module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 365
values | kind stringclasses 368
values |
|---|---|---|---|---|---|---|
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 502,
"column": 33
} | {
"line": 502,
"column": 41
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\nR : Type u_2\ninst✝¹ : Monoid α\ninst✝ : Ring R\nf : α →* R\nx y1 y2 : FreeAbelianGroup α\nih1 : (lift ⇑f) (x * y1) = (lift ⇑f) x * (lift ⇑f) y1\nih2 : (lift ⇑f) (x * y2) = (lift ⇑f) x * (lift ⇑f) y2\n⊢ (lift ⇑f) (x * (y1 + y2)) = (lift ⇑f) x ... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 502,
"column": 60
} | {
"line": 502,
"column": 68
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\nR : Type u_2\ninst✝¹ : Monoid α\ninst✝ : Ring R\nf : α →* R\nx y1 y2 : FreeAbelianGroup α\nih1 : (lift ⇑f) (x * y1) = (lift ⇑f) x * (lift ⇑f) y1\nih2 : (lift ⇑f) (x * y2) = (lift ⇑f) x * (lift ⇑f) y2\n⊢ (lift ⇑f) (x * y1) + (lift ⇑f) (x * y2) ... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 540,
"column": 33
} | {
"line": 540,
"column": 41
} | [
{
"pp": "case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : CommMonoid α\ns : α\ny1 y2 : FreeAbelianGroup α\nih1 : of s * y1 = y1 * of s\nih2 : of s * y2 = y2 * of s\n⊢ of s * (y1 + y2) = (y1 + y2) * of s",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 542,
"column": 40
} | {
"line": 542,
"column": 48
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : CommMonoid α\ny x1 x2 : FreeAbelianGroup α\nih1 : x1 * y = y * x1\nih2 : x2 * y = y * x2\n⊢ x1 * y + x2 * y = y * (x1 + x2)",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"Monoid.toM... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.OreLocalization.Basic | {
"line": 588,
"column": 52
} | {
"line": 588,
"column": 63
} | [
{
"pp": "R : Type u_1\nR' : Type u_2\nM : Type u_3\nX : Type u_4\ninst✝¹³ : Monoid M\nS : Submonoid M\ninst✝¹² : OreSet S\ninst✝¹¹ : MulAction M X\ninst✝¹⁰ : SMul R X\ninst✝⁹ : SMul R M\ninst✝⁸ : IsScalarTower R M M\ninst✝⁷ : IsScalarTower R M X\ninst✝⁶ : SMul R' X\ninst✝⁵ : SMul R' M\ninst✝⁴ : IsScalarTower R'... | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Maps | {
"line": 184,
"column": 2
} | {
"line": 187,
"column": 18
} | [
{
"pp": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type u_3\ninst✝ : CommMonoid P\nf : S.LocalizationMap N\ng : M →* P\nhg : ∀ (y : ↥S), IsUnit (g ↑y)\nj : N →* P\nhj : ∀ (x : M), j (f x) = g x\n⊢ f.lift hg = j",
"usedConstants": [
"Submonoid.Locali... | ext
rw [lift_spec, ← hj, ← hj, ← j.map_mul]
apply congr_arg
rw [← sec_spec'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.MonoidLocalization.Maps | {
"line": 184,
"column": 2
} | {
"line": 187,
"column": 18
} | [
{
"pp": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type u_3\ninst✝ : CommMonoid P\nf : S.LocalizationMap N\ng : M →* P\nhg : ∀ (y : ↥S), IsUnit (g ↑y)\nj : N →* P\nhj : ∀ (x : M), j (f x) = g x\n⊢ f.lift hg = j",
"usedConstants": [
"Submonoid.Locali... | ext
rw [lift_spec, ← hj, ← hj, ← j.map_mul]
apply congr_arg
rw [← sec_spec'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.OreLocalization.Basic | {
"line": 619,
"column": 48
} | {
"line": 619,
"column": 59
} | [
{
"pp": "R : Type u_1\nM : Type u_3\nX : Type u_4\ninst✝⁶ : Monoid M\nS : Submonoid M\ninst✝⁵ : OreSet S\ninst✝⁴ : MulAction M X\ninst✝³ : SMul R X\ninst✝² : SMul R M\ninst✝¹ : IsScalarTower R M M\ninst✝ : IsScalarTower R M X\nr : R\nx : X\n⊢ (r • 1) • x /ₒ 1 = r • x /ₒ 1",
"usedConstants": [
"Eq.mpr"... | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Sub.WithTop | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 56
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Sub α\ninst✝² : Bot α\ninst✝¹ : Sub β\ninst✝ : Bot β\nf : α → β\nh : ∀ (x y : α), f (x - y) = f x - f y\nh₀ : f ⊥ = ⊥\nx✝ : WithTop α\n⊢ map f (x✝ - ⊤) = map f x✝ - map f ⊤",
"usedConstants": [
"congrArg",
"HSub.hSub",
"WithTop.map",
"Bot... | simp only [sub_top, map_coe, h₀, map_top] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Sub.WithTop | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 56
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Sub α\ninst✝² : Bot α\ninst✝¹ : Sub β\ninst✝ : Bot β\nf : α → β\nh : ∀ (x y : α), f (x - y) = f x - f y\nh₀ : f ⊥ = ⊥\nx✝ : WithTop α\n⊢ map f (x✝ - ⊤) = map f x✝ - map f ⊤",
"usedConstants": [
"congrArg",
"HSub.hSub",
"WithTop.map",
"Bot... | simp only [sub_top, map_coe, h₀, map_top] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Sub.WithTop | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 56
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Sub α\ninst✝² : Bot α\ninst✝¹ : Sub β\ninst✝ : Bot β\nf : α → β\nh : ∀ (x y : α), f (x - y) = f x - f y\nh₀ : f ⊥ = ⊥\nx✝ : WithTop α\n⊢ map f (x✝ - ⊤) = map f x✝ - map f ⊤",
"usedConstants": [
"congrArg",
"HSub.hSub",
"WithTop.map",
"Bot... | simp only [sub_top, map_coe, h₀, map_top] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 182,
"column": 28
} | {
"line": 182,
"column": 44
} | [
{
"pp": "M : Type u_1\ninst✝ : CommMonoid M\nS : Submonoid M\nb : Con (M × ↥S)\nH : b ∈ {c | ∀ (y : ↥S), c 1 (↑y, y)}\nx✝² x✝¹ : M × ↥S\np : M\nq : ↥S\nx : M\ny : ↥S\nx✝ : (r' S) (p, q) (x, y)\nt : ↥S\nht : ↑t * (↑(x, y).2 * (p, q).1) = ↑t * (↑(p, q).2 * (x, y).1)\n⊢ b (1 * (p, q)) (x, y)",
"usedConstants":... | ← one_mul (x, y) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 357,
"column": 6
} | {
"line": 357,
"column": 17
} | [
{
"pp": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nR : Type u_4\ninst✝¹ : SMul R M\ninst✝ : IsScalarTower R M M\nc : R\na : M\nb : ↥S\n⊢ (c • 1) • a /ₒ (b * 1) = c • a /ₒ b",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
... | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 362,
"column": 55
} | {
"line": 362,
"column": 66
} | [
{
"pp": "M✝ : Type u_1\ninst✝⁵ : CommMonoid M✝\nS : Submonoid M✝\nN : Type u_2\ninst✝⁴ : CommMonoid N\nP : Type u_3\ninst✝³ : CommMonoid P\nR✝ : Type u_4\nR₁ : Type u_5\nR₂ : Type u_6\nR : Type u_7\nM : Type u_8\ninst✝² : CommMonoid M\ninst✝¹ : SMul R M\ninst✝ : IsScalarTower R M M\nr : R\ns x : M\n⊢ s • (r • 1... | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 492,
"column": 69
} | {
"line": 494,
"column": 73
} | [
{
"pp": "M : Type u_1\ninst✝¹ : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝ : CommMonoid N\nf : M →* N\nh : ∀ (y : ↥S), IsUnit (f ↑y)\ny : ↥S\nw z : N\n⊢ w * ↑((IsUnit.liftRight (f.restrict S) h) y)⁻¹ = z ↔ w = f ↑y * z",
"usedConstants": [
"IsUnit.liftRight",
"Units.val",
"Eq.mpr",... | by
rw [mul_comm]
exact Units.inv_mul_eq_iff_eq_mul (IsUnit.liftRight (f.restrict S) h y) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Ring.WithTop | {
"line": 75,
"column": 33
} | {
"line": 75,
"column": 42
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : WithTop α\nha : ¬a = 0\nhb : b = 0\n⊢ untopD 0 (a * 0) = untopD 0 a * untopD 0 0",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"id",
"MulZeroClass.mul_ze... | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.WithTop | {
"line": 335,
"column": 33
} | {
"line": 335,
"column": 42
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : WithBot α\nha : ¬a = 0\nhb : b = 0\n⊢ unbotD 0 (a * 0) = unbotD 0 a * unbotD 0 0",
"usedConstants": [
"Eq.mpr",
"WithBot",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"WithBot.instMu... | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.SuccPred.Limit | {
"line": 150,
"column": 71
} | {
"line": 152,
"column": 29
} | [
{
"pp": "α : Type u_1\na : α\ninst✝¹ : Preorder α\ninst✝ : OrderBot α\nh : IsSuccLimit a\n⊢ a ≠ ⊥",
"usedConstants": [
"False",
"OrderBot.toBot",
"Preorder.toLE",
"Order.IsSuccLimit",
"Order.not_isSuccLimit_bot",
"Bot.bot",
"Eq.ndrec",
"Eq.symm",
"Eq"
... | by
rintro rfl
exact not_isSuccLimit_bot h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.SuccPred.Archimedean | {
"line": 370,
"column": 4
} | {
"line": 370,
"column": 37
} | [
{
"pp": "case succ\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMax a → a ∈ s → succ a ∈ s → f a ≤ f (succ a)\na : α\nha : a ∈ s\nn : ℕ\nhn : succ^[n] a ∈ s → f a ≤ f (s... | by_cases hb' : IsMax (succ^[n] a) | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Order.SuccPred.Archimedean | {
"line": 401,
"column": 62
} | {
"line": 401,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 401,
"column": 62
} | {
"line": 401,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 401,
"column": 62
} | {
"line": 401,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 404,
"column": 62
} | {
"line": 404,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 404,
"column": 62
} | {
"line": 404,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 404,
"column": 62
} | {
"line": 404,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 407,
"column": 64
} | {
"line": 407,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 407,
"column": 64
} | {
"line": 407,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 407,
"column": 64
} | {
"line": 407,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 410,
"column": 64
} | {
"line": 410,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 410,
"column": 64
} | {
"line": 410,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 410,
"column": 64
} | {
"line": 410,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 458,
"column": 62
} | {
"line": 458,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 458,
"column": 62
} | {
"line": 458,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 458,
"column": 62
} | {
"line": 458,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 461,
"column": 62
} | {
"line": 461,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 461,
"column": 62
} | {
"line": 461,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 461,
"column": 62
} | {
"line": 461,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 464,
"column": 64
} | {
"line": 464,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 464,
"column": 64
} | {
"line": 464,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 464,
"column": 64
} | {
"line": 464,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 467,
"column": 64
} | {
"line": 467,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 467,
"column": 64
} | {
"line": 467,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 467,
"column": 64
} | {
"line": 467,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"usedConstants": [
"Eq.mpr",
... | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 187,
"column": 2
} | {
"line": 188,
"column": 43
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ninst✝¹ : CommMonoid M\ninst✝ : DecidableEq ι\ns t : Finset ι\nf : ι → M\n⊢ (∏ x ∈ s ∩ t, f x) * ∏ x ∈ s \\ t, f x = ∏ x ∈ s, f x",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"HEq.refl",
"Finset",
... | convert (s.prod_piecewise t f f).symm
simp +unfoldPartialApp [Finset.piecewise] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 187,
"column": 2
} | {
"line": 188,
"column": 43
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ninst✝¹ : CommMonoid M\ninst✝ : DecidableEq ι\ns t : Finset ι\nf : ι → M\n⊢ (∏ x ∈ s ∩ t, f x) * ∏ x ∈ s \\ t, f x = ∏ x ∈ s, f x",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"HEq.refl",
"Finset",
... | convert (s.prod_piecewise t f f).symm
simp +unfoldPartialApp [Finset.piecewise] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Vector.Basic | {
"line": 69,
"column": 25
} | {
"line": 69,
"column": 40
} | [
{
"pp": "α : Type u_1\nf : Fin 0 → α\n⊢ nil.toList = List.ofFn f",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.ofFn",
"id",
"instOfNatNat",
"List",
"List.ofFn_zero",
"Nat",
"List.Vector.nil",
"OfNat.ofNat",
"Eq",
"List.Vector.toList"... | List.ofFn_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Vector.Basic | {
"line": 292,
"column": 28
} | {
"line": 292,
"column": 46
} | [
{
"pp": "α : Type u_1\nn : ℕ\nv : Vector α (n + 1)\n⊢ v.reverse.get 0 = v.get (Fin.last n)",
"usedConstants": [
"List.Vector.get",
"Eq.mpr",
"congrArg",
"List.get",
"List.Vector.get_eq_get_toList",
"id",
"Fin.instOfNat",
"instOfNatNat",
"List.Vector.toLi... | get_eq_get_toList, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Sym.Basic | {
"line": 311,
"column": 4
} | {
"line": 313,
"column": 78
} | [
{
"pp": "case succ\nα : Type u_1\nβ : Type u_2\nn n' m : ℕ\ns : Sym α n\na b : α\ninst✝ : Subsingleton α\nn✝ : ℕ\n⊢ ∀ (a b : Sym α (n✝ + 1)), a = b",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Sym.replicate",
"Membership.mem",
"Exists",
"id",
"instOfNatNat",
"i... | · intro s s'
obtain ⟨b, -⟩ := exists_mem s
rw [eq_replicate_of_subsingleton b s', eq_replicate_of_subsingleton b s] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Logic.Small.Set | {
"line": 45,
"column": 6
} | {
"line": 45,
"column": 30
} | [
{
"pp": "α : Type u1\nβ : Type u2\nγ : Type u3\nι : Type u4\nf : α → β → γ\ns : Set α\nt : Set β\ninst✝¹ : Small.{u, u1} ↑s\ninst✝ : Small.{u, u2} ↑t\n⊢ Small.{u, u3} ↑(Set.image2 f s t)",
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Set.Elem",
... | ← Set.image_uncurry_prod | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Hom.Lex | {
"line": 135,
"column": 56
} | {
"line": 136,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\nx y : α\nh : x < y\n⊢ (sumLexIicIoi x).symm y = toLex (Sum.inr ⟨y, h⟩)",
"usedConstants": [
"Eq.mpr",
"Sum.Lex.LE",
"Set.Ioi",
"Equiv.instEquivLike",
"congrArg",
"Lex",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | by
rw [symm_apply_eq, sumLexIicIoi_apply_inr] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteLattice.Chain | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 12
} | [
{
"pp": "case union.a\nα : Type u_1\nr : α → α → Prop\nc₂ : Set α\ns✝ : Set (Set α)\na✝ : ∀ a ∈ s✝, ChainClosure r a\nih : ∀ a ∈ s✝, ∀ {c₁ : Set α}, ChainClosure r c₁ → c₁ ⊆ a → a = c₁ ∨ SuccChain r c₁ ⊆ a\nc₁ : Set α\nhc₁ : ChainClosure r c₁\nh : c₁ ⊆ ⋃₀ s✝\n⊢ ∀ x ∈ s✝, ¬x ⊆ c₁ → ¬SuccChain r c₁ ⊆ ⋃₀ s✝ → Fals... | intro c₃ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Data.Part | {
"line": 449,
"column": 23
} | {
"line": 449,
"column": 32
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\no : Part α\na : α\nh : a ∈ o\nf : α → Part β\n⊢ (some a).bind f = f a",
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part.some",
"Part.bind_some",
"id",
"Eq"
]
}
] | bind_some | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Part | {
"line": 691,
"column": 28
} | {
"line": 691,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ma ++ mb ∈ a ++ b",
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part.mem_bind_iff._simp_1",
"Part.instAppend",
"Membership.mem",
"Exists",
"i... | simp [append_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Part | {
"line": 700,
"column": 2
} | {
"line": 700,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : Part α\nhab : (a ++ b).Dom\n⊢ (a ++ b).get hab = a.get ⋯ ++ b.get ⋯",
"usedConstants": [
"Part",
"Part.right_dom_of_append_dom",
"Part.left_dom_of_append_dom",
"Part.instAppend",
"id",
"Part.get",
"instHAppendOfAppend",... | simp [append_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Part | {
"line": 703,
"column": 2
} | {
"line": 703,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"usedConstants": [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"Part.instAppend",
"funext",
"instHAppendOfAppend",
"Part.map_some",
"True",
"eq_self",
... | simp [append_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Part | {
"line": 703,
"column": 2
} | {
"line": 703,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"usedConstants": [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"Part.instAppend",
"funext",
"instHAppendOfAppend",
"Part.map_some",
"True",
"eq_self",
... | simp [append_def] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Part | {
"line": 703,
"column": 2
} | {
"line": 703,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"usedConstants": [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"Part.instAppend",
"funext",
"instHAppendOfAppend",
"Part.map_some",
"True",
"eq_self",
... | simp [append_def] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.ToNat | {
"line": 68,
"column": 2
} | {
"line": 69,
"column": 20
} | [
{
"pp": "⊢ StrictMonoOn (⇑toNat) (Iio ℵ₀)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroOneClass",
"Preorder.toLT",
"_private.Mathlib.SetTheory.Cardinal.ToNat.0.Cardinal.toNat_strictMonoOn._simp_1_1",
"IsOrderedRing.toZeroLEOneC... | simp only [← range_natCast, StrictMonoOn, forall_mem_range, toNat_natCast, Nat.cast_lt]
exact fun _ _ ↦ id | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.ToNat | {
"line": 68,
"column": 2
} | {
"line": 69,
"column": 20
} | [
{
"pp": "⊢ StrictMonoOn (⇑toNat) (Iio ℵ₀)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroOneClass",
"Preorder.toLT",
"_private.Mathlib.SetTheory.Cardinal.ToNat.0.Cardinal.toNat_strictMonoOn._simp_1_1",
"IsOrderedRing.toZeroLEOneC... | simp only [← range_natCast, StrictMonoOn, forall_mem_range, toNat_natCast, Nat.cast_lt]
exact fun _ _ ↦ id | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.ENat | {
"line": 318,
"column": 75
} | {
"line": 318,
"column": 92
} | [
{
"pp": "m : ℕ∞\n⊢ ℵ₀ + ↑m = ℵ₀",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"id",
"Cardinal.aleph0",
"Cardinal.instAdd",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"... | aleph0_add_ofENat | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Order | {
"line": 340,
"column": 6
} | {
"line": 340,
"column": 14
} | [
{
"pp": "case mk\nα : Type u\n⊢ #α < 2 ^ #α",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"Cardinal.mk",
"id",
"instOfNatNat",
"Ca... | ← mk_set | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Order | {
"line": 414,
"column": 27
} | {
"line": 417,
"column": 32
} | [
{
"pp": "a : Cardinal.{u}\nh : succ (lift.{v, u} a) < lift.{v, u} (succ a)\n⊢ False",
"usedConstants": [
"False",
"Preorder.toLT",
"Order.succ",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Cardinal.instNoMaxOrder",
"Preorder.toLE... | by
rcases lt_lift_iff.1 h with ⟨b, h, e⟩
rw [lt_succ_iff, ← lift_le, e] at h
exact h.not_gt (lt_succ _) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Algebra.Defs | {
"line": 245,
"column": 59
} | {
"line": 245,
"column": 75
} | [
{
"pp": "R : Type u\nS : Type v\nA : Type w\nB : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Module R A\nh₁ : ∀ (r : R) (x y : A), r • x * y = r • (x * y)\nh₂ : ∀ (r : R) (x y : A), x * r • y = r • (x * y)\nr : R\nx : A\n⊢ x * r • 1 = r • x",
"usedConstants": [
"Eq.mpr",
"Non... | rw [h₂, mul_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Algebra.Defs | {
"line": 245,
"column": 59
} | {
"line": 245,
"column": 75
} | [
{
"pp": "R : Type u\nS : Type v\nA : Type w\nB : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Module R A\nh₁ : ∀ (r : R) (x y : A), r • x * y = r • (x * y)\nh₂ : ∀ (r : R) (x y : A), x * r • y = r • (x * y)\nr : R\nx : A\n⊢ x * r • 1 = r • x",
"usedConstants": [
"Eq.mpr",
"Non... | rw [h₂, mul_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Algebra.Defs | {
"line": 245,
"column": 59
} | {
"line": 245,
"column": 75
} | [
{
"pp": "R : Type u\nS : Type v\nA : Type w\nB : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Module R A\nh₁ : ∀ (r : R) (x y : A), r • x * y = r • (x * y)\nh₂ : ∀ (r : R) (x y : A), x * r • y = r • (x * y)\nr : R\nx : A\n⊢ x * r • 1 = r • x",
"usedConstants": [
"Eq.mpr",
"Non... | rw [h₂, mul_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Basic | {
"line": 928,
"column": 2
} | {
"line": 929,
"column": 43
} | [
{
"pp": "α β : Type u\nf : α → β\ns : Set β\nh : Injective f\n⊢ #↑(f ⁻¹' s) ≤ #↑s",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"Cardinal.lift",
"Cardinal.mk",
"Set.Elem",
"id",
"LE.le",
"Cardinal.instLE",
"Set.preimage",
"Eq.symm",
... | rw [← lift_id #(↑(f ⁻¹' s)), ← lift_id #(↑s)]
exact mk_preimage_of_injective_lift f s h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Basic | {
"line": 928,
"column": 2
} | {
"line": 929,
"column": 43
} | [
{
"pp": "α β : Type u\nf : α → β\ns : Set β\nh : Injective f\n⊢ #↑(f ⁻¹' s) ≤ #↑s",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"Cardinal.lift",
"Cardinal.mk",
"Set.Elem",
"id",
"LE.le",
"Cardinal.instLE",
"Set.preimage",
"Eq.symm",
... | rw [← lift_id #(↑(f ⁻¹' s)), ← lift_id #(↑s)]
exact mk_preimage_of_injective_lift f s h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Algebra.Defs | {
"line": 328,
"column": 79
} | {
"line": 329,
"column": 36
} | [
{
"pp": "R : Type u\nA : Type w\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\ns : R\nx y : A\n⊢ x * s • y = s • (x * y)",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"RingHom",
"Algebra.toSMul",... | by
rw [smul_def, smul_def, left_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.GroupAction.DomAct.Basic | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 44
} | [
{
"pp": "M : Type u_1\nβ : Type u_2\nα : Type u_3\nN : Type u_4\ninst✝² : SMul M α\ninst✝¹ : FaithfulSMul M α\ninst✝ : Nontrivial β\nc₁ c₂ : Mᵈᵐᵃ\nh : ∀ (a : α → β), c₁ • a = c₂ • a\na : α\n⊢ mk.symm c₁ • a = mk.symm c₂ • a",
"usedConstants": [
"exists_pair_ne"
]
}
] | rcases exists_pair_ne β with ⟨x, y, hne⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.GroupTheory.GroupAction.Hom | {
"line": 190,
"column": 52
} | {
"line": 190,
"column": 63
} | [
{
"pp": "M' : Type u_1\nX : Type u_5\ninst✝⁶ : SMul M' X\nY : Type u_6\ninst✝⁵ : SMul M' Y\nF : Type u_8\ninst✝⁴ : FunLike F X Y\ninst✝³ : MulOneClass X\ninst✝² : SMul X Y\ninst✝¹ : IsScalarTower M' X Y\ninst✝ : MulActionHomClass F X X Y\nf : F\nm : M'\nx : X\n⊢ (m • x) • f 1 = id m • f x",
"usedConstants":... | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.LinearMap.End | {
"line": 141,
"column": 12
} | {
"line": 141,
"column": 28
} | [
{
"pp": "case zero\nR : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_6\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂ M₂\nσ₁₂ : R →+* R₂\nf : M →ₛₗ[σ₁₂] M₂\ng : End R M\ng₂ : End R₂ M₂\nh : g₂ ∘ₛₗ f = f ∘ₛₗ g\n⊢ (g₂ ^... | simp [one_eq_id] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Module.LinearMap.End | {
"line": 141,
"column": 12
} | {
"line": 141,
"column": 28
} | [
{
"pp": "case zero\nR : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_6\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂ M₂\nσ₁₂ : R →+* R₂\nf : M →ₛₗ[σ₁₂] M₂\ng : End R M\ng₂ : End R₂ M₂\nh : g₂ ∘ₛₗ f = f ∘ₛₗ g\n⊢ (g₂ ^... | simp [one_eq_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.LinearMap.End | {
"line": 141,
"column": 12
} | {
"line": 141,
"column": 28
} | [
{
"pp": "case zero\nR : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_6\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂ M₂\nσ₁₂ : R →+* R₂\nf : M →ₛₗ[σ₁₂] M₂\ng : End R M\ng₂ : End R₂ M₂\nh : g₂ ∘ₛₗ f = f ∘ₛₗ g\n⊢ (g₂ ^... | simp [one_eq_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Module.Submodule.Defs | {
"line": 380,
"column": 28
} | {
"line": 380,
"column": 43
} | [
{
"pp": "case a\nG : Type u''\nS : Type u'\nR : Type u\nM : Type v\nι : Type w\nT : Type u_1\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Semiring S\ninst✝⁶ : Module R M\ninst✝⁵ : SMul S R\ninst✝⁴ : Module S M\ninst✝³ : IsScalarTower S R M\ninst✝² : SetLike T M\ninst✝¹ : AddSubmonoidClass T M\ninst✝... | simp [mul_smul] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.GroupTheory.GroupAction.SubMulAction | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 30
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass S R M\nN : S\nx : M\nh : ∀ (a : R), a • x ∈ N\n⊢ x ∈ N",
"usedConstants": [
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
... | simpa using h 1 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.GroupTheory.GroupAction.SubMulAction | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 30
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass S R M\nN : S\nx : M\nh : ∀ (a : R), a • x ∈ N\n⊢ x ∈ N",
"usedConstants": [
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
... | simpa using h 1 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.GroupAction.SubMulAction | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 30
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass S R M\nN : S\nx : M\nh : ∀ (a : R), a • x ∈ N\n⊢ x ∈ N",
"usedConstants": [
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
... | simpa using h 1 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Module.Submodule.Map | {
"line": 459,
"column": 19
} | {
"line": 459,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_5\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\np p' : Submodule R M\nx : M\n⊢ x ∈ map p.subtype (comap p.subtype p') → x ∈ p ⊓ p'",
"usedConstants": [
"Submodule",
"RingHomSurjective.ids",
"Submodule.addCommMonoid",
"LinearMap.... | rintro ⟨⟨_, h₁⟩, h₂, rfl⟩; exact ⟨h₁, h₂⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.Submodule.Map | {
"line": 459,
"column": 19
} | {
"line": 459,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_5\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\np p' : Submodule R M\nx : M\n⊢ x ∈ map p.subtype (comap p.subtype p') → x ∈ p ⊓ p'",
"usedConstants": [
"Submodule",
"RingHomSurjective.ids",
"Submodule.addCommMonoid",
"LinearMap.... | rintro ⟨⟨_, h₁⟩, h₂, rfl⟩; exact ⟨h₁, h₂⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.GroupWithZero.Center | {
"line": 28,
"column": 28
} | {
"line": 28,
"column": 37
} | [
{
"pp": "M₀ : Type u_1\ninst✝ : MulZeroClass M₀\nx✝¹ x✝ : M₀\n⊢ x✝¹ * x✝ * 0 = x✝¹ * (x✝ * 0)",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"id",
"MulZeroClass.mul_zero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"MulZer... | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.GroupWithZero.Center | {
"line": 28,
"column": 38
} | {
"line": 28,
"column": 47
} | [
{
"pp": "M₀ : Type u_1\ninst✝ : MulZeroClass M₀\nx✝¹ x✝ : M₀\n⊢ 0 = x✝¹ * (x✝ * 0)",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"id",
"MulZeroClass.mul_zero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZe... | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 32,
"column": 24
} | {
"line": 32,
"column": 38
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : ↑n * (x✝¹ * x✝) = ↑n * x✝¹ * x✝\n⊢ ↑(n + 1) * (x✝¹ * x✝) = ↑(n + 1) * x✝¹ * x✝",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.cast_succ",
"HMul.hMul",
"AddMono... | Nat.cast_succ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 35,
"column": 33
} | {
"line": 35,
"column": 42
} | [
{
"pp": "case zero\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\n⊢ x✝¹ * x✝ * 0 = x✝¹ * (x✝ * 0)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalN... | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 35,
"column": 43
} | {
"line": 35,
"column": 52
} | [
{
"pp": "case zero\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\n⊢ 0 = x✝¹ * (x✝ * 0)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemi... | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 24
} | {
"line": 36,
"column": 38
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * x✝ * ↑(n + 1) = x✝¹ * (x✝ * ↑(n + 1))",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.cast_succ",
"HMul.hMul",
"AddMono... | Nat.cast_succ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 39
} | {
"line": 36,
"column": 47
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * x✝ * (↑n + 1) = x✝¹ * (x✝ * (↑n + 1))",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 53
} | {
"line": 36,
"column": 61
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * (x✝ * ↑n) + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * (↑n + 1))",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 62
} | {
"line": 36,
"column": 70
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * (x✝ * ↑n) + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * ↑n + x✝ * 1)",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"H... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Centralizer | {
"line": 27,
"column": 57
} | {
"line": 27,
"column": 65
} | [
{
"pp": "M : Type u_1\nS : Set M\na b : M\ninst✝ : Distrib M\nha : a ∈ S.centralizer\nhb : b ∈ S.centralizer\nc : M\nhc : c ∈ S\n⊢ c * (a + b) = a * c + b * c",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"Distrib.toAdd",
... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 56,
"column": 12
} | {
"line": 56,
"column": 20
} | [
{
"pp": "M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * (-1 + -↑n) = x✝¹ * (x✝ * (-1 + -↑n))",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGrou... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 56,
"column": 21
} | {
"line": 56,
"column": 29
} | [
{
"pp": "M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * (-1 + -↑n))",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAd... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 56,
"column": 30
} | {
"line": 56,
"column": 38
} | [
{
"pp": "M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * -1 + x✝ * -↑n)",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.t... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 64,
"column": 44
} | {
"line": 64,
"column": 52
} | [
{
"pp": "M : Type u_1\ninst✝ : Distrib M\na b : M\nha : a ∈ center M\nhb : b ∈ center M\nx✝ : M\n⊢ a * x✝ + b * x✝ = x✝ * (a + b)",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"Distrib.toAdd",
"instHAdd",
"Distrib.to... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 66,
"column": 28
} | {
"line": 66,
"column": 36
} | [
{
"pp": "M : Type u_1\ninst✝ : Distrib M\na b : M\nha : a ∈ center M\nhb : b ∈ center M\nx✝¹ x✝ : M\n⊢ x✝¹ * x✝ * (a + b) = x✝¹ * (x✝ * (a + b))",
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"Distrib.toAdd",
"instHAdd",
... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.NonUnitalSubring.Basic | {
"line": 561,
"column": 6
} | {
"line": 561,
"column": 24
} | [
{
"pp": "case a.zero_left\nF : Type w\nR✝ : Type u\nS : Type v\ninst✝⁴ : NonUnitalNonAssocRing R✝\ninst✝³ : NonUnitalNonAssocRing S\ninst✝² : FunLike F R✝ S\ninst✝¹ : NonUnitalRingHomClass F R✝ S\nR : Type u\ninst✝ : NonUnitalRing R\ns : Set R\nhcomm : ∀ a ∈ s, ∀ b ∈ s, a * b = b * a\nx✝² x✝¹ : ↥(closure s)\nx✝... | | zero_left x _ => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.RingTheory.NonUnitalSubring.Basic | {
"line": 739,
"column": 39
} | {
"line": 739,
"column": 65
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : NonUnitalNonAssocRing R\ninst✝ : NonUnitalNonAssocRing S\nf : R →ₙ+* S\n⊢ ↑f.range = ↑⊤ ↔ Set.range ⇑f = Set.univ",
"usedConstants": [
"NonUnitalSubring.coe_top",
"NonUnitalSubring.instSetLike",
"Eq.mpr",
"NonUnitalSubring.instTop",
"co... | by rw [coe_range, coe_top] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Prime.Lemmas | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 57
} | [
{
"pp": "M : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\np a : M\nn : ℕ\nhp : Prime p\nx : M\nhb : ¬p ^ 2 ∣ p * x\nhbdiv : p ∣ (p * x) ^ n\ny : M\nhy : a ^ n.succ * (p * x) ^ n = p ^ n.succ * y\n⊢ a ^ n.succ * x ^ n = p * y",
"usedConstants": [
"HMul.hMul",
"MulZeroClass.... | refine mul_left_cancel₀ (pow_ne_zero n hp.ne_zero) ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Algebra.Prime.Lemmas | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 27
} | [
{
"pp": "case inr\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\np a : M\nn : ℕ\nhp : Prime p\ny z : M\nhb : ¬p ^ 2 ∣ p * (p * z)\nhbdiv : p ∣ (p * (p * z)) ^ n\nhy : a ^ n.succ * (p * (p * z)) ^ n = p ^ n.succ * y\nthis : a ^ n.succ * (p * z) ^ n = p * y\nhdvdx : p ∣ (p * z) ^ n\n⊢ p ... | rw [pow_two, ← mul_assoc] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Ring.Subring.Basic | {
"line": 817,
"column": 39
} | {
"line": 817,
"column": 65
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝¹ : NonAssocRing R\ninst✝ : NonAssocRing S\nf : R →+* S\n⊢ ↑f.range = ↑⊤ ↔ Set.range ⇑f = Set.univ",
"usedConstants": [
"Eq.mpr",
"Subring.instSetLike",
"congrArg",
"Set.univ",
"Iff.rfl",
"RingHom",
"id",
"Subring.coe_top"... | by rw [coe_range, coe_top] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.GroupWithZero.Associated | {
"line": 761,
"column": 6
} | {
"line": 761,
"column": 37
} | [
{
"pp": "case succ.inr\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\np : M\nhp : Prime p\nn : ℕ\nih : ∀ {q : M}, q ∣ p ^ n ↔ ∃ i, i ≤ n ∧ q ~ᵤ p ^ i\nq : M\nh : q ∣ p * p ^ n\nhno : q ∣ p ^ n\n⊢ ∃ i, i ≤ n + 1 ∧ q ~ᵤ p ^ i",
"usedConstants": [
"Dvd.dvd",
"semigroupDvd"... | obtain ⟨i, hi, hq⟩ := ih.mp hno | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.