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.LinearAlgebra.AffineSpace.Centroid | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 17
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nι : Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : Invertible 2\np : ι → P\ni₁ i₂ : ι\nh : ¬i₁ = i₂\n⊢ ↑(1 + 1) ≠ 0",
"usedConstants": [
"AddGroupWithOne.toAdd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Centroid | {
"line": 106,
"column": 4
} | {
"line": 108,
"column": 70
} | [
{
"pp": "case neg\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nι : Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : Invertible 2\np : ι → P\ni₁ i₂ : ι\nh : ¬i₁ = i₂\nhc : ↑(#{i₁, i₂}) ≠ 0\n⊢ centroid k {i₁, i₂} p = 2⁻¹ • (p ... | rw [centroid_def,
affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one _ _ _
(sum_centroidWeights_eq_one_of_cast_card_ne_zero _ hc) (p i₁)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.AffineSpace.Combination | {
"line": 455,
"column": 2
} | {
"line": 455,
"column": 60
} | [
{
"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\nι : Type u_4\nι₂ : Type u_5\ns₂ : Finset ι₂\ne : ι₂ ↪ ι\nw : ι → k\np : ι → P\n⊢ (affineCombination k (map e s₂) p) w = (affineCombination k s₂ (p ∘ ⇑e)) (w ∘ ⇑e)",
"usedCons... | simp_rw [affineCombination_apply, weightedVSubOfPoint_map] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.LinearAlgebra.AffineSpace.Combination | {
"line": 455,
"column": 2
} | {
"line": 455,
"column": 60
} | [
{
"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\nι : Type u_4\nι₂ : Type u_5\ns₂ : Finset ι₂\ne : ι₂ ↪ ι\nw : ι → k\np : ι → P\n⊢ (affineCombination k (map e s₂) p) w = (affineCombination k s₂ (p ∘ ⇑e)) (w ∘ ⇑e)",
"usedCons... | simp_rw [affineCombination_apply, weightedVSubOfPoint_map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.AffineSpace.Combination | {
"line": 455,
"column": 2
} | {
"line": 455,
"column": 60
} | [
{
"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\nι : Type u_4\nι₂ : Type u_5\ns₂ : Finset ι₂\ne : ι₂ ↪ ι\nw : ι → k\np : ι → P\n⊢ (affineCombination k (map e s₂) p) w = (affineCombination k s₂ (p ∘ ⇑e)) (w ∘ ⇑e)",
"usedCons... | simp_rw [affineCombination_apply, weightedVSubOfPoint_map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 76,
"column": 4
} | {
"line": 76,
"column": 20
} | [
{
"pp": "case mpr\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : Fintype ι\np : ι → P\ns : Finset ι\nw : ι → k\nhw : ∑ i, (↑s).indicator w i = 0\nhs : (univ.weightedVSub p) ((↑s).indicator w) = 0\ni : ι\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 241,
"column": 4
} | {
"line": 241,
"column": 84
} | [
{
"pp": "R : Type u_1\n𝕜 : Type u_3\nE : Type u_7\ninst✝⁵ : SeminormedRing 𝕜\ninst✝⁴ : AddGroup E\ninst✝³ : SMul 𝕜 E\ninst✝² : SMul R ℝ\ninst✝¹ : SMul R ℝ≥0\ninst✝ : IsScalarTower R ℝ≥0 ℝ\nr : R\np q : Seminorm 𝕜 E\nx y : ℝ\n⊢ r • max x y = max (r • x) (r • y)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 220,
"column": 6
} | {
"line": 220,
"column": 22
} | [
{
"pp": "case mpr\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\nι : Type u_4\np : ι → P\ns : Finset ι\nw : ι → k\nhw : ∑ i ∈ s, w i = 0\nhs : (s.weightedVSub p) w = 0\ni0 : ι\nhi0 : i0 ∈ s\nw1 : ι → k := update (const ι 0) i0 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 230,
"column": 4
} | {
"line": 230,
"column": 58
} | [
{
"pp": "case mp\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : Fintype ι\np : ι → P\nh :\n ∀ (s1 s2 : Finset ι) (w1 w2 : ι → k),\n ∑ i ∈ s1, w1 i = 1 →\n ∑ i ∈ s2, w2 i = 1 →\n (affineComb... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 276,
"column": 58
} | {
"line": 276,
"column": 74
} | [
{
"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\nι : Type u_4\np : ι → P\nha : AffineIndependent k p\nw₁ w₂ : ι → k\ns : Finset ι\nhw₁ : ∑ i ∈ s, w₁ i = 1\nhw₂ : ∑ i ∈ s, w₂ i = 1\nh : (affineCombination k s p) w₁ = (affin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 408,
"column": 2
} | {
"line": 408,
"column": 13
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nι : Type u_4\ninst✝¹ : Fintype ι\nι₂ : Type u_5\ninst✝ : Fintype ι₂\np : ι → P\nha : AffineIndependent k p\nw₁ : ι → k\nw₂ : ι₂ → k\nhw₁ : ∑ i, w₁ i = 1\nhw₂ : ∑ i, w₂ i = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | {
"line": 671,
"column": 2
} | {
"line": 671,
"column": 22
} | [
{
"pp": "k : Type u_1\nV₁ : Type u_2\nP₁ : Type u_3\ninst✝⁶ : Ring k\ninst✝⁵ : AddCommGroup V₁\ninst✝⁴ : Module k V₁\ninst✝³ : AffineSpace V₁ P₁\nV₂ : Type u_8\nP₂ : Type u_9\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module k V₂\ninst✝ : AffineSpace V₂ P₂\ns : Set P₁\nf g : P₁ →ᵃ[k] P₂\nh_span : affineSpan k s = ⊤\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | {
"line": 895,
"column": 8
} | {
"line": 895,
"column": 19
} | [
{
"pp": "case neg.refine_2\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\ns₁ s₂ : AffineSubspace k P\nhd : s₁.direction = s₂.direction\nhb : s₁ = ⊥ ↔ s₂ = ⊥\nhs₁ : ¬s₁ = ⊥\nhs₂ : s₂ ≠ ⊥\np₁ : P\nhp₁ : p₁ ∈ ↑s₁\np₂ : P\nhp₂ : p₂ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 481,
"column": 73
} | {
"line": 481,
"column": 84
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : Nontrivial k\np : ι → P\ns₁ s₂ : Set ι\nfs₁ : Finset ι\nhfs₁ : ↑fs₁ ⊆ s₁\nw₁ : ι → k\nhw₁ : ∑ i ∈ fs₁, w₁ i = 1\nfs₂ : Finset ι\nhfs₂ : ↑fs₂ ⊆ s₂\nw₂ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Pointwise | {
"line": 142,
"column": 9
} | {
"line": 142,
"column": 43
} | [
{
"pp": "case h\nM : Type u_1\nk : Type u_2\nV : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : Monoid M\ninst✝¹ : DistribMulAction M V\ninst✝ : SMulCommClass M k V\na : M\nha : IsUnit a\nx : V\n⊢ x ∈ a • ⊤ ↔ x ∈ ⊤",
"usedConstants": [
"Eq.mpr",
"instHSMul",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 485,
"column": 49
} | {
"line": 485,
"column": 60
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : Nontrivial k\np : ι → P\ns₁ s₂ : Set ι\nfs₁ : Finset ι\nhfs₁ : ↑fs₁ ⊆ s₁\nw₁ : ι → k\nhw₁ : ∑ i ∈ fs₁, w₁ i = 1\nfs₂ : Finset ι\nhfs₂ : ↑fs₂ ⊆ s₂\nw₂ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Basis | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 84
} | [
{
"pp": "ι : Type u_1\nk : Type u_5\nV : Type u_6\nP : Type u_7\ninst✝³ : AddCommGroup V\ninst✝² : AffineSpace V P\ninst✝¹ : Ring k\ninst✝ : Module k V\nb : AffineBasis ι k P\nhι : IsEmpty ι\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 904,
"column": 8
} | {
"line": 904,
"column": 23
} | [
{
"pp": "case inl\n𝕜 : Type u_3\nE : Type u_7\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nι : Sort u_12\np : ι → Seminorm 𝕜 E\nhp : BddAbove (range p)\ne : E\nr : ℝ\nhr : 0 < r\nh✝ : IsEmpty ι\n⊢ (⨆ i, p i).closedBall e r = ⋂ i, (p i).closedBall e r",
"usedConstants": [
"... | iSup_of_empty', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Seminorm | {
"line": 915,
"column": 2
} | {
"line": 921,
"column": 75
} | [
{
"pp": "case inr\n𝕜 : Type u_3\nE : Type u_7\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\np : Seminorm 𝕜 E\nk : 𝕜\nr : ℝ\nhk : k ≠ 0\n⊢ p.ball 0 (‖k‖ * r) ⊆ k • p.ball 0 r",
"usedConstants": [
"Seminorm.instSeminormClass",
"Iff.mpr",
"Seminorm.mem_ball_zero",... | · intro x
rw [Set.mem_smul_set, Seminorm.mem_ball_zero]
refine fun hx => ⟨k⁻¹ • x, ?_, ?_⟩
· rwa [Seminorm.mem_ball_zero, map_smul_eq_mul, norm_inv, ←
mul_lt_mul_iff_right₀ <| norm_pos_iff.mpr hk, ← mul_assoc, ← div_eq_mul_inv ‖k‖ ‖k‖,
div_self (ne_of_gt <| norm_pos_iff.mpr hk), one_mul]
... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | {
"line": 1003,
"column": 6
} | {
"line": 1003,
"column": 28
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ p₄ p₅ p₆ : P\nh₂ : p₂ ∉ affineSpan k {p₁, p₃}\nr₁ : kˣ\nhr₁ : ↑r₁ • (p₂ -ᵥ p₁) = p₅ -ᵥ p₄\nr₂ : k\nhr₂ : r₂ • (p₃ -ᵥ p₂) = p₆ -ᵥ p₅\nr₃ : k\nhr₃ : r₃ • (p₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 1080,
"column": 13
} | {
"line": 1080,
"column": 24
} | [
{
"pp": "case h\n𝕜 : Type u_3\nE : Type u_7\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nr : ℝ\nhp : p.closedBall 0 r ∈ 𝓝 0\nε : ℝ\nhε : ε > 0\nhr : r ≤ 0\n⊢ 0 < ‖1‖ ∧ ‖1‖ * r < ε",
"u... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 1081,
"column": 6
} | {
"line": 1081,
"column": 34
} | [
{
"pp": "case inr\n𝕜 : Type u_3\nE : Type u_7\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nr : ℝ\nhp : p.closedBall 0 r ∈ 𝓝 0\nε : ℝ\nhε : ε > 0\nhr : 0 < r\n⊢ ∃ k, 0 < ‖k‖ ∧ ‖k‖ * r < ε",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 1081,
"column": 4
} | {
"line": 1081,
"column": 67
} | [
{
"pp": "case inr\n𝕜 : Type u_3\nE : Type u_7\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nr : ℝ\nhp : p.closedBall 0 r ∈ 𝓝 0\nε : ℝ\nhε : ε > 0\nhr : 0 < r\n⊢ ∃ k, 0 < ‖k‖ ∧ ‖k‖ * r < ε",... | · simpa [lt_div_iff₀ hr] using exists_norm_lt 𝕜 (div_pos hε hr) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Seminorm | {
"line": 1180,
"column": 2
} | {
"line": 1180,
"column": 35
} | [
{
"pp": "𝕝 : Type u_6\nE : Type u_7\ninst✝³ : SeminormedRing 𝕝\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕝 E\ninst✝ : TopologicalSpace E\np : Seminorm 𝕝 E\nhp : Continuous[inst✝, _] ⇑p\nr : ℝ\nhr : 0 < r\nthis : Tendsto (⇑p) (𝓝 0) (𝓝 0)\n⊢ p.ball 0 r ∈ 𝓝 0",
"usedConstants": [
"Filter.instMembe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 1196,
"column": 4
} | {
"line": 1196,
"column": 48
} | [
{
"pp": "case a\n𝕜 : Type u_3\nE : Type u_7\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\nι : Sort u_12\ninst✝² : UniformSpace E\ninst✝¹ : IsUniformAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np' : ι → Prop\ns : ι → Set E\np : Seminorm 𝕜 E\nhb : (𝓝 0).HasBasis p' s\nh₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 737,
"column": 6
} | {
"line": 737,
"column": 23
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nh : AffineIndependent k fun p ↦ ↑p\np₁ : P\nhsv : Basis (↑(Basis.ofVectorSpaceIndex k V)) k V := Basis.ofVectorSpace k V\nhsvi : LinearIndependent (ι := ↑(Basis.ofVe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 751,
"column": 6
} | {
"line": 751,
"column": 23
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\np₁ : P\nh✝ : LinearIndependent k fun (v : ↑((fun p ↦ p -ᵥ p₁) '' (s \\ {p₁}))) ↦ ↑v\nh : LinearIndepOn k id ((fun p ↦ p -ᵥ p₁) '' (s \\ {p₁}))\nhp₁ : p₁ ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 800,
"column": 2
} | {
"line": 800,
"column": 13
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ : P\nh : p₁ ≠ p₂\ni₁ : { x // x ≠ 0 } := ⟨1, ⋯⟩\nhe' : ∀ (i : { x // x ≠ 0 }), i = i₁\nthis : Unique { x // x ≠ 0 }\n⊢ ![p₁, p₂] ↑i₁ -ᵥ ![p₁, p₂] 0 ≠ 0",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Seminorm | {
"line": 1258,
"column": 2
} | {
"line": 1259,
"column": 9
} | [
{
"pp": "𝕜 : Type u_3\nE : Type u_7\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\np q : Seminorm 𝕜 E\nε C : ℝ\nε_pos : 0 < ε\nc : 𝕜\nhc : 1 < ‖c‖\nhf : ∀ (x : E), ε / ‖c‖ ≤ p x → p x < ε → q x ≤ C * p x\nx : E\nhx : p x ≠ 0\nδ : 𝕜\nhδ : δ ≠ 0\nδxle : p (δ • x) < ε\nleδx : ε / ‖c‖ ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 817,
"column": 6
} | {
"line": 817,
"column": 72
} | [
{
"pp": "case pos\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\ni : ι\nha : AffineIndependent k fun x ↦ p ↑x\nhi : p i ∉ affineSpan k (p '' {x | x ≠ i})\ns : Finset ι\nw : ι → k\nhw : ∑ i ∈ s, w... | have hwm : ∑ i ∈ s, wm i = 0 := by simp [wm, ← Finset.mul_sum, hw] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 823,
"column": 8
} | {
"line": 824,
"column": 32
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\ni : ι\nha : AffineIndependent k fun x ↦ p ↑x\nhi : p i ∉ affineSpan k (p '' {x | x ≠ i})\ns : Finset ι\nw : ι → k\nhw : ∑ i ∈ s, w i = 0\nhs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 203,
"column": 58
} | {
"line": 203,
"column": 69
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_5\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex k P n\nw : Fin (n + 1) → k\nhw : ∑ i, w i = 1\ni : Fin (n + 1)\nh : w i = 0\nhk : Nontrivial k\n⊢ ∀ i_1 ∈ univ, i_1 ∉ {i}ᶜ → w i_1 = 0"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 892,
"column": 73
} | {
"line": 892,
"column": 84
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : DecidableEq ι\np : ι → P\nha : AffineIndependent k p\ni : ι\np₀ : P\nhp₀ : p₀ ∉ affineSpan k (p '' {x | x ≠ i})\nf : ι → P := update p i p₀\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 939,
"column": 6
} | {
"line": 939,
"column": 43
} | [
{
"pp": "case refine_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw : ι → k\ns : Finset ι\nhw : ∑ i ∈ s, w i = 1\ni₁... | rw [Finset.sum_pi_single', if_pos h₁] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 939,
"column": 6
} | {
"line": 939,
"column": 43
} | [
{
"pp": "case refine_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw : ι → k\ns : Finset ι\nhw : ∑ i ∈ s, w i = 1\ni₁... | rw [Finset.sum_pi_single', if_pos h₁] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 939,
"column": 6
} | {
"line": 939,
"column": 43
} | [
{
"pp": "case refine_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw : ι → k\ns : Finset ι\nhw : ∑ i ∈ s, w i = 1\ni₁... | rw [Finset.sum_pi_single', if_pos h₁] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 446,
"column": 79
} | {
"line": 446,
"column": 90
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nI : Set k\nn : ℕ\ns : Simplex k P n\nS : AffineSubspace k P\nhS : affineSpan k (Set.range s.points) ≤ S\nthis : Nonempty ↥S := Nonempty.map (⇑(AffineSubspace.inclusion hS)) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.StdSimplex | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 13
} | [
{
"pp": "𝕜 : Type u_2\nι : Type u_1\ninst✝³ : Semiring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : Fintype ι\ninst✝ : IsOrderedAddMonoid 𝕜\nf : ι → 𝕜\nh : f ∈ stdSimplex 𝕜 ι\n⊢ ∀ (i : ι), f ∈ Function.eval i ⁻¹' Icc (0 i) (1 i)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.StdSimplex | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 52
} | [
{
"pp": "𝕜 : Type u_2\nι : Type u_1\ninst✝⁴ : Semiring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : Fintype ι\ninst✝¹ : DecidableEq ι\ninst✝ : ZeroLEOneClass 𝕜\ni : ι\n⊢ (fun x ↦ if i = x then 1 else 0) ∈ stdSimplex 𝕜 ι",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 517,
"column": 2
} | {
"line": 517,
"column": 17
} | [
{
"pp": "case h\nk : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : PartialOrder k\ns : Simplex k P 0\np : P\nw : Fin 1 → k\nh : w 0 = 1\nhi : ∀ (i : Fin 1), 0 < w i ∧ w i < 1\n⊢ ¬(affineCombination k {0} s.points) w = p",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.StdSimplex | {
"line": 120,
"column": 39
} | {
"line": 120,
"column": 50
} | [
{
"pp": "𝕜 : Type ?u.8350\ninst✝² : Ring 𝕜\ninst✝¹ : PartialOrder 𝕜\ninst✝ : IsOrderedRing 𝕜\nf : ↑(stdSimplex 𝕜 (Fin 2))\n⊢ ↑f 0 + ↑f 1 = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.StdSimplex | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 37
} | [
{
"pp": "S : Type u_1\ninst✝¹ : Semiring S\ninst✝ : PartialOrder S\ns : ↑(stdSimplex S (Fin 2))\n⊢ s 0 + s 1 = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.StdSimplex | {
"line": 306,
"column": 2
} | {
"line": 306,
"column": 18
} | [
{
"pp": "S : Type u_1\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nX : Type u_2\ninst✝¹ : Fintype X\ninst✝ : IsOrderedRing S\ns : ↑(stdSimplex S X)\nx : X\n⊢ s x ≤ ∑ x, s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 551,
"column": 30
} | {
"line": 551,
"column": 41
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nI : Set k\nn : ℕ\ns : Simplex k P n\nfs : Finset (Fin (n + 1))\nm : ℕ\nh : #fs = m + 1\nw : Fin (n + 1) → k\nhw : ∑ i, w i = 1\nx✝ : (∀ i ∈ fs, w i ∈ I) ∧ ∀ i ∉ fs, w i = 0\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.AlexandrovDiscrete | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 53
} | [
{
"pp": "ι : Sort u_1\nα : Type u_3\ninst✝¹ : TopologicalSpace α\ninst✝ : AlexandrovDiscrete α\nf : ι → Set α\n⊢ (closure[inst✝¹] (⋃ i, f i))ᶜ = (⋃ i, closure[inst✝¹] (f i))ᶜ",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.iInter",
"Compl.compl",
"_private.Mathlib.Topology.Alex... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.AlexandrovDiscrete | {
"line": 196,
"column": 27
} | {
"line": 196,
"column": 41
} | [
{
"pp": "α : Type u_3\ninst✝ : TopologicalSpace α\nhα : ∀ (a : α), 𝓝 a = 𝓟 (nhdsKer {a})\nS : Set (Set α)\nhS : ∀ s ∈ S, ∀ (a : α), (nhdsKer {a} ∩ s).Nonempty → a ∈ s\na : α\nha : (nhdsKer {a} ∩ ⋃ i ∈ S, i).Nonempty\n⊢ a ∈ ⋃₀ S",
"usedConstants": [
"congrArg",
"Membership.mem",
"Eq.mp",
... | inter_iUnion₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 644,
"column": 67
} | {
"line": 644,
"column": 78
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁶ : Ring k\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module k V\ninst✝³ : AffineSpace V P\ninst✝² : PartialOrder k\ninst✝¹ : Nontrivial k\ninst✝ : ZeroLEOneClass k\nn : ℕ\ns : Simplex k P n\nfs : Finset (Fin (n + 1))\nhfs : fs ≠ univ\nm : ℕ\nh : #fs = m + 1\na : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 704,
"column": 30
} | {
"line": 704,
"column": 41
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁷ : Ring k\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module k V\ninst✝⁴ : AffineSpace V P\ninst✝³ : LinearOrder k\ninst✝² : IsOrderedAddMonoid k\ninst✝¹ : ZeroLEOneClass k\nn : ℕ\ninst✝ : NeZero n\ns : Simplex k P n\nw : Fin (n + 1) → k\nhw1 : ∑ i, w i = 1\nhp : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 68
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : AddRightMono 𝕜\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nhx : x ∈ closure s\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 40
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : AddRightMono 𝕜\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nhx : x ∈ closure s\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | {
"line": 711,
"column": 2
} | {
"line": 711,
"column": 48
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_4\ninst✝⁸ : Ring k\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : AffineSpace V P\ninst✝⁴ : LinearOrder k\ninst✝³ : Nontrivial k\ninst✝² : IsOrderedAddMonoid k\ninst✝¹ : ZeroLEOneClass k\nn : ℕ\ninst✝ : NeZero n\ns : Simplex k P n\n⊢ s.closedInterior \\ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Connected.LocPathConnected | {
"line": 158,
"column": 33
} | {
"line": 158,
"column": 64
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : LocPathConnectedSpace X\ne : Y → X\nhe : IsOpenEmbedding e\nthis : ∀ (y : Y), (𝓝 y).HasBasis (fun s ↦ s ∈ 𝓝 (e y) ∧ IsPathConnected s ∧ s ⊆ range e) fun x ↦ e ⁻¹' x\nx : Y\ns : Set X\nx✝ : s ∈ 𝓝 (e x) ∧ IsP... | image_preimage_eq_of_subset hse | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Convex.Topology | {
"line": 313,
"column": 4
} | {
"line": 313,
"column": 15
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\ns : Set E\n⊢ (closedConvexHull 𝕜) (closure s) ⊆ (closedConvexHull 𝕜) s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 407,
"column": 4
} | {
"line": 407,
"column": 71
} | [
{
"pp": "case mp\n𝕜 : Type u_4\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\ns : Set 𝕜\nhs : Convex 𝕜 s\nx : 𝕜\nhx : x ∈ s\ny : 𝕜\nhy : y ∈ s\nh : x ≠ y\nhs' : (interior [x -[𝕜] y]).Nonempty → (interior s).Nonempty\n⊢ ... | rw [segment_eq_Icc', interior_Icc, nonempty_Ioo, inf_lt_sup] at hs' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Algebra.Module.LocallyConvex | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 17
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : Field 𝕜\ninst✝⁷ : LinearOrder 𝕜\ninst✝⁶ : IsStrictOrderedRing 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : LocallyConvexSpace 𝕜 E\ns : Set E\nx : E\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 71
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝³ : Field R\ninst✝² : AddCommGroup E\ninst✝¹ : Module R E\nt : Finset ι\nw : ι → R\nz : ι → E\ninst✝ : (i : ι) → Decidable (w i ≠ 0)\ni : ι\nhit : i ∈ t\nhit' : i ∉ {i ∈ t | w i ≠ 0}\n⊢ w i = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns : Set E\nz : E\nhs : Convex ℝ s\n⊢ ConvexOn ℝ s fun z' ↦ dist z' z",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.partialOrder",
"Real",
"instSMulOfMul",
"dist_eq_norm",
"congrAr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 64,
"column": 2
} | {
"line": 64,
"column": 35
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na : E\nr : ℝ\n⊢ Convex ℝ (ball a r)",
"usedConstants": [
"Real.partialOrder",
"Real",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.to... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 41
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na : E\nr : ℝ\n⊢ Convex ℝ (closedBall a r)",
"usedConstants": [
"Real.partialOrder",
"Real",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 77
} | [
{
"pp": "case neg\nF : Type u_2\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : Nontrivial F\nx✝ : F\nr : ℝ\nhr : 0 ≤ r\nx : F\nh : x ∈ closedBall 0 r\nU : Set F\nhU_sub : sphere 0 r ⊆ U\nhU : Convex ℝ U\nzero_mem : 0 ∈ U\nhr₀ : ¬r = 0\nx_zero : ¬x = 0\nz : F := (r * ‖x‖⁻¹) • x\nhz_def : z = (... | have := StarConvex.smul_mem (hU.starConvex zero_mem) hz (by positivity) hr₁ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 173,
"column": 25
} | {
"line": 173,
"column": 41
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nx : E\nhx : x = 0\n⊢ IsConnected {y | SameRay ℝ x y}",
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real",
"IsConnected",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 216,
"column": 2
} | {
"line": 216,
"column": 54
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ns : Set E\nt : Finset ι\nw : ι → R\nz : ι → E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nhs : Convex R s\nh₀ : ∀ i ∈ t, 0 ≤ w i\nh₁ : ∑ i ∈ t, w i = 1\nhz : ∀ i ∈ t, z i ∈ s\n⊢ ∑ i ∈ t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 78
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns : Set E\nα : Type u_2\nf : Filter α\nx : E\ny z : α → E\nr : α → E → Prop\nhy : Tendsto y f (𝓝 x)\nhz : Tendsto z f (𝓝 x)\nhr : ∀ᶠ (p : α × E) in f ×ˢ 𝓝[s] x, r p.1 p.2\nseg : ∀ᶠ (χ : α) in f, [y χ -[ℝ] z χ] ⊆ s\n⊢ ∀ᶠ (p : α... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.UniformConvergence | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 31
} | [
{
"pp": "case hsmul_left\n𝕜 : Type u_1\nα : Type u_2\nE : Type u_3\nH : Type u_4\nhom : Type u_5\ninst✝¹⁰ : NormedField 𝕜\ninst✝⁹ : AddCommGroup H\ninst✝⁸ : Module 𝕜 H\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : UniformSpace E\ninst✝³ : IsUniformAddGroup E\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.UniformConvergence | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 43
} | [
{
"pp": "case hsmul_right\n𝕜 : Type u_1\nα : Type u_2\nE : Type u_3\nH : Type u_4\nhom : Type u_5\ninst✝¹⁰ : NormedField 𝕜\ninst✝⁹ : AddCommGroup H\ninst✝⁸ : Module 𝕜 H\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : UniformSpace E\ninst✝³ : IsUniformAddGroup E\ninst✝² :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 85,
"column": 57
} | {
"line": 85,
"column": 68
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.UniformConvergence | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\nE : Type u_3\nH : Type u_4\nhom : Type u_5\ninst✝⁹ : NormedField 𝕜\ninst✝⁸ : AddCommGroup H\ninst✝⁷ : Module 𝕜 H\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : UniformSpace E\ninst✝³ : IsUniformAddGroup E\ninst✝² : ContinuousSMul 𝕜 E\n𝔖 : Set (Set α)\ninst✝¹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 131,
"column": 14
} | {
"line": 131,
"column": 56
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 371,
"column": 40
} | {
"line": 371,
"column": 51
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁵ : Field R\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module R E\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ns : Set E\nx : E\ninst✝ : Fintype ι\nw : ι → R\nz : ι → E\nhw₀ : ∀ (i : ι), 0 ≤ w i\nhw₁ : ∑ i, w i = 1\nhz : ∀ (i : ι), z i ∈ s\nhx : ∑ i, w... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 371,
"column": 77
} | {
"line": 371,
"column": 88
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁵ : Field R\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module R E\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ns : Set E\nx : E\ninst✝ : Fintype ι\nw : ι → R\nz : ι → E\nhw₀ : ∀ (i : ι), 0 ≤ w i\nhw₁ : ∑ i, w i = 1\nhz : ∀ (i : ι), z i ∈ s\nhx : ∑ i, w... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 385,
"column": 4
} | {
"line": 385,
"column": 66
} | [
{
"pp": "case mp\nR : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns : Set E\nx : E\nι : Type\nt : Finset ι\nw : ι → R\nz : ι → E\nh : (∀ i ∈ t, 0 ≤ w i) ∧ ∑ i ∈ t, w i = 1 ∧ (∀ i ∈ t, z i ∈ s) ∧ t.centerMass w z =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 305,
"column": 32
} | {
"line": 305,
"column": 43
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : LinearOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrderedModule 𝕜 β... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 425,
"column": 2
} | {
"line": 425,
"column": 82
} | [
{
"pp": "R : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns : Set E\nhs : s.Finite\n⊢ (convexHull R) s = {x | ∃ w, (∀ y ∈ s, 0 ≤ w y) ∧ ∑ y ∈ hs.toFinset, w y = 1 ∧ hs.toFinset.centerMass w id = x}",
"usedConst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 541,
"column": 4
} | {
"line": 541,
"column": 29
} | [
{
"pp": "R : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns t₁ t₂ : Finset E\nht₁ : t₁ ⊆ s\nht₂ : t₂ ⊆ s\nx✝ : E\nw₁ : E → R\nh₁w₁ : ∀ y ∈ t₁, 0 ≤ w₁ y\nh₂w₁ : ∑ y ∈ t₁, w₁ y = 1\nh₃w₁ : ∑ y ∈ t₁, w₁ y • y = x✝\nw₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 600,
"column": 55
} | {
"line": 600,
"column": 66
} | [
{
"pp": "𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : Finite ι\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\ns : Set ι\nt✝ : (i : ι) → Set (E i)\nx : (i : ι) → E i\nval✝ : Fintype ι\nt : (i : ι) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 628,
"column": 6
} | {
"line": 628,
"column": 63
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsOrderedRing 𝕜\ninst✝¹ : AddCommGroup V\ninst✝ : Module 𝕜 V\nn : ℕ\ns : Simplex 𝕜 V n\nu : Finset (Fin (n + 1))\nw : Fin (n + 1) → 𝕜\nhw : ∀ i ∈ u, 0 ≤ w i\nhw1 : u.sum w = 1\nhw' : ∀ i ∈ u, w i ≤ 1\n⊢ ∑ i, (↑u).indi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 24
} | [
{
"pp": "case empty\n𝕜 : Type u_11\nE : Type u_12\nι : Type u_13\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\np : SeminormFamily 𝕜 E ι\nhp : ∀ (i : ι), Continuous[inst✝, _] ⇑(p i)\nr : ℝ\nhr : 0 < r\n⊢ Continuous[inst✝, _] ⇑(∅.sup p)",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 403,
"column": 19
} | {
"line": 403,
"column": 58
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\nF : Type u_7\nι : Type u_9\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\np : SeminormFamily 𝕜 E ι\nhp : WithSeminorms p\nu : F → E\nf : Filter F\ny₀ : E\nh : ∀ (s : Finset ι) (ε : ℝ), 0 < ε → ∀ᶠ (x : F) in f, (s.sup p)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM | {
"line": 146,
"column": 24
} | {
"line": 146,
"column": 55
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝⁸ : NormedField 𝕜₁\ninst✝⁷ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜₁ E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜₂ F\ninst✝¹ : UniformSpace F\ninst✝ : IsUniformAddGrou... | UniformSpace.replaceTopology_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 52
} | [
{
"pp": "case mpr\n𝕜 : Type u_2\nE : Type u_6\nι : Type u_9\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\ninst✝ : TopologicalSpace E\ns : Set E\nhp : WithSeminorms p\nh : ∀ (I : Finset ι), ∃ r > 0, ∀ x ∈ s, (I.sup p) x < r\ns' : Set E\nhs' : s' ... | rcases p.basisSets_iff.mp hs' with ⟨I, r, hr, hs'⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 603,
"column": 8
} | {
"line": 603,
"column": 59
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 609,
"column": 4
} | {
"line": 609,
"column": 15
} | [
{
"pp": "case refine_3.h.h.refine_1.a\n𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 625,
"column": 6
} | {
"line": 626,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 629,
"column": 29
} | {
"line": 629,
"column": 40
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 55
} | [
{
"pp": "case h\n𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹² : NormedField 𝕜₁\ninst✝¹¹ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : Module 𝕜₁ E\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup F\ninst✝⁶ : Module 𝕜₂ F\nR : Type u_6\ninst✝⁵ : NormedDivisionR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 632,
"column": 26
} | {
"line": 632,
"column": 37
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 634,
"column": 4
} | {
"line": 634,
"column": 15
} | [
{
"pp": "case refine_3.h.h.refine_2.inr\n𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 747,
"column": 6
} | {
"line": 747,
"column": 17
} | [
{
"pp": "case h\n𝕜 : Type u_2\n𝕜₂ : Type u_3\nE : Type u_6\nF : Type u_7\nι' : Type u_10\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module 𝕜 E\ninst✝⁶ : NormedField 𝕜₂\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Module 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝³ : RingHomIsometric σ₁₂\nκ : Type u_11... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 312,
"column": 36
} | {
"line": 312,
"column": 59
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 754,
"column": 4
} | {
"line": 754,
"column": 85
} | [
{
"pp": "case h\n𝕜 : Type u_2\n𝕜₂ : Type u_3\nE : Type u_6\nF : Type u_7\nι' : Type u_10\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module 𝕜 E\ninst✝⁶ : NormedField 𝕜₂\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Module 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝³ : RingHomIsometric σ₁₂\nκ : Type u_11... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 340,
"column": 14
} | {
"line": 340,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 759,
"column": 40
} | {
"line": 759,
"column": 51
} | [
{
"pp": "𝕜 : Type u_2\n𝕜₂ : Type u_3\nE : Type u_6\nF : Type u_7\nι' : Type u_10\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module 𝕜 E\ninst✝⁶ : NormedField 𝕜₂\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Module 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝³ : RingHomIsometric σ₁₂\nκ : Type u_11\nq : Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 366,
"column": 6
} | {
"line": 366,
"column": 89
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 369,
"column": 4
} | {
"line": 369,
"column": 71
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : Rin... | exact (hf x hx.le).trans ((div_le_iff₀' <| one_pos.trans hc).1 hcx) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 71
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : Rin... | simp only [Seminorm.mem_ball_zero, mem_closedBall_zero_iff] at hf ⊢ | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 428,
"column": 24
} | {
"line": 428,
"column": 78
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 430,
"column": 2
} | {
"line": 430,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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