module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case top.bot\nhx : 0 ≤ ⊤\nhy : 0 ≤ ⊥\n⊢ ⊤.toENNReal = ⊥.toENNReal ↔ ⊤ = ⊥",
"usedConstants": [
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
"instTopEReal",
"Bot.b... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case top.coe\nhx : 0 ≤ ⊤\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ ⊤.toENNReal = (↑a✝).toENNReal ↔ ⊤ = ↑a✝",
"usedConstants": [
"False",
"EReal.toENNReal_of_ne_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"EReal.toENNReal",
"ENNReal.top_ne_ofReal._simp_1"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case top.top\nhx hy : 0 ≤ ⊤\n⊢ ⊤.toENNReal = ⊤.toENNReal ↔ ⊤ = ⊤",
"usedConstants": [
"congrArg",
"EReal.toENNReal",
"EReal",
"instTopEReal",
"iff_self",
"Iff",
"congr",
"True",
"eq_self",
"ENNReal",
"of_eq_true",
"ENNReal.inst... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 773,
"column": 4
} | {
"line": 773,
"column": 12
} | [
{
"pp": "case top\ny : EReal\nh : ⊤ ≤ y\n⊢ ⊤.toENNReal ≤ y.toENNReal",
"usedConstants": [
"instReflLe",
"congrArg",
"EReal.toENNReal",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Std.le_refl._simp_1",
"CoheytingAlgebra.toOrderTop",
"Eq.mp",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 773,
"column": 4
} | {
"line": 773,
"column": 12
} | [
{
"pp": "case top\ny : EReal\nh : ⊤ ≤ y\n⊢ ⊤.toENNReal ≤ y.toENNReal",
"usedConstants": [
"instReflLe",
"congrArg",
"EReal.toENNReal",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Std.le_refl._simp_1",
"CoheytingAlgebra.toOrderTop",
"Eq.mp",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Basic | {
"line": 773,
"column": 4
} | {
"line": 773,
"column": 12
} | [
{
"pp": "case top\ny : EReal\nh : ⊤ ≤ y\n⊢ ⊤.toENNReal ≤ y.toENNReal",
"usedConstants": [
"instReflLe",
"congrArg",
"EReal.toENNReal",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Std.le_refl._simp_1",
"CoheytingAlgebra.toOrderTop",
"Eq.mp",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Real.Pointwise | {
"line": 46,
"column": 4
} | {
"line": 46,
"column": 27
} | [
{
"pp": "case inr.inl\nα : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : MulActionWithZero α ℝ\ninst✝ : IsOrderedModule α ℝ\ns : Set ℝ\nhs : s.Nonempty\nha : 0 ≤ 0\n⊢ sInf 0 = 0",
"usedConstants": [
"Real",
"csInf_singleton",
"Real.instZero",
... | exact csInf_singleton 0 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Real.Pointwise | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 27
} | [
{
"pp": "case inr.inl\nα : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : Module α ℝ\ninst✝ : IsOrderedModule α ℝ\ns : Set ℝ\nhs : s.Nonempty\nha : 0 ≤ 0\n⊢ sInf 0 = 0",
"usedConstants": [
"Real",
"csInf_singleton",
"Real.instZero",
"Cond... | exact csInf_singleton 0 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Real.Pointwise | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 50
} | [
{
"pp": "ι : Sort u_1\nr : ℝ\nha : r ≤ 0\nf : ι → ℝ\n⊢ (⨆ i, f i) * r = ⨅ i, f i * r",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real",
"iInf",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRi... | simp only [Real.mul_iSup_of_nonpos ha, mul_comm] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Real.Pointwise | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 50
} | [
{
"pp": "ι : Sort u_1\nr : ℝ\nha : r ≤ 0\nf : ι → ℝ\n⊢ (⨆ i, f i) * r = ⨅ i, f i * r",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real",
"iInf",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRi... | simp only [Real.mul_iSup_of_nonpos ha, mul_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Real.Pointwise | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 50
} | [
{
"pp": "ι : Sort u_1\nr : ℝ\nha : r ≤ 0\nf : ι → ℝ\n⊢ (⨆ i, f i) * r = ⨅ i, f i * r",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real",
"iInf",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRi... | simp only [Real.mul_iSup_of_nonpos ha, mul_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNReal.Basic | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 35
} | [
{
"pp": "ι : Sort u_2\nf : ι → ℕ\n⊢ BddAbove (range fun x ↦ ↑(f x)) ↔ BddAbove (range f)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"AddMonoidWithOne.toNatCast",
"NNRe... | ← bddAbove_natCast_image_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.NNReal.Basic | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 20
} | [
{
"pp": "ι : Sort u_2\nf : ι → ℝ≥0\na : ℝ≥0\n⊢ ⨆ i, a * f i = ⨆ i, f i * a",
"usedConstants": [
"NNReal.instCommSemiring",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"iSup",
"NNReal",
"CommMagma.toMul",
"NonUnitalCommSemiring.toNonUnitalN... | simp_rw [mul_comm] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Data.ENNReal.Inv | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 12
} | [
{
"pp": "case inl\nb : ℝ≥0∞\nha₀ : 0 = 0 → b = 0\nha : 0 = ∞ → b = 0\n⊢ 0⁻¹ * (0 * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.instCommSemiring",
"MulZer... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 12
} | [
{
"pp": "case inl\nb : ℝ≥0∞\nha₀ : 0 = 0 → b = 0\nha : 0 = ∞ → b = 0\n⊢ 0⁻¹ * (0 * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.instCommSemiring",
"MulZer... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 12
} | [
{
"pp": "case inl\nb : ℝ≥0∞\nha₀ : 0 = 0 → b = 0\nha : 0 = ∞ → b = 0\n⊢ 0⁻¹ * (0 * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.instCommSemiring",
"MulZer... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 12
} | [
{
"pp": "case inr.inl\nb : ℝ≥0∞\nha₀✝ : ∞ = 0 → b = 0\nha : ∞ = ∞ → b = 0\nha₀ : ∞ ≠ 0\n⊢ ∞⁻¹ * (∞ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSemiring",
"MulZeroClass.m... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 12
} | [
{
"pp": "case inr.inl\nb : ℝ≥0∞\nha₀✝ : ∞ = 0 → b = 0\nha : ∞ = ∞ → b = 0\nha₀ : ∞ ≠ 0\n⊢ ∞⁻¹ * (∞ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSemiring",
"MulZeroClass.m... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 12
} | [
{
"pp": "case inr.inl\nb : ℝ≥0∞\nha₀✝ : ∞ = 0 → b = 0\nha : ∞ = ∞ → b = 0\nha₀ : ∞ ≠ 0\n⊢ ∞⁻¹ * (∞ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSemiring",
"MulZeroClass.m... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 12
} | [
{
"pp": "case inl\nb : ℝ≥0∞\nha₀ : 0 = 0 → b = 0\nha : 0 = ∞ → b = 0\n⊢ 0 * (0⁻¹ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.instCommSemiring",
"MulZer... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 12
} | [
{
"pp": "case inl\nb : ℝ≥0∞\nha₀ : 0 = 0 → b = 0\nha : 0 = ∞ → b = 0\n⊢ 0 * (0⁻¹ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.instCommSemiring",
"MulZer... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 12
} | [
{
"pp": "case inl\nb : ℝ≥0∞\nha₀ : 0 = 0 → b = 0\nha : 0 = ∞ → b = 0\n⊢ 0 * (0⁻¹ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.instCommSemiring",
"MulZer... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 12
} | [
{
"pp": "case inr.inl\nb : ℝ≥0∞\nha₀✝ : ∞ = 0 → b = 0\nha : ∞ = ∞ → b = 0\nha₀ : ∞ ≠ 0\n⊢ ∞ * (∞⁻¹ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSemiring",
"MulZeroClass.m... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 12
} | [
{
"pp": "case inr.inl\nb : ℝ≥0∞\nha₀✝ : ∞ = 0 → b = 0\nha : ∞ = ∞ → b = 0\nha₀ : ∞ ≠ 0\n⊢ ∞ * (∞⁻¹ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSemiring",
"MulZeroClass.m... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 12
} | [
{
"pp": "case inr.inl\nb : ℝ≥0∞\nha₀✝ : ∞ = 0 → b = 0\nha : ∞ = ∞ → b = 0\nha₀ : ∞ ≠ 0\n⊢ ∞ * (∞⁻¹ * b) = b",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSemiring",
"MulZeroClass.m... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 12
} | [
{
"pp": "case inl\na : ℝ≥0∞\nhb₀ : 0 = 0 → a = 0\nhb : 0 = ∞ → a = 0\n⊢ a * 0 * 0⁻¹ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.ins... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 12
} | [
{
"pp": "case inl\na : ℝ≥0∞\nhb₀ : 0 = 0 → a = 0\nhb : 0 = ∞ → a = 0\n⊢ a * 0 * 0⁻¹ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.ins... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 12
} | [
{
"pp": "case inl\na : ℝ≥0∞\nhb₀ : 0 = 0 → a = 0\nhb : 0 = ∞ → a = 0\n⊢ a * 0 * 0⁻¹ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.ins... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 142,
"column": 4
} | {
"line": 142,
"column": 12
} | [
{
"pp": "case inr.inl\na : ℝ≥0∞\nhb₀✝ : ∞ = 0 → a = 0\nhb : ∞ = ∞ → a = 0\nhb₀ : ∞ ≠ 0\n⊢ a * ∞ * ∞⁻¹ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSem... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 142,
"column": 4
} | {
"line": 142,
"column": 12
} | [
{
"pp": "case inr.inl\na : ℝ≥0∞\nhb₀✝ : ∞ = 0 → a = 0\nhb : ∞ = ∞ → a = 0\nhb₀ : ∞ ≠ 0\n⊢ a * ∞ * ∞⁻¹ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSem... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 142,
"column": 4
} | {
"line": 142,
"column": 12
} | [
{
"pp": "case inr.inl\na : ℝ≥0∞\nhb₀✝ : ∞ = 0 → a = 0\nhb : ∞ = ∞ → a = 0\nhb₀ : ∞ ≠ 0\n⊢ a * ∞ * ∞⁻¹ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSem... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 12
} | [
{
"pp": "case inl\na : ℝ≥0∞\nhb₀ : 0 = 0 → a = 0\nhb : 0 = ∞ → a = 0\n⊢ a * 0⁻¹ * 0 = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.ins... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 12
} | [
{
"pp": "case inl\na : ℝ≥0∞\nhb₀ : 0 = 0 → a = 0\nhb : 0 = ∞ → a = 0\n⊢ a * 0⁻¹ * 0 = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.ins... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 12
} | [
{
"pp": "case inl\na : ℝ≥0∞\nhb₀ : 0 = 0 → a = 0\nhb : 0 = ∞ → a = 0\n⊢ a * 0⁻¹ * 0 = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.inv_zero",
"ENNReal.ins... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Inv | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 12
} | [
{
"pp": "case inr.inl\na : ℝ≥0∞\nhb₀✝ : ∞ = 0 → a = 0\nhb : ∞ = ∞ → a = 0\nhb₀ : ∞ ≠ 0\n⊢ a * ∞⁻¹ * ∞ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSem... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 12
} | [
{
"pp": "case inr.inl\na : ℝ≥0∞\nhb₀✝ : ∞ = 0 → a = 0\nhb : ∞ = ∞ → a = 0\nhb₀ : ∞ ≠ 0\n⊢ a * ∞⁻¹ * ∞ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSem... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 12
} | [
{
"pp": "case inr.inl\na : ℝ≥0∞\nhb₀✝ : ∞ = 0 → a = 0\nhb : ∞ = ∞ → a = 0\nhb₀ : ∞ ≠ 0\n⊢ a * ∞⁻¹ * ∞ = a",
"usedConstants": [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"instInhabitedTrue",
"Eq.mp",
"id",
"ENNReal.instCommSem... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.IsLUB | {
"line": 255,
"column": 2
} | {
"line": 255,
"column": 94
} | [
{
"pp": "α : Type u_3\ninst✝² : ConditionallyCompleteLinearOrder α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\na b : α\nx✝ : a ≤ b\nf : Ultrafilter α\nhfab : Icc a b ∈ ↑f\nhf : ∀ x ∈ Icc a b, ¬↑f ≤ 𝓝 x\nhpt : ∀ x ∈ Icc a b, {x} ∉ f\ns : Set α := {x | x ∈ Icc a b ∧ Icc a x ∉ f}\nhsb : b ∈ upperBounds... | have : x ∈ Icc a b := ⟨by grind, le_of_not_gt fun h ↦ hxf (mem_of_superset hfab (by grind))⟩ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Order.IsLUB | {
"line": 296,
"column": 4
} | {
"line": 296,
"column": 28
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\nt : Set α\nx : α\ninst✝ : (𝓝 x).IsCountablyGenerated\nhtx : IsLUB t x\nnotMem : x ∉ t\nht : t.Nonempty\nv : ℕ → α\nhvt : ∀ (n : ℕ), v n ∈ t\nhvx : Tendsto v atTop (𝓝 x)\nhvx' : ∀ {n : ℕ}, v n <... | rw [iterate_succ_apply'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Order.IsLUB | {
"line": 297,
"column": 4
} | {
"line": 297,
"column": 28
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\nt : Set α\nx : α\ninst✝ : (𝓝 x).IsCountablyGenerated\nhtx : IsLUB t x\nnotMem : x ∉ t\nht : t.Nonempty\nv : ℕ → α\nhvt : ∀ (n : ℕ), v n ∈ t\nhvx : Tendsto v atTop (𝓝 x)\nhvx' : ∀ {n : ℕ}, v n <... | rw [iterate_succ_apply'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Order.IsLUB | {
"line": 341,
"column": 2
} | {
"line": 341,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : DenselyOrdered α\ninst✝ : FirstCountableTopology α\ns : Set α\nhs : Dense s\nx y : α\nhy : y < x\nhnonempty : (Ioo y x ∩ s).Nonempty\nhx : IsLUB (Ioo y x ∩ s) x\n⊢ ∀ (a : ℕ → α),\n (StrictMono a ∧ (... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Order.IsLUB | {
"line": 348,
"column": 2
} | {
"line": 348,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : LinearOrder α\ninst✝³ : OrderTopology α\ninst✝² : DenselyOrdered α\ninst✝¹ : NoMinOrder α\ninst✝ : FirstCountableTopology α\ns : Set α\nhs : Dense s\nx y : α\nhy : y < x\n⊢ ∀ (a : ℕ → α),\n StrictMono a ∧ (∀ (n : ℕ), a n ∈ Ioo ⋯.choose x ∩ s) ∧ Ten... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ENNReal.Inv | {
"line": 733,
"column": 6
} | {
"line": 733,
"column": 31
} | [
{
"pp": "case h.mpr.left\ny : ℝ≥0∞\nhy : 1 < y\nh'y : y ≠ ∞\nx : ℝ≥0∞\nn : ℤ\nhn : y ^ n ≤ x\nh'n : x < y ^ (n + 1)\n⊢ 0 < x",
"usedConstants": [
"PartialOrder.toPreorder",
"DivInvMonoid.toZPow",
"Int",
"HPow.hPow",
"ENNReal",
"ENNReal.instDivInvMonoid",
"ENNReal.in... | apply lt_of_lt_of_le _ hn | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.ENNReal.Inv | {
"line": 741,
"column": 4
} | {
"line": 742,
"column": 57
} | [
{
"pp": "case ofNat.ofNat\nx : ℝ≥0∞\nhx : 1 ≤ x\na b : ℕ\nh : Int.ofNat a ≤ Int.ofNat b\n⊢ x ^ Int.ofNat a ≤ x ^ Int.ofNat b",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"ENNReal.instIsOrderedRing",
"IsOrderedRing.toPosMulMono",
"IsOrderedRing.toZeroLEOneClass",
"congrA... | simp only [Int.ofNat_eq_natCast, zpow_natCast]
exact pow_right_mono₀ hx (Int.le_of_ofNat_le_ofNat h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Inv | {
"line": 741,
"column": 4
} | {
"line": 742,
"column": 57
} | [
{
"pp": "case ofNat.ofNat\nx : ℝ≥0∞\nhx : 1 ≤ x\na b : ℕ\nh : Int.ofNat a ≤ Int.ofNat b\n⊢ x ^ Int.ofNat a ≤ x ^ Int.ofNat b",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"ENNReal.instIsOrderedRing",
"IsOrderedRing.toPosMulMono",
"IsOrderedRing.toZeroLEOneClass",
"congrA... | simp only [Int.ofNat_eq_natCast, zpow_natCast]
exact pow_right_mono₀ hx (Int.le_of_ofNat_le_ofNat h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.EMetricSpace.Basic | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 41
} | [
{
"pp": "α : Type u\ninst✝ : PseudoEMetricSpace α\nhs : ∀ ε > 0, ∃ t, t.Countable ∧ ⋃ x ∈ t, closedEBall x ε = univ\n⊢ ∀ ε > 0, ∃ t, t.Countable ∧ univ ⊆ ⋃ x ∈ t, closedEBall x ε",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"_private.Mathlib.Topology.EMetricSpace.Basic.0.EMetric.secondC... | simpa only [univ_subset_iff] using hs | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Topology.EMetricSpace.Diam | {
"line": 96,
"column": 2
} | {
"line": 114,
"column": 54
} | [
{
"pp": "X : Type u_2\ns t : Set X\nx y : X\ninst✝ : PseudoEMetricSpace X\nxs : x ∈ s\nyt : y ∈ t\n⊢ ediam (s ∪ t) ≤ ediam s + edist x y + ediam t",
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"Set.mem_union",
"PseudoEMetricSpace.edist_comm",
"ENNReal.instAdd",
"Pse... | have A : ∀ a ∈ s, ∀ b ∈ t, edist a b ≤ ediam s + edist x y + ediam t := fun a ha b hb =>
calc
edist a b ≤ edist a x + edist x y + edist y b := edist_triangle4 _ _ _ _
_ ≤ ediam s + edist x y + ediam t := by
gcongr
exacts [edist_le_ediam_of_mem ha xs, edist_le_ediam_of_mem yt hb]
refine... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.EMetricSpace.Diam | {
"line": 96,
"column": 2
} | {
"line": 114,
"column": 54
} | [
{
"pp": "X : Type u_2\ns t : Set X\nx y : X\ninst✝ : PseudoEMetricSpace X\nxs : x ∈ s\nyt : y ∈ t\n⊢ ediam (s ∪ t) ≤ ediam s + edist x y + ediam t",
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"Set.mem_union",
"PseudoEMetricSpace.edist_comm",
"ENNReal.instAdd",
"Pse... | have A : ∀ a ∈ s, ∀ b ∈ t, edist a b ≤ ediam s + edist x y + ediam t := fun a ha b hb =>
calc
edist a b ≤ edist a x + edist x y + edist y b := edist_triangle4 _ _ _ _
_ ≤ ediam s + edist x y + ediam t := by
gcongr
exacts [edist_le_ediam_of_mem ha xs, edist_le_ediam_of_mem yt hb]
refine... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Encodable.Lattice | {
"line": 45,
"column": 4
} | {
"line": 45,
"column": 75
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : Encodable β\nf : β → Set α\nC : Set α → Prop\nH0 : C ∅\nH1 : ∀ (b : β), C (f b)\nn : ℕ\n⊢ C (⋃ b ∈ none, f b)",
"usedConstants": [
"Eq.mpr",
"False",
"Iff.of_eq",
"Option.ctorIdx",
"congrArg",
"Option.instMembership",
"Fa... | simp only [Option.mem_def, iUnion_of_empty, iUnion_empty, reduceCtorEq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.Filter.AtTopBot.Finset | {
"line": 60,
"column": 61
} | {
"line": 64,
"column": 95
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\n⊢ Tendsto Finset.toLeft atTop atTop",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"Finset.toLeft",
"Finset.disjSum_empty",
"congrArg",
"Finset.inhabitedFinset",
"Filter.map",
"Fins... | by
intro s hs
simp only [mem_atTop_sets, Filter.mem_map, Set.mem_preimage] at hs ⊢
obtain ⟨t, H⟩ := hs
exact ⟨t.disjSum ∅, fun b hb ↦ H _ (by simpa [← Finset.coe_subset, Set.subset_def] using hb)⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Algebra.InfiniteSum.Ring | {
"line": 65,
"column": 2
} | {
"line": 67,
"column": 42
} | [
{
"pp": "ι : Type u_1\nα : Type u_3\nL : SummationFilter ι\ninst✝⁴ : NonUnitalNonAssocSemiring α\ninst✝³ : TopologicalSpace α\ninst✝² : IsTopologicalSemiring α\nf : ι → α\ninst✝¹ : T2Space α\ninst✝ : L.NeBot\na b : α\nh : ∀ (i : ι), SemiconjBy (f i) a b\n⊢ SemiconjBy (∑'[L] (i : ι), f i) a b",
"usedConstant... | by_cases hf : Summable f L
· rw [SemiconjBy, ← hf.tsum_mul_right a, ← hf.tsum_mul_left b, tsum_congr h]
· simp [tsum_eq_zero_of_not_summable hf] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.InfiniteSum.Ring | {
"line": 65,
"column": 2
} | {
"line": 67,
"column": 42
} | [
{
"pp": "ι : Type u_1\nα : Type u_3\nL : SummationFilter ι\ninst✝⁴ : NonUnitalNonAssocSemiring α\ninst✝³ : TopologicalSpace α\ninst✝² : IsTopologicalSemiring α\nf : ι → α\ninst✝¹ : T2Space α\ninst✝ : L.NeBot\na b : α\nh : ∀ (i : ι), SemiconjBy (f i) a b\n⊢ SemiconjBy (∑'[L] (i : ι), f i) a b",
"usedConstant... | by_cases hf : Summable f L
· rw [SemiconjBy, ← hf.tsum_mul_right a, ← hf.tsum_mul_left b, tsum_congr h]
· simp [tsum_eq_zero_of_not_summable hf] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.InfiniteSum.Ring | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 65
} | [
{
"pp": "α : Type u_3\nA : Type u_4\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : HasAntidiagonal A\ninst✝³ : TopologicalSpace α\ninst✝² : NonUnitalNonAssocSemiring α\nf g : A → α\ninst✝¹ : T3Space α\ninst✝ : IsTopologicalSemiring α\nh : Summable fun x ↦ f x.1 * g x.2\n⊢ Summable fun n ↦ ∑ kl ∈ antidiagonal n, f kl.1 * g... | rw [summable_mul_prod_iff_summable_mul_sigma_antidiagonal] at h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Algebra.InfiniteSum.NatInt | {
"line": 431,
"column": 8
} | {
"line": 434,
"column": 11
} | [
{
"pp": "case e_a.refine_2\nM : Type u_1\ninst✝² : CommMonoid M\ninst✝¹ : TopologicalSpace M\nm : M\ninst✝ : ContinuousMul M\nf : ℤ → M\nhf : HasProd f m\nu : Finset ℤ\nv' : Finset ℕ\nhv' : image Int.natAbs u ⊆ v'\nu1 : Finset ℤ := image (fun x ↦ ↑x) v'\nu2 : Finset ℤ := image (fun x ↦ -↑x) v'\nA : u ⊆ u1 ∪ u2\... | intro x hx
simp only [u1, u2, mem_inter, mem_image] at hx
suffices x = 0 by simp only [this, if_true]
lia | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.InfiniteSum.NatInt | {
"line": 431,
"column": 8
} | {
"line": 434,
"column": 11
} | [
{
"pp": "case e_a.refine_2\nM : Type u_1\ninst✝² : CommMonoid M\ninst✝¹ : TopologicalSpace M\nm : M\ninst✝ : ContinuousMul M\nf : ℤ → M\nhf : HasProd f m\nu : Finset ℤ\nv' : Finset ℕ\nhv' : image Int.natAbs u ⊆ v'\nu1 : Finset ℤ := image (fun x ↦ ↑x) v'\nu2 : Finset ℤ := image (fun x ↦ -↑x) v'\nA : u ⊆ u1 ∪ u2\... | intro x hx
simp only [u1, u2, mem_inter, mem_image] at hx
suffices x = 0 by simp only [this, if_true]
lia | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.bot\nhx hy : 0 ≤ ⊥\n⊢ (⊥ + ⊥).toENNReal = ⊥.toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.bot\nhx hy : 0 ≤ ⊥\n⊢ (⊥ + ⊥).toENNReal = ⊥.toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.bot\nhx hy : 0 ≤ ⊥\n⊢ (⊥ + ⊥).toENNReal = ⊥.toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.coe\nhx : 0 ≤ ⊥\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (⊥ + ↑a✝).toENNReal = ⊥.toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toL... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.coe\nhx : 0 ≤ ⊥\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (⊥ + ↑a✝).toENNReal = ⊥.toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toL... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na : α\nha : (Ioi a).Nonempty\n⊢ frontier (Ioi a) = {a}",
"usedConstants": [
"frontier",
"instClosedIicTopology",
"Set.Ioi",
"Set.Ici",
"congrArg",
... | simp [frontier, closure_Ioi' ha] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.coe\nhx : 0 ≤ ⊥\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (⊥ + ↑a✝).toENNReal = ⊥.toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toL... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na : α\nha : (Ioi a).Nonempty\n⊢ frontier (Ioi a) = {a}",
"usedConstants": [
"frontier",
"instClosedIicTopology",
"Set.Ioi",
"Set.Ici",
"congrArg",
... | simp [frontier, closure_Ioi' ha] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na : α\nha : (Ioi a).Nonempty\n⊢ frontier (Ioi a) = {a}",
"usedConstants": [
"frontier",
"instClosedIicTopology",
"Set.Ioi",
"Set.Ici",
"congrArg",
... | simp [frontier, closure_Ioi' ha] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.top\nhx : 0 ≤ ⊥\nhy : 0 ≤ ⊤\n⊢ (⊥ + ⊤).toENNReal = ⊥.toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.top\nhx : 0 ≤ ⊥\nhy : 0 ≤ ⊤\n⊢ (⊥ + ⊤).toENNReal = ⊥.toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case bot.top\nhx : 0 ≤ ⊥\nhy : 0 ≤ ⊤\n⊢ (⊥ + ⊤).toENNReal = ⊥.toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.bot\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊥\n⊢ (↑a✝ + ⊥).toENNReal = (↑a✝).toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toL... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.bot\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊥\n⊢ (↑a✝ + ⊥).toENNReal = (↑a✝).toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toL... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.bot\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊥\n⊢ (↑a✝ + ⊥).toENNReal = (↑a✝).toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toL... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.coe\na✝¹ : ℝ\nhx : 0 ≤ ↑a✝¹\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (↑a✝¹ + ↑a✝).toENNReal = (↑a✝¹).toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"Eq.mpr",
"ENNReal.instAdd",
"EReal.coe_nonneg._simp_1",
"False",
"Real.instLE",
"Real",
"EReal.toENNReal_of_ne_to... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.coe\na✝¹ : ℝ\nhx : 0 ≤ ↑a✝¹\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (↑a✝¹ + ↑a✝).toENNReal = (↑a✝¹).toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"Eq.mpr",
"ENNReal.instAdd",
"EReal.coe_nonneg._simp_1",
"False",
"Real.instLE",
"Real",
"EReal.toENNReal_of_ne_to... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.coe\na✝¹ : ℝ\nhx : 0 ≤ ↑a✝¹\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (↑a✝¹ + ↑a✝).toENNReal = (↑a✝¹).toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"Eq.mpr",
"ENNReal.instAdd",
"EReal.coe_nonneg._simp_1",
"False",
"Real.instLE",
"Real",
"EReal.toENNReal_of_ne_to... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.top\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊤\n⊢ (↑a✝ + ⊤).toENNReal = (↑a✝).toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal_of_ne_top",
"add_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"E... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.top\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊤\n⊢ (↑a✝ + ⊤).toENNReal = (↑a✝).toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal_of_ne_top",
"add_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"E... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case coe.top\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊤\n⊢ (↑a✝ + ⊤).toENNReal = (↑a✝).toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal_of_ne_top",
"add_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"E... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.bot\nhx : 0 ≤ ⊤\nhy : 0 ≤ ⊥\n⊢ (⊤ + ⊥).toENNReal = ⊤.toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.bot\nhx : 0 ≤ ⊤\nhy : 0 ≤ ⊥\n⊢ (⊤ + ⊥).toENNReal = ⊤.toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.bot\nhx : 0 ≤ ⊤\nhy : 0 ≤ ⊥\n⊢ (⊤ + ⊥).toENNReal = ⊤.toENNReal + ⊥.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.coe\nhx : 0 ≤ ⊤\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (⊤ + ↑a✝).toENNReal = ⊤.toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal_of_ne_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"EReal.toENNReal",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.coe\nhx : 0 ≤ ⊤\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (⊤ + ↑a✝).toENNReal = ⊤.toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal_of_ne_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"EReal.toENNReal",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.coe\nhx : 0 ≤ ⊤\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (⊤ + ↑a✝).toENNReal = ⊤.toENNReal + (↑a✝).toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"False",
"EReal.toENNReal_of_ne_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"EReal.toENNReal",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.top\nhx hy : 0 ≤ ⊤\n⊢ (⊤ + ⊤).toENNReal = ⊤.toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"top_ne_bot._simp_1",
"False",
"add_top",
"congrArg",
"EReal.toENNReal",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.t... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.top\nhx hy : 0 ≤ ⊤\n⊢ (⊤ + ⊤).toENNReal = ⊤.toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"top_ne_bot._simp_1",
"False",
"add_top",
"congrArg",
"EReal.toENNReal",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.t... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Operations | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 49
} | [
{
"pp": "case top.top\nhx hy : 0 ≤ ⊤\n⊢ (⊤ + ⊤).toENNReal = ⊤.toENNReal + ⊤.toENNReal",
"usedConstants": [
"ENNReal.instAdd",
"top_ne_bot._simp_1",
"False",
"add_top",
"congrArg",
"EReal.toENNReal",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.t... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 295,
"column": 50
} | {
"line": 295,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ico a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finit... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 295,
"column": 50
} | {
"line": 295,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ico a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finit... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 295,
"column": 50
} | {
"line": 295,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ico a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finit... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 303,
"column": 50
} | {
"line": 303,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ioc a b)",
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 303,
"column": 50
} | {
"line": 303,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ioc a b)",
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 303,
"column": 50
} | {
"line": 303,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ioc a b)",
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 311,
"column": 50
} | {
"line": 311,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ioo a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finit... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 311,
"column": 50
} | {
"line": 311,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ioo a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finit... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.DenselyOrdered | {
"line": 311,
"column": 50
} | {
"line": 311,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsClosed[inst✝³] (Ioo a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finit... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Operations | {
"line": 183,
"column": 25
} | {
"line": 184,
"column": 52
} | [
{
"pp": "x y : EReal\nhy : y ≠ ⊥\nhy' : y ≠ ⊤\n⊢ x + y ≠ ⊤ ↔ x ≠ ⊤",
"usedConstants": [
"False",
"Real",
"eq_false",
"bot_ne_top._simp_2",
"congrArg",
"and_self",
"EReal.coe_ne_top._simp_1",
"CompletelyDistribLattice.toCompleteLattice",
"EReal.bot_add",
... | by
cases x <;> simp [add_ne_top_iff_ne_top₂, hy, hy'] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Order.Compact | {
"line": 123,
"column": 47
} | {
"line": 123,
"column": 55
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsCompact (Ico a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finite",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Order.Compact | {
"line": 123,
"column": 47
} | {
"line": 123,
"column": 55
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsCompact (Ico a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finite",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.Compact | {
"line": 123,
"column": 47
} | {
"line": 123,
"column": 55
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsCompact (Ico a b)",
"usedConstants": [
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finite",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.Compact | {
"line": 128,
"column": 47
} | {
"line": 128,
"column": 55
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsCompact (Ioc a b)",
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Order.Compact | {
"line": 128,
"column": 47
} | {
"line": 128,
"column": 55
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\n⊢ b ≤ a → IsCompact (Ioc a b)",
"usedConstants": [
"Set.Ioc",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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