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.Analysis.SpecialFunctions.Pow.Real | {
"line": 1023,
"column": 70
} | {
"line": 1023,
"column": 80
} | [
{
"pp": "x : ℂ\n⊢ |‖x‖ ^ 2⁻¹ * Real.sin (x.arg / 2)| = √((‖x‖ - x.re) / 2)",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"MulOne.toOne",
"Real.instPow",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Real.lattice",
"Monoid.toMulOneClass",
... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 391,
"column": 20
} | {
"line": 391,
"column": 60
} | [
{
"pp": "x : ℝ\nhx : x ≠ 0\ny z : ℝ≥0\nhyz : (fun y ↦ y ^ x) y = (fun y ↦ y ^ x) z\n⊢ y = z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 415,
"column": 2
} | {
"line": 415,
"column": 24
} | [
{
"pp": "case inr.inr\nx : ℝ≥0\ny z : ℝ\nhx₀ : x ≠ 0\nhx₁ : x ≠ 1\n⊢ x ^ y = x ^ z ↔ y = z ∨ x = 1 ∨ x = 0 ∧ (y = 0 ↔ z = 0)",
"usedConstants": [
"Eq.mpr",
"False",
"Real",
"eq_false",
"Real.instZero",
"congrArg",
"false_and",
"id",
"NNReal",
"NNRe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 419,
"column": 2
} | {
"line": 419,
"column": 28
} | [
{
"pp": "x : ℝ≥0\ny : ℝ\n⊢ x ^ y = x ↔ x = 1 ∨ y = 1 ∨ x = 0 ∧ y ≠ 0",
"usedConstants": [
"Real",
"Real.instZero",
"id",
"NNReal",
"Ne",
"NNReal.instZero",
"Real.instOne",
"And",
"Iff",
"HPow.hPow",
"NNReal.instPowReal",
"One.toOfNat1",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 422,
"column": 29
} | {
"line": 422,
"column": 39
} | [
{
"pp": "x y : ℝ≥0\nz : ℝ\nhz : z ≠ 0\n⊢ x ^ z = (y ^ z⁻¹) ^ z ↔ x ^ z = y",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"Real.instInv",
"Real.instDivInvMonoid",
"id",
... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 425,
"column": 29
} | {
"line": 425,
"column": 39
} | [
{
"pp": "x y : ℝ≥0\nz : ℝ\nhz : z ≠ 0\n⊢ (x ^ z⁻¹) ^ z = y ^ z ↔ x = y ^ z",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"Real.instInv",
"Real.instDivInvMonoid",
"id",
... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.AffineSpace.Midpoint | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 40
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : Invertible 2\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\np₁ p₂ : P\n⊢ p₂ -ᵥ midpoint R p₁ p₂ = ⅟2 • (p₂ -ᵥ p₁)",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"congrArg",
"DistribMulAct... | rw [midpoint_comm, left_vsub_midpoint] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.AffineSpace.Midpoint | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 40
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : Invertible 2\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\np₁ p₂ : P\n⊢ p₂ -ᵥ midpoint R p₁ p₂ = ⅟2 • (p₂ -ᵥ p₁)",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"congrArg",
"DistribMulAct... | rw [midpoint_comm, left_vsub_midpoint] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.AffineSpace.Midpoint | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 40
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : Invertible 2\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\np₁ p₂ : P\n⊢ p₂ -ᵥ midpoint R p₁ p₂ = ⅟2 • (p₂ -ᵥ p₁)",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"congrArg",
"DistribMulAct... | rw [midpoint_comm, left_vsub_midpoint] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.AffineSpace.Midpoint | {
"line": 211,
"column": 64
} | {
"line": 211,
"column": 75
} | [
{
"pp": "R : Type u_1\nV : Type u_2\ninst✝³ : Ring R\ninst✝² : Invertible 2\ninst✝¹ : AddCommGroup V\ninst✝ : Module R V\nx : V\n⊢ midpoint R (-x) x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Algebra | {
"line": 44,
"column": 24
} | {
"line": 44,
"column": 54
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁶ : CommSemiring α\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Semiring β\ninst✝³ : PartialOrder β\ninst✝² : Algebra α β\ninst✝¹ : PosMulMono β\ninst✝ : MulPosMono β\nh : Monotone ⇑(algebraMap α β)\n⊢ Monotone fun x ↦ x • 1",
"usedConstants": [
"Eq.mpr",
"MulOne.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Algebra | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 32
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁶ : CommSemiring α\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Semiring β\ninst✝³ : PartialOrder β\ninst✝² : Algebra α β\ninst✝¹ : ZeroLEOneClass β\ninst✝ : SMulPosMono α β\n⊢ Monotone ⇑(algebraMap α β)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Algebra | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 13
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁶ : CommSemiring α\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Semiring β\ninst✝³ : PartialOrder β\ninst✝² : Algebra α β\ninst✝¹ : ZeroLEOneClass β\ninst✝ : SMulPosMono α β\na : α\nha : 0 ≤ a\n⊢ 0 ≤ (algebraMap α β) a",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Algebra | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 32
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁷ : CommSemiring α\ninst✝⁶ : PartialOrder α\ninst✝⁵ : Semiring β\ninst✝⁴ : PartialOrder β\ninst✝³ : Algebra α β\ninst✝² : ZeroLEOneClass β\ninst✝¹ : Nontrivial β\ninst✝ : SMulPosStrictMono α β\n⊢ StrictMono ⇑(algebraMap α β)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Algebra | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 13
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁷ : CommSemiring α\ninst✝⁶ : PartialOrder α\ninst✝⁵ : Semiring β\ninst✝⁴ : PartialOrder β\ninst✝³ : Algebra α β\ninst✝² : ZeroLEOneClass β\ninst✝¹ : Nontrivial β\ninst✝ : SMulPosStrictMono α β\na : α\nha : 0 < a\n⊢ 0 < (algebraMap α β) a",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 35
} | [
{
"pp": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 ≤ z\n⊢ (x * y) ^ z = x ^ z * y ^ z",
"usedConstants": [
"False",
"Real",
"Preorder.toLT",
"HMul.hMul",
"eq_false",
"LinearOrder.toDecidableEq",
"Real.instZero",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.inst... | simp [hz.not_gt, mul_rpow_eq_ite] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 35
} | [
{
"pp": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 ≤ z\n⊢ (x * y) ^ z = x ^ z * y ^ z",
"usedConstants": [
"False",
"Real",
"Preorder.toLT",
"HMul.hMul",
"eq_false",
"LinearOrder.toDecidableEq",
"Real.instZero",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.inst... | simp [hz.not_gt, mul_rpow_eq_ite] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Pow.NNReal | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 35
} | [
{
"pp": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 ≤ z\n⊢ (x * y) ^ z = x ^ z * y ^ z",
"usedConstants": [
"False",
"Real",
"Preorder.toLT",
"HMul.hMul",
"eq_false",
"LinearOrder.toDecidableEq",
"Real.instZero",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.inst... | simp [hz.not_gt, mul_rpow_eq_ite] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Convex.Segment | {
"line": 122,
"column": 6
} | {
"line": 122,
"column": 89
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Semiring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommMonoid E\ninst✝¹ : ZeroLEOneClass 𝕜\ninst✝ : Module 𝕜 E\nx z : E\nx✝ : z ∈ [x -[𝕜] x]\na b : 𝕜\nleft✝¹ : 0 ≤ a\nleft✝ : 0 ≤ b\nhab : a + b = 1\nhz : a • x + b • x = z\n⊢ z ∈ {x}",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Segment | {
"line": 155,
"column": 27
} | {
"line": 155,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝¹⁰ : Semiring 𝕜\ninst✝⁹ : PartialOrder 𝕜\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : ZeroLEOneClass 𝕜\ninst✝⁶ : Module 𝕜 E\nR : Type u_7\ninst✝⁵ : Semiring R\ninst✝⁴ : PartialOrder R\ninst✝³ : Module R E\ninst✝² : Module R 𝕜\ninst✝¹ : IsScalarTower R 𝕜 E\ninst✝ : SMulPos... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Segment | {
"line": 161,
"column": 27
} | {
"line": 161,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝¹¹ : Semiring 𝕜\ninst✝¹⁰ : PartialOrder 𝕜\ninst✝⁹ : AddCommMonoid E\ninst✝⁸ : ZeroLEOneClass 𝕜\ninst✝⁷ : Module 𝕜 E\nR : Type u_7\ninst✝⁶ : Semiring R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : Module R E\ninst✝³ : Module R 𝕜\ninst✝² : IsScalarTower R 𝕜 E\ninst✝¹ : Nontr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Ray | {
"line": 371,
"column": 4
} | {
"line": 371,
"column": 23
} | [
{
"pp": "case inr.inl\nR : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : IsStrictOrderedRing R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nx : M\ninst✝¹ : IsDomain R\ninst✝ : IsTorsionFree R M\nr : R\nhr : r < 0\nh₀ : r • x = 0\n⊢ x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Segment | {
"line": 185,
"column": 6
} | {
"line": 185,
"column": 78
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : Ring 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddRightMono 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : ZeroLEOneClass 𝕜\ninst✝¹ : Nontrivial 𝕜\ninst✝ : DenselyOrdered 𝕜\nx z : E\nx✝ : z ∈ openSegment 𝕜 x x\na b : 𝕜\nleft✝¹ : 0 < a\nleft✝ : 0 < b\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Segment | {
"line": 317,
"column": 2
} | {
"line": 317,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : CommRing 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ny z : E\nθ : 𝕜\nhθ₀ : 0 ≤ θ\nhθ₁ : θ ≤ 1\n⊢ SameRay 𝕜 ((fun θ ↦ y + θ • (z - y)) θ - y) (z - (fun θ ↦ y + θ • (z - y)) θ)",
"usedConstants": ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Ray | {
"line": 522,
"column": 25
} | {
"line": 522,
"column": 41
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrder R\ninst✝³ : IsStrictOrderedRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsTorsionFree R M\nx y : M\nhx : x = 0\n⊢ SameRay R x y ∨ SameRay R x (-y) ↔ ¬LinearIndependent R ![x, y]",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Ray | {
"line": 523,
"column": 25
} | {
"line": 523,
"column": 41
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrder R\ninst✝³ : IsStrictOrderedRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsTorsionFree R M\nx y : M\nhx : ¬x = 0\nhy : y = 0\n⊢ SameRay R x y ∨ SameRay R x (-y) ↔ ¬LinearIndependent R ![x, y]",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Ray | {
"line": 542,
"column": 6
} | {
"line": 544,
"column": 45
} | [
{
"pp": "case neg.refine_2.inl.inl\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrder R\ninst✝³ : IsStrictOrderedRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsTorsionFree R M\nx y : M\nhx : ¬x = 0\nhy : ¬y = 0\nm : Fin (Nat.succ 0).succ → R\nhm : m 0 • x = -(m 1 • y)\nhmne ... | refine
Or.inr (Or.inr (Or.inr ⟨-m 0, -m 1, Left.neg_pos_iff.2 hm0, Left.neg_pos_iff.2 hm1, ?_⟩))
linear_combination (norm := module) -hm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Ray | {
"line": 542,
"column": 6
} | {
"line": 544,
"column": 45
} | [
{
"pp": "case neg.refine_2.inl.inl\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrder R\ninst✝³ : IsStrictOrderedRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsTorsionFree R M\nx y : M\nhx : ¬x = 0\nhy : ¬y = 0\nm : Fin (Nat.succ 0).succ → R\nhm : m 0 • x = -(m 1 • y)\nhmne ... | refine
Or.inr (Or.inr (Or.inr ⟨-m 0, -m 1, Left.neg_pos_iff.2 hm0, Left.neg_pos_iff.2 hm1, ?_⟩))
linear_combination (norm := module) -hm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Convex.Segment | {
"line": 529,
"column": 4
} | {
"line": 529,
"column": 54
} | [
{
"pp": "case inr.refine_1\n𝕜 : Type u_1\ninst✝² : Field 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nx y z : 𝕜\nhxz : 0 ≤ z - x\nhyz : 0 ≤ y - z\nh : 0 < y - x\n⊢ (y - z) / (y - x) + (z - x) / (y - x) = 1",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"No... | rw [← add_div, sub_add_sub_cancel, div_self h.ne'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Convex.Segment | {
"line": 529,
"column": 4
} | {
"line": 529,
"column": 54
} | [
{
"pp": "case inr.refine_1\n𝕜 : Type u_1\ninst✝² : Field 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nx y z : 𝕜\nhxz : 0 ≤ z - x\nhyz : 0 ≤ y - z\nh : 0 < y - x\n⊢ (y - z) / (y - x) + (z - x) / (y - x) = 1",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"No... | rw [← add_div, sub_add_sub_cancel, div_self h.ne'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Convex.Segment | {
"line": 529,
"column": 4
} | {
"line": 529,
"column": 54
} | [
{
"pp": "case inr.refine_1\n𝕜 : Type u_1\ninst✝² : Field 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nx y z : 𝕜\nhxz : 0 ≤ z - x\nhyz : 0 ≤ y - z\nh : 0 < y - x\n⊢ (y - z) / (y - x) + (z - x) / (y - x) = 1",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"No... | rw [← add_div, sub_add_sub_cancel, div_self h.ne'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Ray | {
"line": 652,
"column": 2
} | {
"line": 652,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Field R\ninst✝³ : LinearOrder R\ninst✝² : IsStrictOrderedRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ (∃ r, 0 < r ∧ x = r • y) ↔ SameRay R y x",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"Preorder.toLT... | simp_rw [eq_comm (a := x)] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.LinearAlgebra.Ray | {
"line": 658,
"column": 2
} | {
"line": 658,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Field R\ninst✝³ : LinearOrder R\ninst✝² : IsStrictOrderedRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhy : y ≠ 0\n⊢ (∃ r, 0 < r ∧ x = r • y) ↔ SameRay R y x ∧ x ≠ 0",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"Preorder.toLT",
... | simp_rw [eq_comm (a := x)] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.LinearAlgebra.Ray | {
"line": 664,
"column": 2
} | {
"line": 664,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Field R\ninst✝³ : LinearOrder R\ninst✝² : IsStrictOrderedRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhy : y ≠ 0\n⊢ (∃ r, 0 ≤ r ∧ x = r • y) ↔ SameRay R y x",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"congrArg",
"Distrib... | simp_rw [eq_comm (a := x)] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 98,
"column": 2
} | {
"line": 103,
"column": 10
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\n⊢ vectorSpan k s = ⊥ ↔ s.Subsingleton",
"usedConstants": [
"Set.not_subsingleton_iff",
"Submodule",
"vsub_mem_vectorSpan",
"False",
... | refine ⟨fun h ↦ ?_, vectorSpan_of_subsingleton _⟩
by_contra hns
rw [Set.not_subsingleton_iff] at hns
obtain ⟨p, hp, q, hq, hpq⟩ := hns
have hpq' := vsub_mem_vectorSpan k hp hq
simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 98,
"column": 2
} | {
"line": 103,
"column": 10
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\n⊢ vectorSpan k s = ⊥ ↔ s.Subsingleton",
"usedConstants": [
"Set.not_subsingleton_iff",
"Submodule",
"vsub_mem_vectorSpan",
"False",
... | refine ⟨fun h ↦ ?_, vectorSpan_of_subsingleton _⟩
by_contra hns
rw [Set.not_subsingleton_iff] at hns
obtain ⟨p, hp, q, hq, hpq⟩ := hns
have hpq' := vsub_mem_vectorSpan k hp hq
simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Convex.Star | {
"line": 163,
"column": 81
} | {
"line": 172,
"column": 22
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : Semiring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\nx : E\ns : Set E\nhx : x ∈ s\n⊢ StarConvex 𝕜 x s ↔ ∀ ⦃y : E⦄, y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ s",
"usedConstants": [
"Eq.mpr",
"... | by
refine ⟨fun h y hy a b ha hb hab => h hy ha.le hb.le hab, ?_⟩
intro h y hy a b ha hb hab
obtain rfl | ha := ha.eq_or_lt
· rw [zero_add] at hab
rwa [hab, one_smul, zero_smul, zero_add]
obtain rfl | hb := hb.eq_or_lt
· rw [add_zero] at hab
rwa [hab, one_smul, zero_smul, add_zero]
exact h hy ha hb... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 256,
"column": 15
} | {
"line": 256,
"column": 26
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\nv : V\np : P\nhp : p ∈ s\nh : v +ᵥ p ∈ s\n⊢ v ∈ s.direction",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 343,
"column": 4
} | {
"line": 343,
"column": 33
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : P\ndirection : Submodule k V\nc : k\np₁ p₂ p₃ : P\nhp₁ : p₁ ∈ {q | q -ᵥ p ∈ direction}\nhp₂ : p₂ ∈ {q | q -ᵥ p ∈ direction}\nhp₃ : p₃ ∈ {q | q -ᵥ p ∈ direction}\n⊢ c • (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 15
} | [
{
"pp": "case h.mp\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : P\ndirection : Submodule k V\np₁ : P\nhp₁ : p₁ ∈ mk' p direction\np₂ : P\nhp₂ : p₂ ∈ mk' p direction\n⊢ p₁ -ᵥ p₂ ∈ direction",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Star | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : Semiring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\nx z : E\ns : Set E\nhs : StarConvex 𝕜 (z + x) s\n⊢ StarConvex 𝕜 x ((fun x ↦ x + z) ⁻¹' s)",
"usedConstants": [
"Eq.mpr",
"congrArg",
"DistribMulAction.toDi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Star | {
"line": 277,
"column": 2
} | {
"line": 277,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : CommSemiring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : StarConvex 𝕜 0 s\nc : 𝕜\n⊢ StarConvex 𝕜 0 (c • s)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Star | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 94
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddRightMono 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMulWithZero 𝕜 E\ns : Set E\nx : E\nx✝ : x ∈ s\nh : ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → a • 0 + b • x ∈ s\na : 𝕜\nha₀ : 0 ≤ a\nha₁ : a ≤ 1\n⊢ a • x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Star | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddRightMono 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nx y : E\ns : Set E\nhs : StarConvex 𝕜 x s\nhy : x + y ∈ s\nt : 𝕜\nht₀ : 0 ≤ t\nht₁ : t ≤ 1\nh : x + t • y = (1 - t) • x + t • (x + y)\n⊢ (1 - t) • x + t • (... | exact hs hy (sub_nonneg_of_le ht₁) ht₀ (sub_add_cancel _ _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Convex.Star | {
"line": 326,
"column": 36
} | {
"line": 326,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddRightMono 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nx : E\ns : Set E\nhs : StarConvex 𝕜 0 s\nhx : x ∈ s\nt : 𝕜\nht₀ : 0 ≤ t\nht₁ : t ≤ 1\n⊢ t • x ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Star | {
"line": 326,
"column": 68
} | {
"line": 326,
"column": 79
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddRightMono 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nx : E\ns : Set E\nhs : StarConvex 𝕜 0 s\nhx : x ∈ s\nt : 𝕜\nht₀ : 0 ≤ t\nht₁ : t ≤ 1\n⊢ 0 + x ∈ s",
"usedConstants": [
"Eq.mpr",
"congrArg",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : Semiring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nz : E\n⊢ Convex 𝕜 ((fun x ↦ x + z) ⁻¹' s)",
"usedConstants": [
"Eq.mpr",
"congrArg",
"DistribMulAction.toDistribSMul",
"A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineMap | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 32
} | [
{
"pp": "case h\nk : Type u_1\nV1 : Type u_2\nP1 : Type u_3\nV2 : Type u_4\nP2 : Type u_5\ninst✝⁶ : Ring k\ninst✝⁵ : AddCommGroup V1\ninst✝⁴ : Module k V1\ninst✝³ : AffineSpace V1 P1\ninst✝² : AddCommGroup V2\ninst✝¹ : Module k V2\ninst✝ : AffineSpace V2 P2\nf g : P1 →ᵃ[k] P2\nh₁ : f.linear = g.linear\np : P1\n... | have := f.map_vadd' q (q -ᵥ p) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Convex.Basic | {
"line": 321,
"column": 56
} | {
"line": 321,
"column": 67
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝¹⁰ : Semiring 𝕜\ninst✝⁹ : PartialOrder 𝕜\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : ZeroLEOneClass 𝕜\ninst✝⁶ : Module 𝕜 E\nR : Type u_5\ninst✝⁵ : Semiring R\ninst✝⁴ : PartialOrder R\ninst✝³ : Module R E\ninst✝² : Module R 𝕜\ninst✝¹ : IsScalarTower R 𝕜 E\ninst✝ : SMulPos... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 898,
"column": 2
} | {
"line": 898,
"column": 13
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np : P\nd₁ d₂ : Submodule k V\nh : ∀ ⦃x : P⦄, x -ᵥ p ∈ d₁ → x -ᵥ p ∈ d₂\nx : V\nhx : x ∈ d₁\n⊢ x ∈ d₂",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 322,
"column": 28
} | {
"line": 322,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝¹⁰ : Semiring 𝕜\ninst✝⁹ : PartialOrder 𝕜\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : ZeroLEOneClass 𝕜\ninst✝⁶ : Module 𝕜 E\nR : Type u_5\ninst✝⁵ : Semiring R\ninst✝⁴ : PartialOrder R\ninst✝³ : Module R E\ninst✝² : Module R 𝕜\ninst✝¹ : IsScalarTower R 𝕜 E\ninst✝ : SMulPos... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | {
"line": 898,
"column": 44
} | {
"line": 898,
"column": 55
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np : P\nd₁ d₂ : Submodule k V\nh : ∀ ⦃x : P⦄, x -ᵥ p ∈ d₁ → x -ᵥ p ∈ d₂\nx : V\nhx : x ∈ d₁\n⊢ (x +ᵥ p) -ᵥ p ∈ d₁",
"usedConstants": [
"Eq.mpr",
"Submodule",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 417,
"column": 2
} | {
"line": 417,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : CommSemiring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nz : E\nc : 𝕜\n⊢ Convex 𝕜 ((fun x ↦ z + c • x) '' s)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 446,
"column": 14
} | {
"line": 446,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : Ring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\na : E\nh : Convex 𝕜 (a +ᵥ s)\n⊢ Convex 𝕜 s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 450,
"column": 33
} | {
"line": 450,
"column": 79
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : Ring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nQ : AffineSubspace 𝕜 E\nx : E\nhx : x ∈ ↑Q\ny : E\nhy : y ∈ ↑Q\na b : 𝕜\nx✝¹ : 0 ≤ a\nx✝ : 0 ≤ b\nhab : a + b = 1\n⊢ a • x + b • y ∈ ↑Q",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 478,
"column": 2
} | {
"line": 478,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : AddRightMono 𝕜\nhs : Convex 𝕜 s\nx : E\nzero_mem : 0 ∈ s\nhx : x ∈ s\nt : 𝕜\nht : t ∈ Icc 0 1\n⊢ t • x ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Basic | {
"line": 478,
"column": 43
} | {
"line": 478,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : AddRightMono 𝕜\nhs : Convex 𝕜 s\nx : E\nzero_mem : 0 ∈ s\nhx : x ∈ s\nt : 𝕜\nht : t ∈ Icc 0 1\n⊢ 0 + x ∈ s",
"usedConstants": [
"Eq.mpr",
"congrA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineMap | {
"line": 570,
"column": 96
} | {
"line": 573,
"column": 22
} | [
{
"pp": "k : Type u_1\nV1 : Type u_2\nP1 : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V1\ninst✝¹ : Module k V1\ninst✝ : AffineSpace V1 P1\np₀ p₁ : P1\nc : k\n⊢ (lineMap p₀ p₁) (1 - c) = (lineMap p₁ p₀) c",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"neg_sub",
"Semiring.toModule"... | by
rw [lineMap_symm p₀, comp_apply]
congr
simp [lineMap_apply] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Convex.Basic | {
"line": 482,
"column": 2
} | {
"line": 482,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : Ring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : AddRightMono 𝕜\nh : Convex 𝕜 s\nx y : E\nhx : x ∈ s\nhy : y ∈ s\n⊢ MapsTo (⇑(AffineMap.lineMap x y)) (Icc 0 1) s",
"usedConstants": [
"Eq.mpr",
"S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineMap | {
"line": 879,
"column": 17
} | {
"line": 879,
"column": 48
} | [
{
"pp": "k : Type u_2\nV1 : Type u_3\nP1 : Type u_4\ninst✝⁵ : CommRing k\ninst✝⁴ : AddCommGroup V1\ninst✝³ : AffineSpace V1 P1\ninst✝² : Module k V1\ninst✝¹ : IsTorsionFree k V1\ninst✝ : IsCancelMulZero k\nc : P1\nr : k\nhr : r ≠ 0\nx✝¹ x✝ : P1\nh : (homothety c r) x✝¹ = (homothety c r) x✝\n⊢ x✝¹ = x✝",
"us... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Bornology.Absorbs | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 35
} | [
{
"pp": "M : Type u_1\nE : Type u_2\ninst✝³ : Monoid M\ninst✝² : AddGroup E\ninst✝¹ : DistribMulAction M E\ninst✝ : Bornology M\ns₁ s₂ t₁ t₂ : Set E\nh₁ : Absorbs M s₁ t₁\nh₂ : Absorbs M s₂ t₂\n⊢ Absorbs M (s₁ - s₂) (t₁ - t₂)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.BalancedCoreHull | {
"line": 172,
"column": 2
} | {
"line": 172,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nx : E\nhx : x ∈ balancedCoreAux 𝕜 s\n⊢ x ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Basic | {
"line": 136,
"column": 15
} | {
"line": 136,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝³ : SeminormedRing 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : NormOneClass 𝕜\nh : Balanced 𝕜 s\nx : E\nhx : -x ∈ s\n⊢ x ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Basic | {
"line": 137,
"column": 16
} | {
"line": 137,
"column": 27
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝³ : SeminormedRing 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : NormOneClass 𝕜\nh : Balanced 𝕜 s\nx : E\nhx : x ∈ s\n⊢ -x ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.BalancedCoreHull | {
"line": 247,
"column": 4
} | {
"line": 247,
"column": 90
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : NormedDivisionRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul 𝕜 E\nU : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nhU : U ∈ 𝓝 0\nh : Tendsto (fun x ↦ x.1 • x.2) (𝓝 (0, 0)) (𝓝 0)\n⊢ ∃ r V, 0 < r ∧ V ∈ 𝓝 0 ∧ ∀ (c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Basic | {
"line": 208,
"column": 28
} | {
"line": 208,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\na : 𝕜\nhs : Balanced 𝕜 s\nha : ‖1‖ ≤ ‖a‖\n⊢ s ⊆ a • s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Basic | {
"line": 245,
"column": 4
} | {
"line": 245,
"column": 78
} | [
{
"pp": "case inr.h\n𝕜 : Type u_1\nE : Type u_3\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\nA : Set E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousSMul 𝕜 E\nhA : Balanced 𝕜 A\na : 𝕜\nha : ‖a‖ ≤ 1\nh : a ≠ 0\n⊢ (fun x ↦ a • x) '' interior A ⊆ interior A",
"usedConstants": ... | exact ((isOpenMap_smul₀ h).mapsTo_interior <| hA.smul_mem ha).image_subset | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.LocallyConvex.Bounded | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 47
} | [
{
"pp": "E : Type u_3\nF : Type u_4\n𝕜₁ : Type u_6\n𝕜₂ : Type u_7\ninst✝⁹ : NormedDivisionRing 𝕜₁\ninst✝⁸ : NormedDivisionRing 𝕜₂\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜₁ E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Module 𝕜₂ F\ninst✝³ : TopologicalSpace E\ninst✝² : TopologicalSpace F\nσ : 𝕜₁ →+* 𝕜₂\ninst✝¹... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Bounded | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_6\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\n𝕝 : Type u_7\ninst✝⁵ : NontriviallyNormedField 𝕝\ninst✝⁴ : NormedAlgebra 𝕜 𝕝\ninst✝³ : Module 𝕝 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul 𝕝 E\ninst✝ : IsScalarTower 𝕜 𝕝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Bounded | {
"line": 309,
"column": 14
} | {
"line": 309,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝⁵ : NormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : ContinuousAdd E\ns : Set E\nx : E\nh : IsVonNBounded 𝕜 (x +ᵥ s)\n⊢ IsVonNBounded 𝕜 s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Equicontinuity | {
"line": 108,
"column": 20
} | {
"line": 108,
"column": 72
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : PseudoMetricSpace α\nι : Type u_4\ninst✝ : PseudoMetricSpace β\nb : ℝ → ℝ\nb_lim : Tendsto b (𝓝 0) (𝓝 0)\nF : ι → β → α\nH : ∀ (x y : β) (i : ι), dist (F i x) (F i y) ≤ b (dist x y)\nε : ℝ\nε0 : ε > 0\nδ : ℝ\nδ0 : δ > 0\nhδ : ∀ ⦃x : ℝ⦄, dist x 0 < δ → dist (b x) 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 101,
"column": 4
} | {
"line": 101,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf g : E → β\nhf : ConvexOn 𝕜 s f\nhfg : EqOn f g s\nx : E\nhx : x ∈ s\ny : E\nhy : y... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf g : E → β\nhf : ConcaveOn 𝕜 s f\nhfg : EqOn f g s\nx : E\nhx : x ∈ s\ny : E\nhy : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 77
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf g : E → β\nhf : StrictConvexOn 𝕜 s f\nhfg : EqOn f g s\nx : E\nhx : x ∈ s\ny : E\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 77
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf g : E → β\nhf : StrictConcaveOn 𝕜 s f\nhfg : EqOn f g s\nx : E\nhx : x ∈ s\ny : E\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : Module 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nhf : ConvexOn 𝕜 s f\nc : E\n⊢ ConvexOn 𝕜 ((fun z ↦ c + z) ⁻¹' s) (f ∘ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 149,
"column": 14
} | {
"line": 149,
"column": 18
} | [
{
"pp": "case hpure\nG : Type u\ninst✝ : Group G\nB : GroupFilterBasis G\nx₀ a : G\nU : Set G\n⊢ U ∈ B.toFilterBasis → a ∈ (fun y ↦ a * y) '' id U",
"usedConstants": [
"instMembershipSetFilterBasis",
"Membership.mem",
"FilterBasis",
"GroupFilterBasis.toFilterBasis",
"Set"
]... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 151,
"column": 14
} | {
"line": 151,
"column": 18
} | [
{
"pp": "case hopen\nG : Type u\ninst✝ : Group G\nB : GroupFilterBasis G\nx₀ a : G\nU : Set G\n⊢ U ∈ B.toFilterBasis →\n ∀ᶠ (x : G) in map (fun y ↦ a * y) B.filter, (fun y ↦ a * y) '' id U ∈ map (fun y ↦ x * y) B.filter",
"usedConstants": [
"instMembershipSetFilterBasis",
"Membership.mem",
... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 199,
"column": 12
} | {
"line": 199,
"column": 16
} | [
{
"pp": "case refine_1\nG : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\nthis : TopologicalSpace G := B.topology\nbasis : (𝓝 1).HasBasis (fun V ↦ V ∈ B) id\nbasis' : (𝓝 1 ×ˢ 𝓝 1).HasBasis (fun i ↦ i.1 ∈ B ∧ i.2 ∈ B) fun i ↦ id i.1 ×ˢ id i.2\nU : Set G\n⊢ U ∈ B → ∃ V W, (V ∈ B ∧ W ∈ B) ∧ ∀ (a b : G), a... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Analysis.Convex.Strict | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝⁵ : Semiring 𝕜\ninst✝⁴ : PartialOrder 𝕜\ninst✝³ : TopologicalSpace E\ninst✝² : AddCancelCommMonoid E\ninst✝¹ : ContinuousAdd E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : StrictConvex 𝕜 s\nz : E\n⊢ StrictConvex 𝕜 ((fun x ↦ x + z) ⁻¹' s)",
"usedConstants": [
"Eq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 205,
"column": 12
} | {
"line": 205,
"column": 16
} | [
{
"pp": "case refine_2\nG : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\nthis : TopologicalSpace G := B.topology\nbasis : (𝓝 1).HasBasis (fun V ↦ V ∈ B) id\nbasis' : (𝓝 1 ×ˢ 𝓝 1).HasBasis (fun i ↦ i.1 ∈ B ∧ i.2 ∈ B) fun i ↦ id i.1 ×ˢ id i.2\nU : Set G\n⊢ U ∈ B → ∃ ia ∈ B, ∀ x ∈ id ia, x⁻¹ ∈ id U",
... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 206,
"column": 4
} | {
"line": 206,
"column": 15
} | [
{
"pp": "case refine_2\nG : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\nthis : TopologicalSpace G := B.topology\nbasis : (𝓝 1).HasBasis (fun V ↦ V ∈ B) id\nbasis' : (𝓝 1 ×ˢ 𝓝 1).HasBasis (fun i ↦ i.1 ∈ B ∧ i.2 ∈ B) fun i ↦ id i.1 ×ˢ id i.2\nU : Set G\nU_in : U ∈ B\n⊢ ∃ ia ∈ B, ∀ x ∈ id ia, x⁻¹ ∈ id U... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Strict | {
"line": 233,
"column": 2
} | {
"line": 233,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝⁵ : Semiring 𝕜\ninst✝⁴ : PartialOrder 𝕜\ninst✝³ : TopologicalSpace E\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : ContinuousAdd E\ns : Set E\nhs : StrictConvex 𝕜 s\nz : E\n⊢ StrictConvex 𝕜 ((fun x ↦ z + x) '' s)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Strict | {
"line": 236,
"column": 49
} | {
"line": 236,
"column": 76
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝⁵ : Semiring 𝕜\ninst✝⁴ : PartialOrder 𝕜\ninst✝³ : TopologicalSpace E\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : ContinuousAdd E\ns : Set E\nhs : StrictConvex 𝕜 s\nz : E\n⊢ StrictConvex 𝕜 ((fun x ↦ x + z) '' s)",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 212,
"column": 12
} | {
"line": 212,
"column": 16
} | [
{
"pp": "case refine_4\nG : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\nthis : TopologicalSpace G := B.topology\nbasis : (𝓝 1).HasBasis (fun V ↦ V ∈ B) id\nbasis' : (𝓝 1 ×ˢ 𝓝 1).HasBasis (fun i ↦ i.1 ∈ B ∧ i.2 ∈ B) fun i ↦ id i.1 ×ˢ id i.2\nx₀ : G\nU : Set G\n⊢ U ∈ B → ∃ ia ∈ B, ∀ x ∈ id ia, x₀ * x *... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 227,
"column": 2
} | {
"line": 227,
"column": 13
} | [
{
"pp": "G : Type u\ninst✝ : Group G\nt : TopologicalSpace G\nF : GroupFilterBasis G\nhG : F.topology = t\n⊢ {1} ⊆ ⋂₀ F.sets",
"usedConstants": [
"Eq.mpr",
"InvOneClass.toOne",
"instMembershipSetFilterBasis",
"DivInvOneMonoid.toInvOneClass",
"Group.toDivisionMonoid",
"Mem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 274,
"column": 12
} | {
"line": 274,
"column": 16
} | [
{
"pp": "case hmul\nR✝ : Type u\ninst✝¹ : Ring R✝\nB✝ : RingFilterBasis R✝\nR : Type u\ninst✝ : Ring R\nB : RingFilterBasis R\nB' : AddGroupFilterBasis R := B.toAddGroupFilterBasis\nthis✝ : TopologicalSpace R := B'.topology\nbasis : (𝓝 0).HasBasis (fun V ↦ V ∈ B') id\nbasis' : (𝓝 0 ×ˢ 𝓝 0).HasBasis (fun i ↦ ... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Analysis.Convex.Strict | {
"line": 312,
"column": 2
} | {
"line": 312,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝⁵ : Ring 𝕜\ninst✝⁴ : PartialOrder 𝕜\ninst✝³ : TopologicalSpace E\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\nx : E\ninst✝ : AddRightStrictMono 𝕜\nhs : StrictConvex 𝕜 s\nzero_mem : 0 ∈ s\nhx : x ∈ s\nhx₀ : x ≠ 0\nt : 𝕜\nht₀ : 0 < t\nht₁ : t < 1\n⊢ t ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Strict | {
"line": 312,
"column": 43
} | {
"line": 312,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_3\ninst✝⁵ : Ring 𝕜\ninst✝⁴ : PartialOrder 𝕜\ninst✝³ : TopologicalSpace E\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\nx : E\ninst✝ : AddRightStrictMono 𝕜\nhs : StrictConvex 𝕜 s\nzero_mem : 0 ∈ s\nhx : x ∈ s\nhx₀ : x ≠ 0\nt : 𝕜\nht₀ : 0 < t\nht₁ : t < 1\n⊢ 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 282,
"column": 4
} | {
"line": 282,
"column": 15
} | [
{
"pp": "case hmul_left\nR✝ : Type u\ninst✝¹ : Ring R✝\nB✝ : RingFilterBasis R✝\nR : Type u\ninst✝ : Ring R\nB : RingFilterBasis R\nB' : AddGroupFilterBasis R := B.toAddGroupFilterBasis\nthis✝ : TopologicalSpace R := B'.topology\nbasis : (𝓝 0).HasBasis (fun V ↦ V ∈ B') id\nbasis' : (𝓝 0 ×ˢ 𝓝 0).HasBasis (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 286,
"column": 4
} | {
"line": 286,
"column": 15
} | [
{
"pp": "case hmul_right\nR✝ : Type u\ninst✝¹ : Ring R✝\nB✝ : RingFilterBasis R✝\nR : Type u\ninst✝ : Ring R\nB : RingFilterBasis R\nB' : AddGroupFilterBasis R := B.toAddGroupFilterBasis\nthis✝ : TopologicalSpace R := B'.topology\nbasis : (𝓝 0).HasBasis (fun V ↦ V ∈ B') id\nbasis' : (𝓝 0 ×ˢ 𝓝 0).HasBasis (fu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 391,
"column": 21
} | {
"line": 391,
"column": 32
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : TopologicalSpace R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nB : ModuleFilterBasis R M\ninst✝ : IsTopologicalRing R\nB' : AddGroupFilterBasis M := B.toAddGroupFilterBasis\nx✝² : TopologicalSpace M := B'.topology\nx✝¹ : IsTopologicalAddGroup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 787,
"column": 4
} | {
"line": 787,
"column": 26
} | [
{
"pp": "case mp\n𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁷ : Semiring 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommGroup β\ninst✝³ : PartialOrder β\ninst✝² : IsOrderedAddMonoid β\ninst✝¹ : SMul 𝕜 E\ninst✝ : Module 𝕜 β\ns : Set E\nf : E → β\nhconv : Convex 𝕜 s\nh :\n ∀ ⦃x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 392,
"column": 10
} | {
"line": 392,
"column": 21
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : TopologicalSpace R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nB : ModuleFilterBasis R M\ninst✝ : IsTopologicalRing R\nB' : AddGroupFilterBasis M := B.toAddGroupFilterBasis\nx✝¹ : TopologicalSpace M := B'.topology\nx✝ : IsTopologicalAddGroup ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 403,
"column": 14
} | {
"line": 403,
"column": 18
} | [
{
"pp": "R✝ : Type u_1\nM✝ : Type u_2\ninst✝⁶ : CommRing R✝\ninst✝⁵ : TopologicalSpace R✝\ninst✝⁴ : AddCommGroup M✝\ninst✝³ : Module R✝ M✝\nB : ModuleFilterBasis R✝ M✝\nR : Type u_3\nM : Type u_4\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nBR : RingFilterBasis R\nBM : AddGroupFilterBasis ... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Analysis.Convex.Function | {
"line": 884,
"column": 2
} | {
"line": 884,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCancelCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : Module 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nhf : StrictConvexOn 𝕜 s f\nc : E\n⊢ StrictConvexOn 𝕜 ((fun z ↦ c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 889,
"column": 2
} | {
"line": 889,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : PartialOrder 𝕜\ninst✝⁴ : AddCancelCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : Module 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nhf : StrictConcaveOn 𝕜 s f\nc : E\n⊢ StrictConcaveOn 𝕜 ((fun z ↦... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.FilterBasis | {
"line": 408,
"column": 17
} | {
"line": 408,
"column": 21
} | [
{
"pp": "R✝ : Type u_1\nM✝ : Type u_2\ninst✝⁶ : CommRing R✝\ninst✝⁵ : TopologicalSpace R✝\ninst✝⁴ : AddCommGroup M✝\ninst✝³ : Module R✝ M✝\nB : ModuleFilterBasis R✝ M✝\nR : Type u_3\nM : Type u_4\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nBR : RingFilterBasis R\nBM : AddGroupFilterBasis ... | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Analysis.Convex.Function | {
"line": 977,
"column": 4
} | {
"line": 977,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁷ : Field 𝕜\ninst✝⁶ : LinearOrder 𝕜\ninst✝⁵ : IsStrictOrderedRing 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nh :\n ∀ ⦃x : E⦄,\n x ∈ s →\n ∀ ⦃y : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Function | {
"line": 995,
"column": 4
} | {
"line": 995,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_5\ninst✝⁷ : Field 𝕜\ninst✝⁶ : LinearOrder 𝕜\ninst✝⁵ : IsStrictOrderedRing 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nh :\n ∀ ⦃x : E⦄,\n x ∈ s →\n ∀ ⦃y : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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