module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.GroupWithZero.Action.Defs | {
"line": 424,
"column": 15
} | {
"line": 424,
"column": 53
} | {
"line": 424,
"column": 53
} | [
{
"pp": "α : Type u_10\nβ : Type u_11\ninst✝² : Group α\ninst✝¹ : AddMonoid β\ninst✝ : DistribMulAction α β\na : α\nx : β\nh : a • x = 0\n⊢ x = 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"congrArg",
"DistribM... | [] | rw [← inv_smul_smul a x, h, smul_zero] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.GroupWithZero.Action.Defs | {
"line": 424,
"column": 15
} | {
"line": 424,
"column": 53
} | {
"line": 424,
"column": 53
} | [
{
"pp": "α : Type u_10\nβ : Type u_11\ninst✝² : Group α\ninst✝¹ : AddMonoid β\ninst✝ : DistribMulAction α β\na : α\nx : β\nh : a • x = 0\n⊢ x = 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"congrArg",
"DistribM... | [] | rw [← inv_smul_smul a x, h, smul_zero] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.Cast.Basic | {
"line": 127,
"column": 73
} | {
"line": 127,
"column": 92
} | {
"line": 129,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : AddGroupWithOne R\nn : ℤ\n⊢ n • 1 = ↑n",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Int.cast",
"NegZeroClass.toNeg",
"Int.cast_natCast",
"instHSMul",
"AddMonoid.toAddS... | [] | by cases n <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.Even | {
"line": 176,
"column": 70
} | {
"line": 176,
"column": 75
} | {
"line": 178,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nG : Type u_4\ninst✝ : CommGroup G\na b c d e : G\nha : IsSquare a\nn : ℕ\nk : ℤ\nhk : Even k\n⊢ IsSquare (a * (b * b) / c ^ 2 * d ^ k * e ^ (n + n))",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Even | {
"line": 176,
"column": 70
} | {
"line": 176,
"column": 75
} | {
"line": 178,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nG : Type u_4\ninst✝ : CommGroup G\na b c d e : G\nha : IsSquare a\nn : ℕ\nk : ℤ\nhk : Even k\n⊢ IsSquare (a * (b * b) / c ^ 2 * d ^ k * e ^ (n + n))",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Even | {
"line": 176,
"column": 70
} | {
"line": 176,
"column": 75
} | {
"line": 178,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nG : Type u_4\ninst✝ : CommGroup G\na b c d e : G\nha : IsSquare a\nn : ℕ\nk : ℤ\nhk : Even k\n⊢ IsSquare (a * (b * b) / c ^ 2 * d ^ k * e ^ (n + n))",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Even | {
"line": 179,
"column": 60
} | {
"line": 179,
"column": 65
} | {
"line": 180,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nG : Type u_4\ninst✝ : AddCommGroup G\na b c d e : G\nha : Even a\nn : ℕ\nk : ℤ\nhk : Even k\n⊢ Even (a + (b + b) - 2 • c + k • d + (n + n) • e)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"instHSMul",
"AddCommGroup.toAddCom... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Even | {
"line": 179,
"column": 60
} | {
"line": 179,
"column": 65
} | {
"line": 180,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nG : Type u_4\ninst✝ : AddCommGroup G\na b c d e : G\nha : Even a\nn : ℕ\nk : ℤ\nhk : Even k\n⊢ Even (a + (b + b) - 2 • c + k • d + (n + n) • e)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"instHSMul",
"AddCommGroup.toAddCom... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Even | {
"line": 179,
"column": 60
} | {
"line": 179,
"column": 65
} | {
"line": 180,
"column": 0
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nG : Type u_4\ninst✝ : AddCommGroup G\na b c d e : G\nha : Even a\nn : ℕ\nk : ℤ\nhk : Even k\n⊢ Even (a + (b + b) - 2 • c + k • d + (n + n) • e)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"instHSMul",
"AddCommGroup.toAddCom... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.TFAE | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 39
} | {
"line": 89,
"column": 2
} | [
{
"pp": "α : Type u_1\nl : List (α → Prop)\nH : ∀ (a : α), (map (fun p ↦ p a) l).TFAE\n⊢ (map (fun p ↦ ∀ (a : α), p a) l).TFAE",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.map",
"Membership.mem",
"List.TFAE",
"id",
"_private.Mathlib.Da... | [
"α : Type u_1\nl : List (α → Prop)\nH : ∀ (a : α), (map (fun p ↦ p a) l).TFAE\n⊢ ∀ (j : α → Prop), j ∈ l → ∀ (j_1 : α → Prop), j_1 ∈ l → ((∀ (a : α), j a) ↔ ∀ (a : α), j_1 a)"
] | simp only [TFAE, List.forall_mem_map] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.TFAE | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 39
} | {
"line": 108,
"column": 2
} | [
{
"pp": "α : Type u_1\nl : List (α → Prop)\nH : ∀ (a : α), (map (fun p ↦ p a) l).TFAE\n⊢ (map (fun p ↦ ∃ a, p a) l).TFAE",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.map",
"Membership.mem",
"Exists",
"List.TFAE",
"id",
"List",
... | [
"α : Type u_1\nl : List (α → Prop)\nH : ∀ (a : α), (map (fun p ↦ p a) l).TFAE\n⊢ ∀ (j : α → Prop), j ∈ l → ∀ (j_1 : α → Prop), j_1 ∈ l → ((∃ a, j a) ↔ ∃ a, j_1 a)"
] | simp only [TFAE, List.forall_mem_map] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.Basic | {
"line": 166,
"column": 55
} | {
"line": 166,
"column": 81
} | {
"line": 166,
"column": 81
} | [
{
"pp": "α : Type u_3\ninst✝¹ : NonAssocRing α\ninst✝ : Nontrivial α\na : α\nh : a - 1 = a\n⊢ a + -1 = a + -0",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup"... | [] | simp [← sub_eq_add_neg, h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.Basic | {
"line": 166,
"column": 55
} | {
"line": 166,
"column": 81
} | {
"line": 166,
"column": 81
} | [
{
"pp": "α : Type u_3\ninst✝¹ : NonAssocRing α\ninst✝ : Nontrivial α\na : α\nh : a - 1 = a\n⊢ a + -1 = a + -0",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup"... | [] | simp [← sub_eq_add_neg, h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Basic | {
"line": 166,
"column": 55
} | {
"line": 166,
"column": 81
} | {
"line": 166,
"column": 81
} | [
{
"pp": "α : Type u_3\ninst✝¹ : NonAssocRing α\ninst✝ : Nontrivial α\na : α\nh : a - 1 = a\n⊢ a + -1 = a + -0",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup"... | [] | simp [← sub_eq_add_neg, h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Ring.Basic | {
"line": 195,
"column": 4
} | {
"line": 195,
"column": 32
} | {
"line": 195,
"column": 32
} | [
{
"pp": "R : Type u_3\ninst✝ : NonUnitalNonAssocRing R\n⊢ [NoZeroDivisors R, ∀ {a : R}, a ≠ 0 → ∀ (x : R), a * x = 0 → x = 0, ∀ {a : R}, a ≠ 0 → ∀ (x : R), x * a = 0 → x = 0,\n ∀ {a : R}, a ≠ 0 → IsRegular a].TFAE",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"R : Type u_3\ninst✝ : NonUnitalNonAssocRing R\n⊢ [NoZeroDivisors R, ∀ {a : R}, a ≠ 0 → ∀ (x : R), a * x = 0 → x = 0, ∀ {a : R}, a ≠ 0 → ∀ (x : R), x * a = 0 → x = 0,\n ∀ {a : R}, a ≠ 0 → (∀ (x : R), a * x = 0 → x = 0) ∧ ∀ (x : R), x * a = 0 → x = 0].TFAE"
] | isRegular_iff_eq_zero_of_mul | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Ring.Basic | {
"line": 279,
"column": 59
} | {
"line": 279,
"column": 78
} | {
"line": 279,
"column": 79
} | [
{
"pp": "R : Type u_1\ninst✝¹ : DivisionMonoid R\ninst✝ : HasDistribNeg R\na b : R\n⊢ -a / -b = a / b",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"id",
"MulOne.toMul",
"HDiv.hDiv",
... | [
"R : Type u_1\ninst✝¹ : DivisionMonoid R\ninst✝ : HasDistribNeg R\na b : R\n⊢ -(-a / b) = a / b"
] | div_neg_eq_neg_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.GroupWithZero.Units.Basic | {
"line": 401,
"column": 40
} | {
"line": 401,
"column": 49
} | {
"line": 401,
"column": 50
} | [
{
"pp": "G₀ : Type u_3\ninst✝ : GroupWithZero G₀\na : G₀\nha : a ≠ 0\nm n : ℤ\n⊢ a ^ m * a ^ (-n) = a ^ m / a ^ n",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"HMul.hM... | [
"G₀ : Type u_3\ninst✝ : GroupWithZero G₀\na : G₀\nha : a ≠ 0\nm n : ℤ\n⊢ a ^ m * (a ^ n)⁻¹ = a ^ m / a ^ n"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.NatInt | {
"line": 100,
"column": 22
} | {
"line": 100,
"column": 90
} | {
"line": 101,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nM : Type u_3\nM₂ : Type u_4\ninst✝² : Ring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\na : M\n⊢ 0 • a = 0",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"instHSMul",
... | [] | simp_rw [HSMul.hSMul, SMul.smul, Int.cast_zero]; exact zero_smul R a | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.NatInt | {
"line": 100,
"column": 22
} | {
"line": 100,
"column": 90
} | {
"line": 101,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nM : Type u_3\nM₂ : Type u_4\ninst✝² : Ring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\na : M\n⊢ 0 • a = 0",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"instHSMul",
... | [] | simp_rw [HSMul.hSMul, SMul.smul, Int.cast_zero]; exact zero_smul R a | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Sub.Defs | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 29
} | {
"line": 130,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c : α\ninst✝ : AddLeftMono α\n⊢ a + b - c ≤ a - c + b",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"Preorder.toL... | [
"α : Type u_1\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c : α\ninst✝ : AddLeftMono α\n⊢ b + a - c ≤ b + (a - c)"
] | rw [add_comm, add_comm _ b] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Sub.Defs | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 27
} | {
"line": 180,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝³ : Preorder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\nhb : AddLECancellable b\n⊢ a ≤ b + a - b",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"AddLECancellable.le_add_tsub_swap"
],
"usedFVars": [
"α",
... | [] | exact hb.le_add_tsub_swap | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Sub.Defs | {
"line": 177,
"column": 2
} | {
"line": 178,
"column": 27
} | {
"line": 180,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝³ : Preorder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\nhb : AddLECancellable b\n⊢ a ≤ a + b - b",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddLECancellable.le_add_tsub_swap",
"congrArg",
... | [] | rw [add_comm]
exact hb.le_add_tsub_swap | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Sub.Defs | {
"line": 177,
"column": 2
} | {
"line": 178,
"column": 27
} | {
"line": 180,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝³ : Preorder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\nhb : AddLECancellable b\n⊢ a ≤ a + b - b",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddLECancellable.le_add_tsub_swap",
"congrArg",
... | [] | rw [add_comm]
exact hb.le_add_tsub_swap | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 147,
"column": 44
} | {
"line": 147,
"column": 69
} | {
"line": 149,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : MulRightMono α\na b c : α\n⊢ a * b⁻¹ * b ≤ c * b ↔ a ≤ c * b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toM... | [] | rw [inv_mul_cancel_right] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 147,
"column": 44
} | {
"line": 147,
"column": 69
} | {
"line": 149,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : MulRightMono α\na b c : α\n⊢ a * b⁻¹ * b ≤ c * b ↔ a ≤ c * b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toM... | [] | rw [inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 147,
"column": 44
} | {
"line": 147,
"column": 69
} | {
"line": 149,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : MulRightMono α\na b c : α\n⊢ a * b⁻¹ * b ≤ c * b ↔ a ≤ c * b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toM... | [] | rw [inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 151,
"column": 44
} | {
"line": 151,
"column": 69
} | {
"line": 153,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : MulRightMono α\na b c : α\n⊢ c * b ≤ a * b⁻¹ * b ↔ c * b ≤ a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toM... | [] | rw [inv_mul_cancel_right] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 151,
"column": 44
} | {
"line": 151,
"column": 69
} | {
"line": 153,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : MulRightMono α\na b c : α\n⊢ c * b ≤ a * b⁻¹ * b ↔ c * b ≤ a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toM... | [] | rw [inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 151,
"column": 44
} | {
"line": 151,
"column": 69
} | {
"line": 153,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : MulRightMono α\na b c : α\n⊢ c * b ≤ a * b⁻¹ * b ↔ c * b ≤ a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toM... | [] | rw [inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 195,
"column": 44
} | {
"line": 195,
"column": 69
} | {
"line": 197,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : MulRightStrictMono α\na b c : α\n⊢ c * b < a * b⁻¹ * b ↔ c * b < a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Mono... | [] | rw [inv_mul_cancel_right] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 195,
"column": 44
} | {
"line": 195,
"column": 69
} | {
"line": 197,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : MulRightStrictMono α\na b c : α\n⊢ c * b < a * b⁻¹ * b ↔ c * b < a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Mono... | [] | rw [inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 195,
"column": 44
} | {
"line": 195,
"column": 69
} | {
"line": 197,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : MulRightStrictMono α\na b c : α\n⊢ c * b < a * b⁻¹ * b ↔ c * b < a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Mono... | [] | rw [inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 274,
"column": 2
} | {
"line": 275,
"column": 25
} | {
"line": 277,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝³ : Group α\ninst✝² : LT α\ninst✝¹ : MulLeftStrictMono α\na b c d : α\ninst✝ : MulRightStrictMono α\n⊢ a * b⁻¹ < d⁻¹ * c ↔ d * a < c * b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMu... | [] | rw [← mul_lt_mul_iff_left d, ← mul_lt_mul_iff_right b, mul_inv_cancel_left, mul_assoc,
inv_mul_cancel_right] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 274,
"column": 2
} | {
"line": 275,
"column": 25
} | {
"line": 277,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝³ : Group α\ninst✝² : LT α\ninst✝¹ : MulLeftStrictMono α\na b c d : α\ninst✝ : MulRightStrictMono α\n⊢ a * b⁻¹ < d⁻¹ * c ↔ d * a < c * b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMu... | [] | rw [← mul_lt_mul_iff_left d, ← mul_lt_mul_iff_right b, mul_inv_cancel_left, mul_assoc,
inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.Unbundled.Basic | {
"line": 274,
"column": 2
} | {
"line": 275,
"column": 25
} | {
"line": 277,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝³ : Group α\ninst✝² : LT α\ninst✝¹ : MulLeftStrictMono α\na b c d : α\ninst✝ : MulRightStrictMono α\n⊢ a * b⁻¹ < d⁻¹ * c ↔ d * a < c * b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMu... | [] | rw [← mul_lt_mul_iff_left d, ← mul_lt_mul_iff_right b, mul_inv_cancel_left, mul_assoc,
inv_mul_cancel_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Defs | {
"line": 67,
"column": 22
} | {
"line": 67,
"column": 34
} | {
"line": 67,
"column": 34
} | [
{
"pp": "α✝ : Type u_1\nα : Type u_2\ninst✝¹ : CommMonoid α\ninst✝ : Preorder α\nmul_le_mul_left : ∀ (a b : α), a ≤ b → ∀ (c : α), a * c ≤ b * c\nmul_le_mul_right : ∀ (a b : α), a ≤ b → ∀ (c : α), c * a ≤ c * b\ntoIsOrderedMonoid : IsOrderedMonoid α := { mul_le_mul_left := mul_le_mul_left }\nle_of_mul_le_mul_le... | [
"α✝ : Type u_1\nα : Type u_2\ninst✝¹ : CommMonoid α\ninst✝ : Preorder α\nmul_le_mul_left : ∀ (a b : α), a ≤ b → ∀ (c : α), a * c ≤ b * c\nmul_le_mul_right : ∀ (a b : α), a ≤ b → ∀ (c : α), c * a ≤ c * b\ntoIsOrderedMonoid : IsOrderedMonoid α := { mul_le_mul_left := mul_le_mul_left }\nle_of_mul_le_mul_left : ∀ (a b ... | mul_comm _ a | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Monoid.Defs | {
"line": 124,
"column": 54
} | {
"line": 124,
"column": 92
} | {
"line": 126,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : CommMonoid α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedMonoid α\na : α\n⊢ a * a ≤ 1 ↔ a ≤ 1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Preorder.toLT",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
... | [] | contrapose!; exact one_lt_mul_self_iff | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Defs | {
"line": 124,
"column": 54
} | {
"line": 124,
"column": 92
} | {
"line": 126,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : CommMonoid α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedMonoid α\na : α\n⊢ a * a ≤ 1 ↔ a ≤ 1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Preorder.toLT",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
... | [] | contrapose!; exact one_lt_mul_self_iff | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Defs | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 70
} | {
"line": 113,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : Ring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedAddMonoid R\ninst✝¹ : ZeroLEOneClass R\ninst✝ : Nontrivial R\nmul_pos : ∀ (a b : R), 0 < a → 0 < b → 0 < a * b\na : R\nha : 0 < a\nb c : R\nhbc : b < c\n⊢ b * a < c * a",
"ppTerm": "?m.39",
"assigned": true,
"usedConsta... | [] | simpa only [sub_mul, sub_pos] using mul_pos _ _ (sub_pos.2 hbc) ha | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Order.Ring.Defs | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 70
} | {
"line": 113,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : Ring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedAddMonoid R\ninst✝¹ : ZeroLEOneClass R\ninst✝ : Nontrivial R\nmul_pos : ∀ (a b : R), 0 < a → 0 < b → 0 < a * b\na : R\nha : 0 < a\nb c : R\nhbc : b < c\n⊢ b * a < c * a",
"ppTerm": "?m.39",
"assigned": true,
"usedConsta... | [] | simpa only [sub_mul, sub_pos] using mul_pos _ _ (sub_pos.2 hbc) ha | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Defs | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 70
} | {
"line": 113,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁴ : Ring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedAddMonoid R\ninst✝¹ : ZeroLEOneClass R\ninst✝ : Nontrivial R\nmul_pos : ∀ (a b : R), 0 < a → 0 < b → 0 < a * b\na : R\nha : 0 < a\nb c : R\nhbc : b < c\n⊢ b * a < c * a",
"ppTerm": "?m.39",
"assigned": true,
"usedConsta... | [] | simpa only [sub_mul, sub_pos] using mul_pos _ _ (sub_pos.2 hbc) ha | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 509,
"column": 2
} | {
"line": 509,
"column": 7
} | {
"line": 511,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : ExistsAddOfLE R\ninst✝³ : MulPosStrictMono R\ninst✝² : PosMulStrictMono R\ninst✝¹ : AddLeftMono R\ninst✝ : AddLeftReflectLE R\na b c : R\nor_a : 0 ≤ a ∨ a ≤ 0\nor_b : 0 ≤ b ∨ b ≤ 0\nor_c : 0 ≤ c ∨ c ≤ 0\n⊢ (0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0)... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Order.Ring.Unbundled.Basic | {
"line": 574,
"column": 4
} | {
"line": 574,
"column": 51
} | {
"line": 576,
"column": 0
} | [
{
"pp": "case mpr.inl\nR : Type u\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : ExistsAddOfLE R\ninst✝³ : PosMulStrictMono R\ninst✝² : MulPosStrictMono R\ninst✝¹ : AddLeftStrictMono R\ninst✝ : AddLeftReflectLT R\na : R\nh✝ : a ≠ 0\nh : a < 0\n⊢ 0 < a * a",
"ppTerm": "?mpr.inl",
"assigned": true... | [] | exacts [mul_pos_of_neg_of_neg h h, mul_pos h h] | Batteries.Tactic._aux_Batteries_Tactic_Init___elabRules_Batteries_Tactic_exacts_1 | Batteries.Tactic.exacts |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 433,
"column": 16
} | {
"line": 434,
"column": 90
} | {
"line": 436,
"column": 0
} | [
{
"pp": "M₀ : Type u_2\ninst✝² : MonoidWithZero M₀\ninst✝¹ : Preorder M₀\na : M₀\ninst✝ : PosMulMono M₀\nh₀ : 0 ≤ a\nh₁ : a < 1\nn : ℕ\nx✝ : n + 1 ≠ 0\n⊢ a ^ (n + 1) < 1",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Preorder.toLT",
"HMul... | [] | by
rw [pow_succ']; exact mul_lt_one_of_nonneg_of_lt_one_left h₀ h₁ (pow_le_one₀ h₀ h₁.le) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 967,
"column": 27
} | {
"line": 967,
"column": 36
} | {
"line": 967,
"column": 37
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nha : 0 ≤ a\nn : ℕ\n⊢ 0 ≤ a ^ (-↑(n + 1))",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nha : 0 ≤ a\nn : ℕ\n⊢ 0 ≤ (a ^ ↑(n + 1))⁻¹"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.GroupWithZero.Basic | {
"line": 971,
"column": 27
} | {
"line": 971,
"column": 36
} | {
"line": 971,
"column": 37
} | [
{
"pp": "G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nha : 0 < a\nn : ℕ\n⊢ 0 < a ^ (-↑(n + 1))",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
... | [
"G₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : PartialOrder G₀\ninst✝¹ : PosMulReflectLT G₀\na : G₀\ninst✝ : ZeroLEOneClass G₀\nha : 0 < a\nn : ℕ\n⊢ 0 < (a ^ ↑(n + 1))⁻¹"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Hom.Basic | {
"line": 489,
"column": 23
} | {
"line": 489,
"column": 28
} | {
"line": 489,
"column": 29
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝⁴ : Preorder α\ninst✝³ : Preorder β\ninst✝² : Preorder γ\ninst✝¹ : Preorder δ\nι : Type u_6\nπ : ι → Type u_7\ninst✝ : (i : ι) → Preorder (π i)\np q : α → Prop\nh : ∀ (a : α), p a → q a\n⊢ ∀ {a b : { x // p x }}, (Subtype.impEmb... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Hom.Basic | {
"line": 489,
"column": 23
} | {
"line": 489,
"column": 28
} | {
"line": 489,
"column": 29
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝⁴ : Preorder α\ninst✝³ : Preorder β\ninst✝² : Preorder γ\ninst✝¹ : Preorder δ\nι : Type u_6\nπ : ι → Type u_7\ninst✝ : (i : ι) → Preorder (π i)\np q : α → Prop\nh : ∀ (a : α), p a → q a\n⊢ ∀ {a b : { x // p x }}, (Subtype.impEmb... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Hom.Basic | {
"line": 489,
"column": 23
} | {
"line": 489,
"column": 28
} | {
"line": 489,
"column": 29
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type u_5\ninst✝⁴ : Preorder α\ninst✝³ : Preorder β\ninst✝² : Preorder γ\ninst✝¹ : Preorder δ\nι : Type u_6\nπ : ι → Type u_7\ninst✝ : (i : ι) → Preorder (π i)\np q : α → Prop\nh : ∀ (a : α), p a → q a\n⊢ ∀ {a b : { x // p x }}, (Subtype.impEmb... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Abs | {
"line": 87,
"column": 38
} | {
"line": 87,
"column": 57
} | {
"line": 87,
"column": 58
} | [
{
"pp": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b c : G\n⊢ b ≤ a * c ∧ a / b ≤ c ↔ a / b ≤ c ∧ b / a ≤ c",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
... | [
"G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : LinearOrder G\ninst✝ : IsOrderedMonoid G\na b c : G\n⊢ b ≤ a * c ∧ a ≤ b * c ↔ a ≤ b * c ∧ b / a ≤ c"
] | div_le_iff_le_mul', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 21
} | {
"line": 147,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\na b : α\n⊢ 1 ≤ |b / a|ₘ",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"instHDiv",
"CommMonoid.toCommSemigroup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeIn... | [] | exact one_le_mabs _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 174,
"column": 22
} | {
"line": 174,
"column": 34
} | {
"line": 174,
"column": 35
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\na b c : α\nthis : DistribLattice α := CommGroup.toDistribLattice α\n⊢ ((b ⊔ a) ⊓ c) * (b ⊔ a ⊔ c) / ((b ⊓ a ⊔ c) * (b ⊓ a ⊓ c)) = (b ⊔ a) * c / ((b ⊓ a) * c)",
"ppTerm": "?m.338",
"assigned": true,
"usedConstants... | [
"α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\na b c : α\nthis : DistribLattice α := CommGroup.toDistribLattice α\n⊢ (b ⊔ a) * c / ((b ⊓ a ⊔ c) * (b ⊓ a ⊓ c)) = (b ⊔ a) * c / ((b ⊓ a) * c)"
] | inf_mul_sup, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.Unbundled.Abs | {
"line": 265,
"column": 47
} | {
"line": 265,
"column": 54
} | {
"line": 265,
"column": 54
} | [
{
"pp": "α : Type u_1\ninst✝³ : Group α\ninst✝² : LinearOrder α\ninst✝¹ : MulLeftMono α\na b : α\ninst✝ : MulRightMono α\n⊢ a⁻¹ < b ∧ a < b ↔ b⁻¹ < a ∧ a < b",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"instIsRightCancelMulOfMulRightReflectLE",
"inv_lt'",
"Eq.mpr",
... | [
"α : Type u_1\ninst✝³ : Group α\ninst✝² : LinearOrder α\ninst✝¹ : MulLeftMono α\na b : α\ninst✝ : MulRightMono α\n⊢ b⁻¹ < a ∧ a < b ↔ b⁻¹ < a ∧ a < b"
] | inv_lt' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Int.GCD | {
"line": 125,
"column": 41
} | {
"line": 125,
"column": 49
} | {
"line": 125,
"column": 49
} | [
{
"pp": "x y : ℕ\n⊢ x.P y (x, 1, 0)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"Int",
"Int.instAddMonoid",
"Nat.cast",
"Int.instMonoid",
"Int.instMul",
... | [] | simp [P] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Int.GCD | {
"line": 125,
"column": 41
} | {
"line": 125,
"column": 49
} | {
"line": 125,
"column": 49
} | [
{
"pp": "x y : ℕ\n⊢ x.P y (x, 1, 0)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"Int",
"Int.instAddMonoid",
"Nat.cast",
"Int.instMonoid",
"Int.instMul",
... | [] | simp [P] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Int.GCD | {
"line": 125,
"column": 41
} | {
"line": 125,
"column": 49
} | {
"line": 125,
"column": 49
} | [
{
"pp": "x y : ℕ\n⊢ x.P y (x, 1, 0)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"Int",
"Int.instAddMonoid",
"Nat.cast",
"Int.instMonoid",
"Int.instMul",
... | [] | simp [P] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.GCD | {
"line": 125,
"column": 55
} | {
"line": 125,
"column": 63
} | {
"line": 125,
"column": 63
} | [
{
"pp": "x y : ℕ\n⊢ x.P y (y, 0, 1)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"Int",
"Int.instAddMonoid",
"zero_add",
"Nat.cast",
"Int.instMonoid",
... | [] | simp [P] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Int.GCD | {
"line": 125,
"column": 55
} | {
"line": 125,
"column": 63
} | {
"line": 125,
"column": 63
} | [
{
"pp": "x y : ℕ\n⊢ x.P y (y, 0, 1)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"Int",
"Int.instAddMonoid",
"zero_add",
"Nat.cast",
"Int.instMonoid",
... | [] | simp [P] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Int.GCD | {
"line": 125,
"column": 55
} | {
"line": 125,
"column": 63
} | {
"line": 125,
"column": 63
} | [
{
"pp": "x y : ℕ\n⊢ x.P y (y, 0, 1)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"Int",
"Int.instAddMonoid",
"zero_add",
"Nat.cast",
"Int.instMonoid",
... | [] | simp [P] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.GCD | {
"line": 309,
"column": 32
} | {
"line": 309,
"column": 37
} | {
"line": 309,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : GroupWithZero α\na b : α\nm n : ℕ\nhab : Commute a b\nhmn : m.Coprime n\nh : a ^ m = b ^ n\nh✝¹ : ¬m = 0\nh✝ : ¬n = 0\nhb : ¬b = 0\nha : ¬a = 0\n⊢ Commute a b",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hab"
],
"usedGo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Int.GCD | {
"line": 309,
"column": 32
} | {
"line": 309,
"column": 37
} | {
"line": 309,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : GroupWithZero α\na b : α\nm n : ℕ\nhab : Commute a b\nhmn : m.Coprime n\nh : a ^ m = b ^ n\nh✝¹ : ¬m = 0\nh✝ : ¬n = 0\nhb : ¬b = 0\nha : ¬a = 0\n⊢ Commute a b",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hab"
],
"usedGo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Int.GCD | {
"line": 309,
"column": 32
} | {
"line": 309,
"column": 37
} | {
"line": 309,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : GroupWithZero α\na b : α\nm n : ℕ\nhab : Commute a b\nhmn : m.Coprime n\nh : a ^ m = b ^ n\nh✝¹ : ¬m = 0\nh✝ : ¬n = 0\nhb : ¬b = 0\nha : ¬a = 0\n⊢ Commute a b",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hab"
],
"usedGo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.GCD | {
"line": 309,
"column": 32
} | {
"line": 309,
"column": 37
} | {
"line": 309,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : GroupWithZero α\na b : α\nm n : ℕ\nhab : Commute a b\nhmn : m.Coprime n\nh : a ^ m = b ^ n\nh✝¹ : ¬m = 0\nh✝ : ¬n = 0\nhb : ¬b = 0\nha : ¬a = 0\n⊢ Commute b b",
"ppTerm": "?m.233",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"Mono... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Int.GCD | {
"line": 309,
"column": 32
} | {
"line": 309,
"column": 37
} | {
"line": 309,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : GroupWithZero α\na b : α\nm n : ℕ\nhab : Commute a b\nhmn : m.Coprime n\nh : a ^ m = b ^ n\nh✝¹ : ¬m = 0\nh✝ : ¬n = 0\nhb : ¬b = 0\nha : ¬a = 0\n⊢ Commute b b",
"ppTerm": "?m.233",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"Mono... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Int.GCD | {
"line": 309,
"column": 32
} | {
"line": 309,
"column": 37
} | {
"line": 309,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : GroupWithZero α\na b : α\nm n : ℕ\nhab : Commute a b\nhmn : m.Coprime n\nh : a ^ m = b ^ n\nh✝¹ : ¬m = 0\nh✝ : ¬n = 0\nhb : ¬b = 0\nha : ¬a = 0\n⊢ Commute b b",
"ppTerm": "?m.233",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"Mono... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.GCD | {
"line": 321,
"column": 45
} | {
"line": 321,
"column": 50
} | {
"line": 323,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : CommGroupWithZero α\nm n : ℕ\nhmn : m.Coprime n\na : α\n⊢ (∃ c, a = c ^ n) ↔ ∃ y, y ^ n = a",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"Exists",
"exists_apply_eq_apply._simp_1",
"NPow.toPow",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.WithOne.Defs | {
"line": 217,
"column": 87
} | {
"line": 218,
"column": 22
} | {
"line": 220,
"column": 0
} | [
{
"pp": "α : Type u\nd : α\nx : WithOne α\n⊢ unoneD d x = d ↔ x = ↑d ∨ x = 1",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"WithOne",
"and_true",
"_private.Mathlib.Algebra.Group.WithOne.Defs.0.WithOne.unoneD_eq_self_iff._simp_1_1",
"congrArg",
"WithOne.coe",
... | [] | by
simp [unoneD_eq_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.WithOne.Defs | {
"line": 226,
"column": 86
} | {
"line": 227,
"column": 22
} | {
"line": 229,
"column": 0
} | [
{
"pp": "α : Type u\nd : α\nx : WithOne α\nhx : x ≠ 1\n⊢ unoneD d x = unone hx",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"WithOne.unone",
"WithOne",
"congrArg",
"true_or",
"WithOne.coe_unone",
"WithOne.coe",
"And",
"True",
"WithOne... | [] | by
simp [unoneD_eq_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.GroupWithZero.WithZero | {
"line": 349,
"column": 20
} | {
"line": 349,
"column": 39
} | {
"line": 351,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : AddMonoidWithOne α\nn : ℕ\n⊢ (if n + 1 = 0 then 0 else ↑↑(n + 1)) = (if n = 0 then 0 else ↑↑n) + 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"False",
"WithZero.instAdd",
"AddMonoid.toAddSemigroup",
"co... | [] | by cases n <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 35,
"column": 51
} | {
"line": 36,
"column": 55
} | {
"line": 38,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : AddCommMonoid α\ninst✝³ : PartialOrder α\ninst✝² : CanonicallyOrderedAdd α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b : α\n⊢ a - b = 0 ↔ a ≤ b",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"instIsBotZeroClass",
... | [] | by
rw [← nonpos_iff_eq_zero, tsub_le_iff_left, add_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Find | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 30
} | {
"line": 159,
"column": 4
} | [
{
"pp": "case refine_2\nn : ℕ\np : ℕ → Prop\ninst✝ : DecidablePred p\nhₘ : ∃ m, p (m + n)\nhₙ : ∃ n, p n\nhn : n ≤ Nat.find hₙ\nm : ℕ\nhm : m < Nat.find hₙ - n\nhpm : p (m + n)\n⊢ Nat.find hₙ - n ≤ m",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"case refine_2\nn : ℕ\np : ℕ → Prop\ninst✝ : DecidablePred p\nhₘ : ∃ m, p (m + n)\nhₙ : ∃ n, p n\nhn : n ≤ Nat.find hₙ\nm : ℕ\nhm : m < Nat.find hₙ - n\nhpm : p (m + n)\n⊢ Nat.find hₙ ≤ m + n"
] | rw [Nat.sub_le_iff_le_add] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.WithBot | {
"line": 717,
"column": 22
} | {
"line": 719,
"column": 49
} | {
"line": 721,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : DistribLattice α\nx y z : WithTop α\n⊢ (x ⊔ y) ⊓ (x ⊔ z) ≤ x ⊔ y ⊓ z",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"WithTop.coe_le_coe._simp_1",
... | [] | by
cases x <;> cases y <;> cases z <;> simp [← WithTop.coe_inf, ← WithTop.coe_sup]
simpa [← coe_inf, ← coe_sup] using le_sup_inf | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 361,
"column": 58
} | {
"line": 363,
"column": 26
} | {
"line": 365,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorSemiring R\ninst✝ : IsStrictOrderedRing R\na b : R\n⊢ ⌈a + b⌉₊ ≤ ⌈a⌉₊ + ⌈b⌉₊",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.t... | [] | by
rw [ceil_le, Nat.cast_add]
gcongr <;> apply le_ceil | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.WithBot | {
"line": 964,
"column": 51
} | {
"line": 964,
"column": 94
} | {
"line": 966,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LE α\nx : WithTop αᵒᵈ\ny : WithBot α\n⊢ x ≤ WithBot.toDual y ↔ y ≤ WithTop.ofDual x",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"OrderDual.instLE",
"OrderDual.toDual",
"False",
"WithBot.some",
"WithBot",
"Equiv.instEquiv... | [] | by cases x <;> cases y <;> simp [le_toDual] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.WithBot | {
"line": 976,
"column": 43
} | {
"line": 976,
"column": 86
} | {
"line": 978,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LE α\nx : WithTop α\ny : WithBot αᵒᵈ\n⊢ x ≤ WithBot.ofDual y ↔ y ≤ WithTop.toDual x",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"OrderDual.instLE",
"OrderDual.toDual",
"False",
"WithBot.some",
"WithBot",
"_private.Mathli... | [] | by cases x <;> cases y <;> simp [le_toDual] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Ring.Invertible | {
"line": 30,
"column": 16
} | {
"line": 30,
"column": 32
} | {
"line": 31,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx : AddUnits R\ny : R\n⊢ y * ↑x + y * x.neg = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.Invertible | {
"line": 30,
"column": 16
} | {
"line": 30,
"column": 32
} | {
"line": 31,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx : AddUnits R\ny : R\n⊢ y * ↑x + y * x.neg = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Invertible | {
"line": 30,
"column": 16
} | {
"line": 30,
"column": 32
} | {
"line": 31,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx : AddUnits R\ny : R\n⊢ y * ↑x + y * x.neg = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Ring.Invertible | {
"line": 31,
"column": 16
} | {
"line": 31,
"column": 32
} | {
"line": 33,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx : AddUnits R\ny : R\n⊢ y * x.neg + y * ↑x = 0",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.Invertible | {
"line": 31,
"column": 16
} | {
"line": 31,
"column": 32
} | {
"line": 33,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx : AddUnits R\ny : R\n⊢ y * x.neg + y * ↑x = 0",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Invertible | {
"line": 31,
"column": 16
} | {
"line": 31,
"column": 32
} | {
"line": 33,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx : AddUnits R\ny : R\n⊢ y * x.neg + y * ↑x = 0",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Ring.Invertible | {
"line": 48,
"column": 2
} | {
"line": 48,
"column": 18
} | {
"line": 50,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : NonUnitalNonAssocSemiring R\nx y : AddUnits R\n⊢ ↑x * ↑(-y) + ↑(x.mulRight ↑y) = 0",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"AddUnits.val",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
... | [] | simp [← mul_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.GroupWithZero.Units.Lemmas | {
"line": 37,
"column": 6
} | {
"line": 37,
"column": 50
} | {
"line": 38,
"column": 6
} | [
{
"pp": "case inl\nM : Type u_1\nG₀ : Type u_3\nF : Type u_6\ninst✝³ : Monoid M\ninst✝² : GroupWithZero G₀\ninst✝¹ : FunLike F G₀ M\ninst✝ : MonoidHomClass F G₀ M\nf : F\nh : IsUnit (f 0)\nt : G₀\nht : f t ≠ 1\nthis : f (t * 0) = f t * f 0\n⊢ f t = 1",
"ppTerm": "?inl",
"assigned": true,
"usedConsta... | [
"case inl\nM : Type u_1\nG₀ : Type u_3\nF : Type u_6\ninst✝³ : Monoid M\ninst✝² : GroupWithZero G₀\ninst✝¹ : FunLike F G₀ M\ninst✝ : MonoidHomClass F G₀ M\nf : F\nh : IsUnit (f 0)\nt : G₀\nht : f t ≠ 1\nthis : 1 * f 0 = f t * f 0\n⊢ f t = 1"
] | rw [← one_mul (f (t * 0)), mul_zero] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Ring.Invertible | {
"line": 133,
"column": 4
} | {
"line": 134,
"column": 35
} | {
"line": 136,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝ : Semiring R\na b : R\nh : IsUnit a ↔ IsUnit b\nha : ¬IsUnit a\n⊢ a⁻¹ʳ + b⁻¹ʳ = a⁻¹ʳ * (a + b) * b⁻¹ʳ",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"HMul.hMul",
"eq_false",
... | [] | have hb := h.not.mp ha
simp [inverse_non_unit, ha, hb] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Invertible | {
"line": 133,
"column": 4
} | {
"line": 134,
"column": 35
} | {
"line": 136,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝ : Semiring R\na b : R\nh : IsUnit a ↔ IsUnit b\nha : ¬IsUnit a\n⊢ a⁻¹ʳ + b⁻¹ʳ = a⁻¹ʳ * (a + b) * b⁻¹ʳ",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"HMul.hMul",
"eq_false",
... | [] | have hb := h.not.mp ha
simp [inverse_non_unit, ha, hb] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Ring.Invertible | {
"line": 144,
"column": 4
} | {
"line": 145,
"column": 35
} | {
"line": 146,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝ : Ring R\na b : R\nh : IsUnit a ↔ IsUnit b\nha : ¬IsUnit a\n⊢ a⁻¹ʳ - b⁻¹ʳ = a⁻¹ʳ * (b - a) * b⁻¹ʳ",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"False",
"HMul.hMul",
"eq_false",
"sub_self",
"AddGroupWithOne.toAddGroup",... | [] | have hb := h.not.mp ha
simp [inverse_non_unit, ha, hb] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Invertible | {
"line": 144,
"column": 4
} | {
"line": 145,
"column": 35
} | {
"line": 146,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝ : Ring R\na b : R\nh : IsUnit a ↔ IsUnit b\nha : ¬IsUnit a\n⊢ a⁻¹ʳ - b⁻¹ʳ = a⁻¹ʳ * (b - a) * b⁻¹ʳ",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"False",
"HMul.hMul",
"eq_false",
"sub_self",
"AddGroupWithOne.toAddGroup",... | [] | have hb := h.not.mp ha
simp [inverse_non_unit, ha, hb] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Field.Basic | {
"line": 92,
"column": 65
} | {
"line": 92,
"column": 84
} | {
"line": 92,
"column": 85
} | [
{
"pp": "K : Type u_1\ninst✝ : DivisionRing K\na : K\nh : a ≠ 0\n⊢ a / -a = -1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
... | [
"K : Type u_1\ninst✝ : DivisionRing K\na : K\nh : a ≠ 0\n⊢ -(a / a) = -1"
] | div_neg_eq_neg_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 32,
"column": 4
} | {
"line": 32,
"column": 87
} | {
"line": 33,
"column": 4
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedMonoid α\nn : ℤ\na : α\nn0 : n ≤ 0\nm : ℕ\nh : -n = ↑m\n⊢ |a ^ n|ₘ = |a|ₘ ^ |n|",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"AddGroup.toSubtractionMonoid",
"... | [
"case inr\nα : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedMonoid α\nn : ℤ\na : α\nn0 : n ≤ 0\nm : ℕ\nh : -n = ↑m\n⊢ |a ^ m|ₘ = |a|ₘ ^ m"
] | rw [← mabs_inv, ← zpow_neg, ← abs_neg, h, zpow_natCast, Nat.abs_cast, zpow_natCast] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 231,
"column": 18
} | {
"line": 231,
"column": 76
} | {
"line": 233,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na b : R\nn : ℕ\nhn✝ : n ≠ 0\nhn : Odd n ∧ ¬Even n\n⊢ a ^ n = b ^ n ↔ a = b ∨ a = -b ∧ Even n",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"False",
"eq_f... | [] | simp [hn, (hn.1.strictMono_pow (R := R)).injective.eq_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 231,
"column": 18
} | {
"line": 231,
"column": 76
} | {
"line": 233,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na b : R\nn : ℕ\nhn✝ : n ≠ 0\nhn : Odd n ∧ ¬Even n\n⊢ a ^ n = b ^ n ↔ a = b ∨ a = -b ∧ Even n",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"False",
"eq_f... | [] | simp [hn, (hn.1.strictMono_pow (R := R)).injective.eq_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 231,
"column": 18
} | {
"line": 231,
"column": 76
} | {
"line": 233,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na b : R\nn : ℕ\nhn✝ : n ≠ 0\nhn : Odd n ∧ ¬Even n\n⊢ a ^ n = b ^ n ↔ a = b ∨ a = -b ∧ Even n",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"False",
"eq_f... | [] | simp [hn, (hn.1.strictMono_pow (R := R)).injective.eq_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 508,
"column": 15
} | {
"line": 508,
"column": 66
} | {
"line": 510,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\na b x : α\n⊢ x ∈ Icc a b \\ {a} ↔ x ∈ Ioc a b",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.... | [] | by simp [lt_iff_le_and_ne, eq_comm, and_right_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 520,
"column": 17
} | {
"line": 520,
"column": 31
} | {
"line": 520,
"column": 32
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ Icc a b \\ ({a} ∪ {b}) = Ioo a b",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Set.instUnion",
"Set.instSingletonSet",
"id",
"SDiff.sdiff"... | [
"α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ (Icc a b \\ {a}) \\ {b} = Ioo a b"
] | ← sdiff_sdiff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Equiv.Set | {
"line": 612,
"column": 4
} | {
"line": 612,
"column": 9
} | {
"line": 613,
"column": 2
} | [
{
"pp": "case pos\nα : Type u_1\nE : Type u_2\nβ : Sort u_3\nγ : Sort u_4\np : α → Prop\ninst✝³ : EquivLike E { x // p x } β\ne : E\nv : β → γ\nw : α → γ\nj : β\nx : γ\ninst✝² : DecidableEq β\ninst✝¹ : DecidableEq α\ninst✝ : (j : α) → Decidable (p j)\ni : α\nh : p i\n⊢ (if h_1 : True then if e ⟨i, ⋯⟩ = j then x... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 764,
"column": 52
} | {
"line": 764,
"column": 57
} | {
"line": 765,
"column": 0
} | [
{
"pp": "⊢ Iic False = {False}",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"iff_false",
"congrArg",
"PartialOrder.toPreorder",
"eq_iff_iff._simp_1",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 764,
"column": 52
} | {
"line": 764,
"column": 57
} | {
"line": 765,
"column": 0
} | [
{
"pp": "⊢ Iic False = {False}",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"iff_false",
"congrArg",
"PartialOrder.toPreorder",
"eq_iff_iff._simp_1",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 764,
"column": 52
} | {
"line": 764,
"column": 57
} | {
"line": 765,
"column": 0
} | [
{
"pp": "⊢ Iic False = {False}",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"iff_false",
"congrArg",
"PartialOrder.toPreorder",
"eq_iff_iff._simp_1",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 765,
"column": 47
} | {
"line": 765,
"column": 52
} | {
"line": 766,
"column": 0
} | [
{
"pp": "⊢ Iic True = univ",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
"LE.le",
"if... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 765,
"column": 47
} | {
"line": 765,
"column": 52
} | {
"line": 766,
"column": 0
} | [
{
"pp": "⊢ Iic True = univ",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
"LE.le",
"if... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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