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.Calculus.ContDiff.Comp | {
"line": 637,
"column": 29
} | {
"line": 637,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nx₀ : E\nm n : ℕ∞ω\nf : E ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 494,
"column": 4
} | {
"line": 494,
"column": 52
} | [
{
"pp": "case mp\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nf : E → F\nx : E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Deriv | {
"line": 123,
"column": 2
} | {
"line": 123,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nm n : ℕ∞ω\nf : 𝕜 → F\nx : 𝕜\nH : ContDiffAt 𝕜 n f x\nhmn : m + 1 ≤ n\n⊢ ContDiffAt 𝕜 m (deriv f) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 510,
"column": 15
} | {
"line": 510,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nf : E → F\nn : ℕ∞ω\ne : G... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 605,
"column": 4
} | {
"line": 605,
"column": 67
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns t : Set E\nf : E → F\nn : ℕ∞ω\nhf : ContDiffOn 𝕜 n f s\nhf' : ContDiffOn 𝕜 n f t\nhs : IsOpen[... | exact (hf x hx).contDiffAt (hs.mem_nhds hx) |>.contDiffWithinAt | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 605,
"column": 4
} | {
"line": 605,
"column": 67
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns t : Set E\nf : E → F\nn : ℕ∞ω\nhf : ContDiffOn 𝕜 n f s\nhf' : ContDiffOn 𝕜 n f t\nhs : IsOpen[... | exact (hf x hx).contDiffAt (hs.mem_nhds hx) |>.contDiffWithinAt | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.ContDiff.Basic | {
"line": 605,
"column": 4
} | {
"line": 605,
"column": 67
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns t : Set E\nf : E → F\nn : ℕ∞ω\nhf : ContDiffOn 𝕜 n f s\nhf' : ContDiffOn 𝕜 n f t\nhs : IsOpen[... | exact (hf x hx).contDiffAt (hs.mem_nhds hx) |>.contDiffWithinAt | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.OpenPartialHomeomorph.IsImage | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 47
} | [
{
"pp": "X : Type u_1\nY : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ne : OpenPartialHomeomorph X Y\ns : Set X\nt : Set Y\nh : e.IsImage s t\n⊢ e.IsImage (interior s) (interior t)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Inverse | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 39
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nh : HasDerivAt f f' x\nhf' : f' ≠ 0\n⊢ Tendsto f (𝓝[≠] x) (𝓝[≠] f x)",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Inverse | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 39
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nc : F\nh : HasDerivAt f f' x\nhf' : f' ≠ 0\n⊢ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z ≠ c",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Inverse | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 39
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nh : HasDerivAt f f' x\nhf' : f' ≠ 0\nt : Set F\nht : ¬AccPt (f x) (𝓟 t)\n⊢ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z ∉ t",
"usedConstants": [
"Eq.mpr",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Inverse | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 13
} | [
{
"pp": "𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nf g : 𝕜 → 𝕜\na : 𝕜\ns t : Set 𝕜\nha : a ∈ s\nhsu : UniqueDiffWithinAt 𝕜 s a\nhf : HasDerivWithinAt f 0 t (g a)\nhst : MapsTo g s t\nhfg : f ∘ g =ᶠ[𝓝[s] a] id\nhg : DifferentiableWithinAt 𝕜 g s a\nthis : HasDerivWithinAt id (0 * derivWithin g s a) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Inverse | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 13
} | [
{
"pp": "𝕜 : Type u\ninst✝ : NontriviallyNormedField 𝕜\nf g : 𝕜 → 𝕜\na : 𝕜\nhf : HasDerivAt f 0 (g a)\nhfg : f ∘ g =ᶠ[𝓝 a] id\nhg : DifferentiableAt 𝕜 g a\nthis : HasDerivAt id (0 * deriv g a) a\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 359,
"column": 29
} | {
"line": 359,
"column": 40
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\nx : E\nn : ℕ∞ω\nhn : n ≠ ∞\n⊢ n + 1 ≠ ∞",
"usedConstants": [
"Eq.mpr",
"in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 97
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\nn : ℕ∞ω\nm : ℕ\nh : ContDiffOn 𝕜 n f s\nhmn : ↑m ≤ n\nhs : UniqueDiffOn 𝕜 s\n⊢ ContinuousOn (iteratedDerivWithin m f s) s",
"usedConstants": [
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 156,
"column": 2
} | {
"line": 157,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\nn : ℕ∞ω\nm : ℕ\nh : ContDiffWithinAt 𝕜 n f s x\nhmn : ↑m < n\nhs : UniqueDiffOn 𝕜 (insert x s)\n⊢ DifferentiableWithinAt 𝕜 (iteratedDerivWithin m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\nx : 𝕜\n⊢ ‖iteratedFDeriv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"Eq.mpr"... | rw [iteratedDeriv_eq_equiv_comp, Function.comp_apply, LinearIsometryEquiv.norm_map] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\nx : 𝕜\n⊢ ‖iteratedFDeriv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"Eq.mpr"... | rw [iteratedDeriv_eq_equiv_comp, Function.comp_apply, LinearIsometryEquiv.norm_map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\nx : 𝕜\n⊢ ‖iteratedFDeriv 𝕜 n f x‖ = ‖iteratedDeriv n f x‖",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"Eq.mpr"... | rw [iteratedDeriv_eq_equiv_comp, Function.comp_apply, LinearIsometryEquiv.norm_map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nx : 𝕜\n⊢ iteratedDeriv n (fun x ↦ 0) x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Defs | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nx : 𝕜\ns : Set 𝕜\n⊢ iteratedDerivWithin n (fun x ↦ 0) s x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 129,
"column": 27
} | {
"line": 129,
"column": 38
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 140,
"column": 2
} | {
"line": 140,
"column": 37
} | [
{
"pp": "n : ℕ\nc : OrderedFinpartition n\n⊢ c.length ≤ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 37
} | [
{
"pp": "n : ℕ\nc : OrderedFinpartition n\nm : Fin c.length\n⊢ c.partSize m ≤ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 185,
"column": 2
} | {
"line": 185,
"column": 13
} | [
{
"pp": "n : ℕ\nc : OrderedFinpartition n\nm : Fin c.length\nr r' : Fin (c.partSize m)\nh : c.emb m r = c.emb m r'\n⊢ ⟨m, r⟩ = ⟨m, r'⟩",
"usedConstants": [
"Eq.mpr",
"congrArg",
"heq_eq_eq",
"id",
"Sigma.mk.injEq",
"And",
"congr",
"True",
"eq_self",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 235,
"column": 4
} | {
"line": 235,
"column": 77
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 248,
"column": 2
} | {
"line": 248,
"column": 18
} | [
{
"pp": "n : ℕ\nc : OrderedFinpartition n\ni : Fin c.length\nj : Fin n\nhc : range (c.emb i) = {j}\nthis : Fintype.card ↑(range (c.emb i)) = Fintype.card (Fin (c.partSize i))\n⊢ c.partSize i = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 18
} | [
{
"pp": "case inl\nn : ℕ\nc : OrderedFinpartition (n + 1)\nhc : range (c.emb 0) ≠ {0}\nthis : c.partSize (c.index 0) = Nat.card ↑(range (c.emb (c.index 0)))\nh : c.index 0 = 0\n⊢ 1 < Nat.card ↑(range (c.emb (c.index 0)))",
"usedConstants": [
"instNeZeroNatHAdd_1",
"congrArg",
"OrderedFinpa... | rw [← h] at hc | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 263,
"column": 6
} | {
"line": 263,
"column": 56
} | [
{
"pp": "n : ℕ\nc : OrderedFinpartition (n + 1)\nhc : range (c.emb (c.index 0)) ≠ {0}\nthis : c.partSize (c.index 0) = Nat.card ↑(range (c.emb (c.index 0)))\nh : c.index 0 = 0\n⊢ {0} ⊆ range (c.emb (c.index 0))",
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"_private.Mathlib.Analysi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 264,
"column": 4
} | {
"line": 264,
"column": 15
} | [
{
"pp": "case inl\nn : ℕ\nc : OrderedFinpartition (n + 1)\nhc : range (c.emb (c.index 0)) ≠ {0}\nthis✝ : c.partSize (c.index 0) = Nat.card ↑(range (c.emb (c.index 0)))\nh : c.index 0 = 0\nthis : {0} ⊂ range (c.emb (c.index 0))\n⊢ 1 < Nat.card ↑(range (c.emb (c.index 0)))",
"usedConstants": [
"Eq.mpr",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 311,
"column": 37
} | {
"line": 311,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 623,
"column": 6
} | {
"line": 623,
"column": 22
} | [
{
"pp": "case mp.refine_1\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\nx : E\nhx : x ∈ s\nh : ContDiffWithinAt 𝕜 0 f s x\nu : Set E\nH : u ∈ �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 332,
"column": 37
} | {
"line": 332,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 357,
"column": 6
} | {
"line": 357,
"column": 22
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 382,
"column": 39
} | {
"line": 382,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 393,
"column": 8
} | {
"line": 393,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 401,
"column": 6
} | {
"line": 401,
"column": 21
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 500,
"column": 56
} | {
"line": 500,
"column": 67
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 512,
"column": 36
} | {
"line": 512,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 966,
"column": 2
} | {
"line": 966,
"column": 39
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nn : ℕ∞ω\nh : ContDiffAt 𝕜 n f x\n⊢ ContinuousAt f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 990,
"column": 2
} | {
"line": 990,
"column": 47
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nn : ℕ∞ω\nh : ContDiffAt 𝕜 n f x\nhn : n ≠ 0\n⊢ DifferentiableAt 𝕜 f x",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 1002,
"column": 2
} | {
"line": 1002,
"column": 56
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nh : ContDiffAt 𝕜 1 f x\n⊢ DifferentiableAt 𝕜 f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 1006,
"column": 2
} | {
"line": 1006,
"column": 31
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nm n : ℕ∞ω\nh : ContDiffAt 𝕜 n f x\nhm : m ≤ n\nh' : m = ∞ → n = ω\n⊢ ∃ u ∈ 𝓝 x, ContDiffOn �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 529,
"column": 6
} | {
"line": 529,
"column": 17
} | [
{
"pp": "case inl\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 536,
"column": 8
} | {
"line": 536,
"column": 19
} | [
{
"pp": "case pos.refine_1\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 1028,
"column": 2
} | {
"line": 1028,
"column": 31
} | [
{
"pp": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nn : ℕ∞ω\nh : ContDiffAt 𝕜 n f x\nh' : n ≠ ∞\n⊢ ∀ᶠ (y : E) in 𝓝 x, ContDiffAt 𝕜 n f y",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 546,
"column": 62
} | {
"line": 546,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Defs | {
"line": 1041,
"column": 4
} | {
"line": 1041,
"column": 15
} | [
{
"pp": "case h\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\nx : E\nn : ℕ\nhs : UniqueDiffOn 𝕜 s\nh : ContDiffAt 𝕜 (↑n) f x\nhx : x ∈ s\nu : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 591,
"column": 6
} | {
"line": 591,
"column": 21
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 620,
"column": 8
} | {
"line": 620,
"column": 19
} | [
{
"pp": "case inl.refine_1\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 41,
"column": 2
} | {
"line": 41,
"column": 13
} | [
{
"pp": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nh : HasStrictDerivAt e e' ↑z\nA : HasStrictFDerivAt ofReal ofRealCLM z\nB : HasStrictFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (ofRealCLM z)\nC : HasStrictFDerivAt re reCLM (e (ofRealCLM z))\n⊢ HasStrictDerivAt (fun x ↦ (e ↑x).re) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | [
{
"pp": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nh : HasDerivAt e e' ↑z\nA : HasFDerivAt ofReal ofRealCLM z\nB : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (ofRealCLM z)\nC : HasFDerivAt re reCLM (e (ofRealCLM z))\n⊢ HasDerivAt (fun x ↦ (e ↑x).re) e'.re z",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nx : ℂ\nf' : E\nh : HasStrictDerivAt f f' x\n⊢ HasStrictFDerivAt f (reCLM.smulRight f' + I • imCLM.smulRight f') x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nx : ℂ\nf' : E\nh : HasDerivAt f f' x\n⊢ HasFDerivAt f (reCLM.smulRight f' + I • imCLM.smulRight f') x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\ns : Set ℂ\nx : ℂ\nf' : E\nh : HasDerivWithinAt f f' s x\n⊢ HasFDerivWithinAt f (reCLM.smulRight f' + I • imCLM.smulRight f') s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 60
} | [
{
"pp": "f : ℂ → ℂ\nf' x : ℂ\nh : HasStrictDerivAt f f' x\n⊢ HasStrictFDerivAt f (f' • 1) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 60
} | [
{
"pp": "f : ℂ → ℂ\nf' x : ℂ\nh : HasDerivAt f f' x\n⊢ HasFDerivAt f (f' • 1) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 93,
"column": 2
} | {
"line": 93,
"column": 60
} | [
{
"pp": "f : ℂ → ℂ\ns : Set ℂ\nf' x : ℂ\nh : HasDerivWithinAt f f' s x\n⊢ HasFDerivWithinAt f (f' • 1) s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 57
} | [
{
"pp": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nhf : HasDerivAt e e' ↑z\n⊢ HasDerivAt (fun y ↦ e ↑y) e' z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 104,
"column": 2
} | {
"line": 104,
"column": 68
} | [
{
"pp": "z : ℝ\nf : ℝ → ℝ\nu : ℝ\nhf : HasDerivAt f u z\n⊢ HasDerivAt (fun y ↦ ↑(f y)) (↑u) z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 626,
"column": 8
} | {
"line": 626,
"column": 48
} | [
{
"pp": "case inl.refine_2.e_a\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt ... | simp only [val_cast, val_succ, val_pred] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Complex.RealDeriv | {
"line": 109,
"column": 2
} | {
"line": 109,
"column": 57
} | [
{
"pp": "z : ℝ\nf : ℝ → ℝ\ns : Set ℝ\nu : ℝ\nhf : HasDerivWithinAt f u s z\n⊢ HasDerivWithinAt (fun y ↦ ↑(f y)) (↑u) s z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 304,
"column": 2
} | {
"line": 304,
"column": 65
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CompleteSpace 𝔸\ninst✝ : CharZero 𝕂\nx : 𝔸\nhx : x ∈ Metric.eball 0 (expSeries 𝕂 𝔸).radius\n⊢ HasSum (fun n ↦ (expSeries 𝕂 𝔸 n) fun x_1 ↦ x) (exp x)",
"usedConsta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 315,
"column": 2
} | {
"line": 315,
"column": 65
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CompleteSpace 𝔸\ninst✝ : CharZero 𝕂\nh : 0 < (expSeries 𝕂 𝔸).radius\n⊢ HasFPowerSeriesOnBall exp (expSeries 𝕂 𝔸) 0 (expSeries 𝕂 𝔸).radius",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 320,
"column": 2
} | {
"line": 320,
"column": 46
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CompleteSpace 𝔸\ninst✝ : CharZero 𝕂\nh : 0 < (expSeries 𝕂 𝔸).radius\n⊢ HasFPowerSeriesAt exp (expSeries 𝕂 𝔸) 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 326,
"column": 2
} | {
"line": 326,
"column": 65
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CompleteSpace 𝔸\ninst✝ : CharZero 𝕂\nthis : ContinuousOn (expSeries 𝕂 𝔸).sum (Metric.eball 0 (expSeries 𝕂 𝔸).radius)\n⊢ ContinuousOn exp (Metric.eball 0 (expSeries 𝕂 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 419,
"column": 2
} | {
"line": 420,
"column": 45
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedDivisionRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CharZero 𝕂\ninst✝ : CompleteSpace 𝔸\nx : 𝔸\nhx : x ∈ Metric.eball 0 (expSeries 𝕂 𝔸).radius\n⊢ HasSum (fun n ↦ x ^ n / ↑n !) (exp x)",
"usedConstants": [
... | rw [← expSeries_apply_eq_div' (𝕂 := 𝕂) x]
exact expSeries_hasSum_exp_of_mem_ball x hx | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 419,
"column": 2
} | {
"line": 420,
"column": 45
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedDivisionRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CharZero 𝕂\ninst✝ : CompleteSpace 𝔸\nx : 𝔸\nhx : x ∈ Metric.eball 0 (expSeries 𝕂 𝔸).radius\n⊢ HasSum (fun n ↦ x ^ n / ↑n !) (exp x)",
"usedConstants": [
... | rw [← expSeries_apply_eq_div' (𝕂 := 𝕂) x]
exact expSeries_hasSum_exp_of_mem_ball x hx | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Algebra.Exponential | {
"line": 554,
"column": 2
} | {
"line": 554,
"column": 68
} | [
{
"pp": "𝔸 : Type u_1\ninst✝² : NormedRing 𝔸\ninst✝¹ : NormedAlgebra ℚ 𝔸\ninst✝ : CompleteSpace 𝔸\nx a b : 𝔸\nh : SemiconjBy x a b\nthis : Invertible (exp b) := invertibleExp b\n⊢ exp (-b) * x * exp a = x",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Semigroup.toMul",
"N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.CauSeqFilter | {
"line": 32,
"column": 52
} | {
"line": 32,
"column": 63
} | [
{
"pp": "β : Type v\ninst✝¹ : NormedRing β\nhn : IsAbsoluteValue norm\nf : CauSeq β norm\ninst✝ : IsComplete β norm\ns : Set β\nos : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nlfs : f.lim ∈ s\nthis : ∃ a, ∀ b ≥ a, ↑f b ∈ s\n⊢ ↑f ⁻¹' s ∈ atTop",
"usedConstants": [
"Filter.instMember... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 716,
"column": 14
} | {
"line": 716,
"column": 25
} | [
{
"pp": "case neg.emb.refine_2.inl.inl\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 717,
"column": 53
} | {
"line": 717,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.CauSeqFilter | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 28
} | [
{
"pp": "case a\nβ : Type v\ninst✝¹ : NormedField β\ninst✝ : CauSeq.IsComplete β norm\nu : ℕ → β\nhu : CauchySeq u\nC : IsCauSeq norm u\nε : ℝ\nεpos : ε > 0\nN : ℕ\nhN : ∀ j ≥ N, ‖↑(⟨u, C⟩ - CauSeq.const norm (CauSeq.lim ⟨u, C⟩)) j‖ < ε\n⊢ ∀ n ≥ N, dist (u n) (CauSeq.lim ⟨u, C⟩) < ε",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Exponential | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 13
} | [
{
"pp": "𝕂 : Type u_1\ninst✝² : NontriviallyNormedField 𝕂\ninst✝¹ : CompleteSpace 𝕂\ninst✝ : CharZero 𝕂\nx : 𝕂\nhx : x ∈ Metric.eball 0 (expSeries 𝕂 𝕂).radius\n⊢ HasStrictDerivAt exp (exp x) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 836,
"column": 2
} | {
"line": 836,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ns : Set E\nt : Set F\nq : F → Formal... | simp only [one_mul, compAlongOrderedFinpartitionₗ_apply_apply] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.SpecialFunctions.Exponential | {
"line": 320,
"column": 2
} | {
"line": 320,
"column": 13
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : CharZero 𝕂\ninst✝² : NormedRing 𝔸\ninst✝¹ : NormedAlgebra 𝕂 𝔸\ninst✝ : CompleteSpace 𝔸\nx : 𝔸\nt : 𝕂\nhtx : t • x ∈ Metric.eball 0 (expSeries 𝕂 𝔸).radius\n⊢ HasStrictDerivAt (fun u ↦ exp (u • x)) (exp (t • x) * x) t",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Exponential | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 13
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : CharZero 𝕂\ninst✝² : NormedRing 𝔸\ninst✝¹ : NormedAlgebra 𝕂 𝔸\ninst✝ : CompleteSpace 𝔸\nx : 𝔸\nt : 𝕂\nhtx : t • x ∈ Metric.eball 0 (expSeries 𝕂 𝔸).radius\n⊢ HasStrictDerivAt (fun u ↦ exp (u • x)) (x * exp (t • x)) t",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 945,
"column": 4
} | {
"line": 945,
"column": 27
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nα : Type u_5\nH : Ty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | {
"line": 949,
"column": 4
} | {
"line": 949,
"column": 15
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nα : Type u_5\nH : Ty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 13
} | [
{
"pp": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns : Set E\nx y : E\nh : [x -[ℝ] x + y] ⊆ s\n⊢ y ∈ posTangentConeAt s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 129,
"column": 55
} | {
"line": 129,
"column": 66
} | [
{
"pp": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\ns : Set E\na y : E\nh : IsLocalMaxOn f s a\nhf : HasFDerivWithinAt f f' s a\nhy : y ∈ posTangentConeAt s a\nhy' : -y ∈ posTangentConeAt s a\n⊢ 0 ≤ f' y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 13
} | [
{
"pp": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\ns : Set E\na y : E\nh : IsLocalMinOn f s a\nhf : HasFDerivWithinAt f f' s a\nhy : y ∈ posTangentConeAt s a\n⊢ 0 ≤ f' y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 13
} | [
{
"pp": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\ns : Set E\na y : E\nh : IsLocalMinOn f s a\nhf : HasFDerivWithinAt f f' s a\nhy : y ∈ posTangentConeAt s a\nhy' : -y ∈ posTangentConeAt s a\n⊢ f' y = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 220,
"column": 6
} | {
"line": 220,
"column": 33
} | [
{
"pp": "s : Set ℝ\na : ℝ\nh : 1 ∈ posTangentConeAt s a\nι : Type\nl : Filter ι\nhl : l.NeBot\nc : ι → ℝ≥0\nd : ι → ℝ\nhd₀ : Tendsto d l (𝓝 0)\nhd : ∀ᶠ (n : ι) in l, a + d n ∈ s\nhcd : Tendsto (fun n ↦ c n • d n) l (𝓝 1)\n⊢ Tendsto (fun x ↦ a + d x) l (𝓝 a)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 15
} | [
{
"pp": "case h\ns : Set ℝ\na : ℝ\nh : 1 ∈ posTangentConeAt s a\nι : Type\nl : Filter ι\nhl : l.NeBot\nc : ι → ℝ≥0\nd : ι → ℝ\nhd₀ : Tendsto d l (𝓝 0)\nhd : ∀ᶠ (n : ι) in l, a + d n ∈ s\nhcd : Tendsto (fun n ↦ c n • d n) l (𝓝 1)\nthis : Tendsto (fun x ↦ a + d x) l (𝓝 a)\nn : ι\nhcdn : 0 < c n • d n\nhdn : a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 227,
"column": 36
} | {
"line": 227,
"column": 61
} | [
{
"pp": "case mpr.h\ns : Set ℝ\na : ℝ\nh : ∃ᶠ (x : ℝ) in 𝓝 a, x ∈ Ioi a ∩ s\n⊢ ∃ᶠ (t : ℝ) in 𝓝[>] 0, a + t • 1 ∈ s",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Real",
"Set.Ioi",
"congrArg",
"Filter.map",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUn... | ← map_add_left_nhds_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 228,
"column": 4
} | {
"line": 228,
"column": 54
} | [
{
"pp": "case mpr.h\ns : Set ℝ\na : ℝ\nh : ∃ᶠ (a_1 : ℝ) in 𝓝 0, a + a_1 ∈ Ioi a ∩ s\n⊢ ∃ᶠ (t : ℝ) in 𝓝[>] 0, a + t • 1 ∈ s",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"instHSMul",
"Preorder.toLT",
"Real.instZero",
"congrArg",
"DistribMulAction.toDistri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LocalExtr.Basic | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 13
} | [
{
"pp": "f : ℝ → ℝ\nf' a : ℝ\nh : IsLocalMin f a\nhf : HasDerivAt f f' a\n⊢ f' = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ExtendFrom | {
"line": 78,
"column": 30
} | {
"line": 78,
"column": 59
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : RegularSpace Y\nf : X → Y\nA B : Set X\nhB : B ⊆ closure[inst✝²] A\nhf : ∀ x ∈ B, ∃ y, Tendsto f (𝓝[A] x) (𝓝 y)\nφ : X → Y := extendFrom A f\nx : X\nx_in : x ∈ B\nV' : Set Y\nV'_in : V' ∈ 𝓝 (φ x)\nV'_closed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ExtendFrom | {
"line": 86,
"column": 53
} | {
"line": 86,
"column": 64
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : RegularSpace Y\nf : X → Y\nA : Set X\nhA : Dense A\nhf : ∀ (x : X), ∃ y, Tendsto f (𝓝[A] x) (𝓝 y)\n⊢ ∀ x ∈ univ, ∃ y, Tendsto f (𝓝[A] x) (𝓝 y)",
"usedConstants": [
"Eq.mpr",
"Set.mem_univ._... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Rolle | {
"line": 43,
"column": 2
} | {
"line": 44,
"column": 39
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝⁶ : ConditionallyCompleteLinearOrder X\ninst✝⁵ : DenselyOrdered X\ninst✝⁴ : TopologicalSpace X\ninst✝³ : OrderTopology X\ninst✝² : LinearOrder Y\ninst✝¹ : TopologicalSpace Y\ninst✝ : OrderTopology Y\nf : X → Y\na b : X\nhab : a < b\nhfc : ContinuousOn f (Icc a b)\nhfI :... | obtain ⟨c, cmem, cle⟩ : ∃ c ∈ Icc a b, ∀ x ∈ Icc a b, f c ≤ f x :=
isCompact_Icc.exists_isMinOn ne hfc | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 171,
"column": 2
} | {
"line": 175,
"column": 22
} | [
{
"pp": "case pos\nf : ℝ → ℝ\na : ℝ\nhf : Tendsto (derivWithin f (Ioi a)) (𝓝[>] a) atTop\nhcont_at_a : ContinuousWithinAt f (Ici a) a\n⊢ ¬DifferentiableWithinAt ℝ f (Ioi a) a",
"usedConstants": []
},
{
"pp": "case neg\nf : ℝ → ℝ\na : ℝ\nhf : Tendsto (derivWithin f (Ioi a)) (𝓝[>] a) atTop\nhcont_at... | case neg =>
intro hcontra
have := hcontra.continuousWithinAt
rw [← ContinuousWithinAt.diff_iff this] at hcont_at_a
simp at hcont_at_a | Lean.Elab.Tactic.evalCase | Lean.Parser.Tactic.case |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nx : 𝕜\ns : Set 𝕜\nhx : x ∈ s\nh : UniqueDiffOn 𝕜 s\nf g : 𝕜 → F\nhf : ContDiffWithinAt 𝕜 (↑n) f s x\nhg : ContDiffWithinAt 𝕜 (↑n) g s x\n⊢ iteratedDerivWithin n (fun z... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 248,
"column": 70
} | {
"line": 248,
"column": 81
} | [
{
"pp": "f : ℝ → ℝ\na : ℝ\nf' : ℝ → ℝ := f ∘ Neg.neg\nb : ℝ\nhb₁ : b < a\nhb₂ : ∀ ⦃x : ℝ⦄, x ∈ Ioo b a → deriv f x ∈ Iic (-1)\nx : ℝ\nhx : x ∈ Ioo (-a) (-b)\nthis : deriv f' x = deriv f (-x) * deriv Neg.neg x\n⊢ deriv f' x = -deriv f (-x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 35
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\ns : Set 𝕜\nf : 𝕜 → F\nc : 𝕜\n⊢ iteratedDerivWithin n (fun z ↦ f (z - c)) s = fun x ↦ iteratedDerivWithin n f (-c +ᵥ s) (x - c)",
"usedConstants": [
"NormedCommR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 379,
"column": 2
} | {
"line": 379,
"column": 38
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ x ∈ interior D, 0 < deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nthis : DifferentiableOn ℝ f (interior D)\n⊢ x < y → f x < f y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 412,
"column": 2
} | {
"line": 412,
"column": 41
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_nonneg : ∀ x ∈ interior D, 0 ≤ deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nhxy : x ≤ y\n⊢ f x ≤ f y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 445,
"column": 2
} | {
"line": 445,
"column": 42
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ x ∈ interior D, deriv f x < 0\nx : ℝ\nhx : x ∈ D\ny : ℝ\n⊢ y ∈ D → x < y → f y < f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 481,
"column": 2
} | {
"line": 481,
"column": 41
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_nonpos : ∀ x ∈ interior D, deriv f x ≤ 0\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nhxy : x ≤ y\n⊢ f y ≤ f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 533,
"column": 2
} | {
"line": 533,
"column": 17
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\ns : Set E\nx y : E\nf' : E → StrongDual ℝ E\nhf : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s x\nhs : Convex ℝ s\nxs : x ∈ s\nys : y ∈ s\ng : ℝ → E := fun t ↦ (AffineMap.lineMap x y) t\nI : Set ℝ := Icc 0 1\nhsub : Ioo 0 1 ⊆ I\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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