": [
"False",
"DivisionCommMonoid.toDivisionMonoid",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 283,
"column": 6
} | {
"line": 283,
"column": 14
} | [
{
"pp": "case inr.inl\nR : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx : R\nhx : x ≠ 0\nh : mk x = mk 0\n⊢ (fun x ↦ mk x⁻¹) x = (fun x ↦ mk x⁻¹) 0",
"usedConstants": [
"False",
"DivisionCommMonoid.toDivisionMonoid",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 283,
"column": 6
} | {
"line": 283,
"column": 14
} | [
{
"pp": "case inr.inl\nR : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx : R\nhx : x ≠ 0\nh : mk x = mk 0\n⊢ (fun x ↦ mk x⁻¹) x = (fun x ↦ mk x⁻¹) 0",
"usedConstants": [
"False",
"DivisionCommMonoid.toDivisionMonoid",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 665,
"column": 46
} | {
"line": 665,
"column": 54
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : LinearOrder Γ\ninst✝² : Zero Γ\ninst✝¹ : NonAssocRing R\ninst✝ : Nontrivial R\nx : R⟦Γ⟧\nh : x.orderTop = 0 ∧ x.leadingCoeff = 1\n⊢ 0 = min x.orderTop (orderTop 1)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NeZero.one",
"AddGroupWith... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 665,
"column": 46
} | {
"line": 665,
"column": 54
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : LinearOrder Γ\ninst✝² : Zero Γ\ninst✝¹ : NonAssocRing R\ninst✝ : Nontrivial R\nx : R⟦Γ⟧\nh : x.orderTop = 0 ∧ x.leadingCoeff = 1\n⊢ 0 = min x.orderTop (orderTop 1)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NeZero.one",
"AddGroupWith... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 665,
"column": 46
} | {
"line": 665,
"column": 54
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : LinearOrder Γ\ninst✝² : Zero Γ\ninst✝¹ : NonAssocRing R\ninst✝ : Nontrivial R\nx : R⟦Γ⟧\nh : x.orderTop = 0 ∧ x.leadingCoeff = 1\n⊢ 0 = min x.orderTop (orderTop 1)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NeZero.one",
"AddGroupWith... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 656,
"column": 66
} | {
"line": 668,
"column": 30
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : LinearOrder Γ\ninst✝² : Zero Γ\ninst✝¹ : NonAssocRing R\ninst✝ : Nontrivial R\nx : R⟦Γ⟧\n⊢ 0 < (x - 1).orderTop ↔ x.orderTop = 0 ∧ x.leadingCoeff = 1",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"MulOne.toOne",
"WithTop.... | by
constructor
· intro hx
constructor
· rw [← sub_add_cancel x 1, add_comm, ← orderTop_one (R := R)]
exact orderTop_add_eq_left (Γ := Γ) (R := R) (orderTop_one (R := R) (Γ := Γ) ▸ hx)
· rw [← sub_add_cancel x 1, add_comm, ← leadingCoeff_one (Γ := Γ) (R := R)]
exact leadingCoeff_add_eq_left (... | [anonymous] | Lean.Parser.Term.byTactic |
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