module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Topology.Sheaves.MayerVietoris | {
"line": 54,
"column": 8
} | {
"line": 54,
"column": 67
} | {
"line": 54,
"column": 67
} | [
{
"pp": "case inr\nT : Type u\ninst✝ : TopologicalSpace T\nsq : Square (Opens T)\nh₄ : sq.X₄ = sq.X₂ ⊔ sq.X₃\nh₁ : sq.X₁ = sq.X₂ ⊓ sq.X₃\nx : T\nhx : x ∈ ↑sq.X₃\n⊢ ∃ U f, (Sieve.ofTwoArrows sq.f₂₄ sq.f₃₄).arrows f ∧ x ∈ U",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"CategoryTheory... | [] | exact ⟨_, _, ⟨Sieve.ofArrows_mk _ _ WalkingPair.right, hx⟩⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Subpath | {
"line": 177,
"column": 2
} | {
"line": 183,
"column": 62
} | {
"line": 185,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nn : ℕ\np : Fin (n + 1) → X\nF G : (k : Fin n) → Path (p k.castSucc) (p k.succ)\nH : (k : Fin n) → (F k).Homotopy (G k)\n⊢ (concat p F).Homotopy (concat p G)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"in... | [] | induction n with
| zero =>
rw [concat_zero, concat_zero]
exact refl (Path.refl _)
| succ n ih =>
rw [concat_succ, concat_succ]
exact hcomp (ih _ _ _ (fun k ↦ H k.castSucc)) (H (last n)) | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Topology.Subpath | {
"line": 177,
"column": 2
} | {
"line": 183,
"column": 62
} | {
"line": 185,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nn : ℕ\np : Fin (n + 1) → X\nF G : (k : Fin n) → Path (p k.castSucc) (p k.succ)\nH : (k : Fin n) → (F k).Homotopy (G k)\n⊢ (concat p F).Homotopy (concat p G)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"in... | [] | induction n with
| zero =>
rw [concat_zero, concat_zero]
exact refl (Path.refl _)
| succ n ih =>
rw [concat_succ, concat_succ]
exact hcomp (ih _ _ _ (fun k ↦ H k.castSucc)) (H (last n)) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Subpath | {
"line": 177,
"column": 2
} | {
"line": 183,
"column": 62
} | {
"line": 185,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nn : ℕ\np : Fin (n + 1) → X\nF G : (k : Fin n) → Path (p k.castSucc) (p k.succ)\nH : (k : Fin n) → (F k).Homotopy (G k)\n⊢ (concat p F).Homotopy (concat p G)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"in... | [] | induction n with
| zero =>
rw [concat_zero, concat_zero]
exact refl (Path.refl _)
| succ n ih =>
rw [concat_succ, concat_succ]
exact hcomp (ih _ _ _ (fun k ↦ H k.castSucc)) (H (last n)) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.UniformSpace.Dini | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 97
} | {
"line": 67,
"column": 2
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nG : Type u_3\ninst✝⁵ : Preorder ι\ninst✝⁴ : TopologicalSpace α\ninst✝³ : NormedAddCommGroup G\ninst✝² : Lattice G\ninst✝¹ : HasSolidNorm G\ninst✝ : IsOrderedAddMonoid G\nF : ι → α → G\nf : α → G\nhF_cont : ∀ (i : ι), Continuous[inst✝⁴, PseudoMetricSpace.toUniformSpace.toTopo... | [
"ι : Type u_1\nα : Type u_2\nG : Type u_3\ninst✝⁵ : Preorder ι\ninst✝⁴ : TopologicalSpace α\ninst✝³ : NormedAddCommGroup G\ninst✝² : Lattice G\ninst✝¹ : HasSolidNorm G\ninst✝ : IsOrderedAddMonoid G\nF : ι → α → G\nf : α → G\nhF_cont : ∀ (i : ι), Continuous[inst✝⁴, PseudoMetricSpace.toUniformSpace.toTopologicalSpace... | refine ⟨{y | ‖F n y - f y‖ < ε}, ⟨isOpen_lt (by fun_prop) continuous_const |>.mem_nhds hn, ?_⟩⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.UniformSpace.Path | {
"line": 76,
"column": 8
} | {
"line": 76,
"column": 35
} | {
"line": 76,
"column": 36
} | [
{
"pp": "X : Type u_1\ninst✝ : UniformSpace X\nx y z : X\nU : Set (X × X)\nhU : U ∈ 𝓤 X\nx✝² x✝¹ : Path x y × Path y z\nt : ↑I\nfst✝¹ : Path x y\nsnd✝¹ : Path y z\nfst✝ : Path x y\nsnd✝ : Path y z\nx✝ :\n ((fst✝¹, snd✝¹), fst✝, snd✝) ∈\n entourageProd {γ | ∀ (t : ↑I), (γ.1 t, γ.2 t) ∈ (U, U).1} {γ | ∀ (t :... | [
"case pos\nX : Type u_1\ninst✝ : UniformSpace X\nx y z : X\nU : Set (X × X)\nhU : U ∈ 𝓤 X\nx✝² x✝¹ : Path x y × Path y z\nt : ↑I\nfst✝¹ : Path x y\nsnd✝¹ : Path y z\nfst✝ : Path x y\nsnd✝ : Path y z\nx✝ :\n ((fst✝¹, snd✝¹), fst✝, snd✝) ∈\n entourageProd {γ | ∀ (t : ↑I), (γ.1 t, γ.2 t) ∈ (U, U).1} {γ | ∀ (t : ↑... | by_cases ht : (t : ℝ) ≤ 2⁻¹ | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Topology.UniformSpace.OfCompactT2 | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 16
} | {
"line": 59,
"column": 4
} | [
{
"pp": "γ : Type u_1\ninst✝² : TopologicalSpace γ\ninst✝¹ : CompactSpace γ\ninst✝ : R1Space γ\n𝓝Δ : Filter (γ × γ) := 𝓝ˢ (diagonal γ)\nF : Filter (γ × γ) := 𝓝Δ.lift' fun s ↦ s ○ s\n⊢ ∀ V ∈ 𝓝Δ, F ⊓ 𝓟 Vᶜ = ⊥",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Filter.instMembership",... | [
"γ : Type u_1\ninst✝² : TopologicalSpace γ\ninst✝¹ : CompactSpace γ\ninst✝ : R1Space γ\n𝓝Δ : Filter (γ × γ) := 𝓝ˢ (diagonal γ)\nF : Filter (γ × γ) := 𝓝Δ.lift' fun s ↦ s ○ s\nV : Set (γ × γ)\nV_in : V ∈ 𝓝Δ\n⊢ F ⊓ 𝓟 Vᶜ = ⊥"
] | intro V V_in | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Sion | {
"line": 327,
"column": 4
} | {
"line": 327,
"column": 93
} | {
"line": 328,
"column": 4
} | [
{
"pp": "case insert.inr\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\n... | [
"case insert.inr\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝³ : Mod... | refine exists_lt_iInf_of_lt_iInf_of_sup ne_X kX hfy hfy' cY hfx hfx' hb hy1 fun x hx ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.Sion | {
"line": 329,
"column": 4
} | {
"line": 329,
"column": 48
} | {
"line": 330,
"column": 4
} | [
{
"pp": "case pos\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝³ ... | [
"case neg\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module ℝ F... | · exact (hty1 x hx').trans_le (le_sup_right) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.VectorBundle.ContinuousAlternatingMap | {
"line": 170,
"column": 4
} | {
"line": 170,
"column": 31
} | {
"line": 171,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nι : Type u_2\ninst✝¹⁹ : NontriviallyNormedField 𝕜\nB : Type u_3\ninst✝¹⁸ : TopologicalSpace B\nF₁ : Type u_4\ninst✝¹⁷ : NormedAddCommGroup F₁\ninst✝¹⁶ : NormedSpace 𝕜 F₁\nE₁ : B → Type u_5\ninst✝¹⁵ : (x : B) → AddCommGroup (E₁ x)\ninst✝¹⁴ : (x : B) → Module 𝕜 (E₁ x)\ninst✝¹³ : Topolog... | [
"𝕜 : Type u_1\nι : Type u_2\ninst✝¹⁹ : NontriviallyNormedField 𝕜\nB : Type u_3\ninst✝¹⁸ : TopologicalSpace B\nF₁ : Type u_4\ninst✝¹⁷ : NormedAddCommGroup F₁\ninst✝¹⁶ : NormedSpace 𝕜 F₁\nE₁ : B → Type u_5\ninst✝¹⁵ : (x : B) → AddCommGroup (E₁ x)\ninst✝¹⁴ : (x : B) → Module 𝕜 (E₁ x)\ninst✝¹³ : TopologicalSpace (T... | rintro ⟨x, f⟩ ⟨⟨h₁, h₂⟩, -⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Data.Nat.BinaryRec | {
"line": 38,
"column": 47
} | {
"line": 38,
"column": 62
} | {
"line": 38,
"column": 63
} | [
{
"pp": "case inl\nn : Nat\nh : n % 2 = 0\n⊢ (bif decide (n % 2 = 1) then 2 * (n / 2) + 1 else 2 * (n / 2)) = n",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"cond",
"Eq.mpr",
"False",
"instHDiv",
"HMul.hMul",
"congrArg",
"Decidable.decide.congr_s... | [
"case inl\nn : Nat\nh : n % 2 = 0\n⊢ 2 * (n / 2) = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.BinaryRec | {
"line": 38,
"column": 47
} | {
"line": 38,
"column": 62
} | {
"line": 38,
"column": 63
} | [
{
"pp": "case inr\nn : Nat\nh : n % 2 = 1\n⊢ (bif decide (n % 2 = 1) then 2 * (n / 2) + 1 else 2 * (n / 2)) = n",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"cond",
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"instDecidableTrue",
"congrArg",
"Decidable.de... | [
"case inr\nn : Nat\nh : n % 2 = 1\n⊢ 2 * (n / 2) + 1 = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.BinaryRec | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 78
} | {
"line": 99,
"column": 79
} | [
{
"pp": "case succ.succ\nn : Nat\nn0 : ¬n + 1 + 1 = 0\nthis : (n + 1 + 1) >>> 1 ≠ 0\n⊢ (if (n + 1 + 1) >>> 1 = 0 then 0 else ((n + 1 + 1) >>> 1).log2.succ) <\n if n + 1 + 1 = 0 then 0 else (n + 1 + 1).log2.succ",
"ppTerm": "?succ.succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"case succ.succ\nn : Nat\nn0 : ¬n + 1 + 1 = 0\nthis : (n + 1 + 1) >>> 1 ≠ 0\n⊢ ((n + 1 + 1) >>> 1).log2.succ < ((n + 1 + 1) >>> 1).log2.succ.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 171,
"column": 24
} | {
"line": 171,
"column": 35
} | {
"line": 171,
"column": 36
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b c : α\ninst✝¹ : DecidableRel r\ninst✝ : Irrefl r\na : α\n⊢ ¬Decidable.decide (r a a) = true",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Bool.true",
"Bool",
"decide_eq_true_eq"... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b c : α\ninst✝¹ : DecidableRel r\ninst✝ : Irrefl r\na : α\n⊢ ¬r a a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 175,
"column": 22
} | {
"line": 175,
"column": 33
} | {
"line": 175,
"column": 34
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b c : α\ninst✝¹ : DecidableRel r\ninst✝ : Refl r\na : α\n⊢ Decidable.decide (r a a) = true",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Bool.true",
"Bool",
"decide_eq_true_eq",
"Decidable.de... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b c : α\ninst✝¹ : DecidableRel r\ninst✝ : Refl r\na : α\n⊢ r a a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 179,
"column": 27
} | {
"line": 179,
"column": 38
} | {
"line": 179,
"column": 39
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c✝ : α\ninst✝¹ : DecidableRel r\ninst✝ : IsTrans α r\na b c : α\n⊢ Decidable.decide (r a b) = true → Decidable.decide (r b c) = true → Decidable.decide (r a c) = true",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c✝ : α\ninst✝¹ : DecidableRel r\ninst✝ : IsTrans α r\na b c : α\n⊢ r a b → r b c → r a c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 183,
"column": 24
} | {
"line": 183,
"column": 35
} | {
"line": 183,
"column": 36
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Symm r\na b : α\n⊢ Decidable.decide (r a b) = true → Decidable.decide (r b a) = true",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Bool.true",
"implies_congr",
... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Symm r\na b : α\n⊢ r a b → r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 187,
"column": 50
} | {
"line": 187,
"column": 61
} | {
"line": 187,
"column": 62
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Antisymm r\na b : α\nh₁ : Decidable.decide (r a b) = true\nh₂ : Decidable.decide (r b a) = true\n⊢ r a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Antisymm r\na b : α\nh₁ : Decidable.decide (r a b) = true\nh₂ : Decidable.decide (r b a) = true\n⊢ r a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 187,
"column": 70
} | {
"line": 187,
"column": 81
} | {
"line": 187,
"column": 82
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Antisymm r\na b : α\nh₁ : Decidable.decide (r a b) = true\nh₂ : Decidable.decide (r b a) = true\n⊢ r b a",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Antisymm r\na b : α\nh₁ : Decidable.decide (r a b) = true\nh₂ : Decidable.decide (r b a) = true\n⊢ r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 191,
"column": 25
} | {
"line": 191,
"column": 36
} | {
"line": 191,
"column": 37
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Asymm r\na b : α\n⊢ Decidable.decide (r a b) = true → ¬Decidable.decide (r b a) = true",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Bool.true",
... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Asymm r\na b : α\n⊢ r a b → ¬r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 195,
"column": 25
} | {
"line": 195,
"column": 36
} | {
"line": 195,
"column": 37
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Total r\na b : α\n⊢ Decidable.decide (r a b) = true ∨ Decidable.decide (r b a) = true",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Bool.true",
... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Total r\na b : α\n⊢ r a b ∨ r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.Unbundled | {
"line": 199,
"column": 25
} | {
"line": 199,
"column": 36
} | {
"line": 199,
"column": 37
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Trichotomous r\na b : α\n⊢ ¬Decidable.decide (r a b) = true → ¬Decidable.decide (r b a) = true → a = b",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
... | [
"α : Sort u_1\nr : α → α → Prop\na✝ b✝ c : α\ninst✝¹ : DecidableRel r\ninst✝ : Trichotomous r\na b : α\n⊢ ¬r a b → ¬r b a → a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Defs | {
"line": 774,
"column": 23
} | {
"line": 774,
"column": 51
} | {
"line": 774,
"column": 52
} | [
{
"pp": "M : Type u_2\ninst✝ : Monoid M\nex : ∀ (x y : M), x * y = 1 → ∃ z, y * z = 1\nx y : M\nh : x * y = 1\nz : M\nhz : y * z = 1\n⊢ x = z",
"ppTerm": "?m.43",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_2\ninst✝ : Monoid M\nex : ∀ (x y : M), x * y = 1 → ∃ z, y * z = 1\nx y : M\nh : x * y = 1\nz : M\nhz : y * z = 1\n⊢ x = z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Defs | {
"line": 781,
"column": 23
} | {
"line": 781,
"column": 49
} | {
"line": 781,
"column": 50
} | [
{
"pp": "M : Type u_2\ninst✝ : Monoid M\nex : ∀ (x y : M), x * y = 1 → ∃ z, z * x = 1\nx y : M\nh : x * y = 1\nz : M\nhz : z * x = 1\n⊢ y = z",
"ppTerm": "?m.43",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_2\ninst✝ : Monoid M\nex : ∀ (x y : M), x * y = 1 → ∃ z, z * x = 1\nx y : M\nh : x * y = 1\nz : M\nhz : z * x = 1\n⊢ y = z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Function.Defs | {
"line": 139,
"column": 39
} | {
"line": 139,
"column": 61
} | {
"line": 139,
"column": 62
} | [
{
"pp": "case pos\nα : Type u_1\nβ : Type u_2\ninst✝³ : BEq α\ninst✝² : LawfulBEq α\ninst✝¹ : BEq β\ninst✝ : LawfulBEq β\nf : α → β\nI : Injective f\na b : α\nh : (a == b) = true\n⊢ f a = f b",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Function.Injective.eq_iff",... | [
"case pos\nα : Type u_1\nβ : Type u_2\ninst✝³ : BEq α\ninst✝² : LawfulBEq α\ninst✝¹ : BEq β\ninst✝ : LawfulBEq β\nf : α → β\nI : Injective f\na b : α\nh : (a == b) = true\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Function.Defs | {
"line": 139,
"column": 39
} | {
"line": 139,
"column": 61
} | {
"line": 139,
"column": 62
} | [
{
"pp": "case neg\nα : Type u_1\nβ : Type u_2\ninst✝³ : BEq α\ninst✝² : LawfulBEq α\ninst✝¹ : BEq β\ninst✝ : LawfulBEq β\nf : α → β\nI : Injective f\na b : α\nh : ¬(a == b) = true\n⊢ ¬f a = f b",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Functio... | [
"case neg\nα : Type u_1\nβ : Type u_2\ninst✝³ : BEq α\ninst✝² : LawfulBEq α\ninst✝¹ : BEq β\ninst✝ : LawfulBEq β\nf : α → β\nI : Injective f\na b : α\nh : ¬(a == b) = true\n⊢ ¬a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.ExistsUnique | {
"line": 118,
"column": 60
} | {
"line": 119,
"column": 60
} | {
"line": 121,
"column": 0
} | [
{
"pp": "α : Sort u_1\na' : α\n⊢ ∃! a, a' = a",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Logic.ExistsUnique.0.existsUnique_eq'._simp_1_3",
"congrArg",
"and_self",
"Exists",
"funext",
"And",
"True",
"of_eq_true",
"E... | [] | by
simp only [ExistsUnique, and_self, forall_eq', exists_eq'] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Logic.Basic | {
"line": 704,
"column": 52
} | {
"line": 704,
"column": 72
} | {
"line": 704,
"column": 73
} | [
{
"pp": "p : Prop → Prop\nx✝ : ∃ h, p h\nh₁ : Prop\nh₂ : p h₁\nH : h₁\n⊢ p True",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : Prop → Prop\nx✝ : ∃ h, p h\nh₁ : Prop\nh₂ : p h₁\nH : h₁\n⊢ p True"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Basic | {
"line": 705,
"column": 24
} | {
"line": 705,
"column": 44
} | {
"line": 705,
"column": 45
} | [
{
"pp": "p : Prop → Prop\nx✝ : ∃ h, p h\nh₁ : Prop\nh₂ : p h₁\nH : ¬h₁\n⊢ p False",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : Prop → Prop\nx✝ : ∃ h, p h\nh₁ : Prop\nh₂ : p h₁\nH : ¬h₁\n⊢ p False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Function.Basic | {
"line": 315,
"column": 4
} | {
"line": 315,
"column": 15
} | {
"line": 315,
"column": 16
} | [
{
"pp": "case refine_2\nα : Sort u_1\nβ : Sort u_2\nf : α → β\nγ : Type u_4\ninst✝ : Nontrivial γ\nnot_surj : ¬Surjective f\ninj : Injective fun g ↦ g ∘ f\nc c' : γ\nb₀ : β\nhb : ¬∃ a, f a = b₀\nthis : (fun x ↦ c) = fun x ↦ if x = b₀ then c' else c\n⊢ c = c'",
"ppTerm": "?refine_2",
"assigned": false,
... | [
"case refine_2\nα : Sort u_1\nβ : Sort u_2\nf : α → β\nγ : Type u_4\ninst✝ : Nontrivial γ\nnot_surj : ¬Surjective f\ninj : Injective fun g ↦ g ∘ f\nc c' : γ\nb₀ : β\nhb : ¬∃ a, f a = b₀\nthis : (fun x ↦ c) = fun x ↦ if x = b₀ then c' else c\n⊢ c = c'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Function.Basic | {
"line": 806,
"column": 6
} | {
"line": 806,
"column": 17
} | {
"line": 806,
"column": 18
} | [
{
"pp": "case refine_2\nι : Sort u_1\nα : ι → Sort u_2\nβ : ι → Sort u_3\ninst✝ : ∀ (i : ι), Nonempty (α i)\nf : (i : ι) → α i → β i\ni : ι\nx y : α i\nhxy : f i x = f i y\nthis : Inhabited ((i : ι) → α i)\nh : update default i x = update default i y\n⊢ x = y",
"ppTerm": "?refine_2",
"assigned": false,
... | [
"case refine_2\nι : Sort u_1\nα : ι → Sort u_2\nβ : ι → Sort u_3\ninst✝ : ∀ (i : ι), Nonempty (α i)\nf : (i : ι) → α i → β i\ni : ι\nx y : α i\nhxy : f i x = f i y\nthis : Inhabited ((i : ι) → α i)\nh : update default i x = update default i y\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 270,
"column": 4
} | {
"line": 270,
"column": 32
} | {
"line": 271,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nε : Type u_5\nζ : Type u_6\nr✝ : α → β → Prop\nf✝ : α → γ\ng : β → δ\nc : γ\nd : δ\nr : α → α → Prop\ninst✝ : Std.Symm r\nf : α → β\nx✝¹ x✝ : β\n⊢ Relation.Map r f f x✝¹ x✝ → Relation.Map r f f x✝ x✝¹",
"ppTerm": "?m.11",
"assigned": true,... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nε : Type u_5\nζ : Type u_6\nr✝ : α → β → Prop\nf✝ : α → γ\ng : β → δ\nc : γ\nd : δ\nr : α → α → Prop\ninst✝ : Std.Symm r\nf : α → β\nx y : α\nhxy : r x y\n⊢ Relation.Map r f f (f y) (f x)"
] | rintro ⟨x, y, hxy, rfl, rfl⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Logic.Relation | {
"line": 496,
"column": 4
} | {
"line": 496,
"column": 22
} | {
"line": 498,
"column": 0
} | [
{
"pp": "case mpr.inr\nα : Type u_1\nr : α → α → Prop\na b c : α\nhac : r a c\nhcb : ReflTransGen r c b\n⊢ ReflTransGen r a b",
"ppTerm": "?mpr.inr",
"assigned": true,
"usedConstants": [
"Relation.ReflTransGen.head"
],
"usedFVars": [
"α",
"r",
"a",
"c",
"b... | [] | exact head hac hcb | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Logic.Relation | {
"line": 496,
"column": 4
} | {
"line": 496,
"column": 22
} | {
"line": 498,
"column": 0
} | [
{
"pp": "case mpr.inr\nα : Type u_1\nr : α → α → Prop\na b c : α\nhac : r a c\nhcb : ReflTransGen r c b\n⊢ ReflTransGen r a b",
"ppTerm": "?mpr.inr",
"assigned": true,
"usedConstants": [
"Relation.ReflTransGen.head"
],
"usedFVars": [
"α",
"r",
"a",
"c",
"b... | [] | exact head hac hcb | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 496,
"column": 4
} | {
"line": 496,
"column": 22
} | {
"line": 498,
"column": 0
} | [
{
"pp": "case mpr.inr\nα : Type u_1\nr : α → α → Prop\na b c : α\nhac : r a c\nhcb : ReflTransGen r c b\n⊢ ReflTransGen r a b",
"ppTerm": "?mpr.inr",
"assigned": true,
"usedConstants": [
"Relation.ReflTransGen.head"
],
"usedFVars": [
"α",
"r",
"a",
"c",
"b... | [] | exact head hac hcb | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 603,
"column": 2
} | {
"line": 603,
"column": 54
} | {
"line": 603,
"column": 55
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝ : Std.Refl r\nx y : α\n⊢ ReflGen r x y ↔ r x y",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.reflGen_eq_self._simp_1_2",
"Eq.mpr",
"congrArg",
"id",
"Iff",
"_pri... | [
"α : Type u_1\nr : α → α → Prop\ninst✝ : Std.Refl r\nx y : α\n⊢ y = x → r x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 609,
"column": 2
} | {
"line": 609,
"column": 31
} | {
"line": 609,
"column": 32
} | [
{
"pp": "α : Type u_1\nr r' : α → α → Prop\ninst✝ : Std.Refl r'\nh : r ≤ r'\n⊢ ReflGen r ≤ r'",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr r' : α → α → Prop\ninst✝ : Std.Refl r'\nh : r ≤ r'\n⊢ ReflGen r ≤ r'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 669,
"column": 2
} | {
"line": 669,
"column": 32
} | {
"line": 669,
"column": 33
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (TransGen p on f)\ni✝¹ i✝ : α\nhab : TransGen r i✝¹ i✝\n⊢ (TransGen p on f) i✝¹ i✝",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (TransGen p on f)\ni✝¹ i✝ : α\nhab : TransGen r i✝¹ i✝\n⊢ (TransGen p on f) i✝¹ i✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 682,
"column": 2
} | {
"line": 682,
"column": 32
} | {
"line": 682,
"column": 33
} | [
{
"pp": "α : Type u_1\nr r' : α → α → Prop\ninst✝ : IsTrans α r'\nh : r ≤ r'\n⊢ TransGen r ≤ r'",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr r' : α → α → Prop\ninst✝ : IsTrans α r'\nh : r ≤ r'\n⊢ TransGen r ≤ r'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 751,
"column": 2
} | {
"line": 751,
"column": 36
} | {
"line": 751,
"column": 37
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (ReflTransGen p on f)\ni✝¹ i✝ : α\nhab : ReflTransGen r i✝¹ i✝\n⊢ (ReflTransGen p on f) i✝¹ i✝",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (ReflTransGen p on f)\ni✝¹ i✝ : α\nhab : ReflTransGen r i✝¹ i✝\n⊢ (ReflTransGen p on f) i✝¹ i✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 773,
"column": 4
} | {
"line": 773,
"column": 38
} | {
"line": 773,
"column": 39
} | [
{
"pp": "case refine_1\nα : Type u_1\nr : α → α → Prop\nx y : α\nh : TransGen (ReflGen r) x y\n⊢ ReflTransGen r x y",
"ppTerm": "?refine_1",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case refine_1\nα : Type u_1\nr : α → α → Prop\nx y : α\nh : TransGen (ReflGen r) x y\n⊢ ReflTransGen r x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Relation | {
"line": 959,
"column": 2
} | {
"line": 959,
"column": 36
} | {
"line": 959,
"column": 37
} | [
{
"pp": "α : Type u_1\nr r' : α → α → Prop\ninst✝¹ : Std.Refl r\ninst✝ : IsTrans α r\nh : r' ≤ r\n⊢ ReflTransGen r' ≤ r",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr r' : α → α → Prop\ninst✝¹ : Std.Refl r\ninst✝ : IsTrans α r\nh : r' ≤ r\n⊢ ReflTransGen r' ≤ r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Equiv.Defs | {
"line": 746,
"column": 16
} | {
"line": 746,
"column": 27
} | {
"line": 746,
"column": 28
} | [
{
"pp": "α : Sort u\nβ : Sort v\nq : β → Prop\ne : α ≃ β\nh : ∀ (a : α), q (e a)\na : β\n⊢ q a",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u\nβ : Sort v\nq : β → Prop\ne : α ≃ β\nh : ∀ (a : α), q (e a)\na : β\n⊢ q a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Equiv.Defs | {
"line": 758,
"column": 51
} | {
"line": 758,
"column": 62
} | {
"line": 758,
"column": 63
} | [
{
"pp": "α : Sort u\nβ : Sort v\nq : β → Prop\ne : α ≃ β\nx✝ : ∃ b, q b\na : β\nh : q a\n⊢ q (e (e.symm a))",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"id",
"Equiv",
"Equiv... | [
"α : Sort u\nβ : Sort v\nq : β → Prop\ne : α ≃ β\nx✝ : ∃ b, q b\na : β\nh : q a\n⊢ q a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Function.Iterate | {
"line": 70,
"column": 51
} | {
"line": 70,
"column": 55
} | {
"line": 70,
"column": 56
} | [
{
"pp": "α : Type u\nn✝ n : ℕ\nihn : id^[n] = id\n⊢ id^[n] ∘ id = id",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
"id",
"Nat.iterate",
"Eq"
],
"usedFVars": [
"α",
"n",
"ihn"
],
"... | [
"α : Type u\nn✝ n : ℕ\nihn : id^[n] = id\n⊢ id ∘ id = id"
] | ihn, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Equiv.Defs | {
"line": 773,
"column": 23
} | {
"line": 773,
"column": 34
} | {
"line": 773,
"column": 35
} | [
{
"pp": "α : Sort u\nβ : Sort v\nq : β → Prop\ne : α ≃ β\n⊢ ∀ (a : α),\n ((fun a ↦ q (e a)) a ∧ ∀ (y : α), (fun a ↦ q (e a)) y → y = a) ↔\n (fun b ↦ q b) (e a) ∧ ∀ (y : β), (fun b ↦ q b) y → y = e a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEq... | [
"α : Sort u\nβ : Sort v\nq : β → Prop\ne : α ≃ β\n⊢ ∀ (a : α), q (e a) → ((∀ (y : α), q (e y) → y = a) ↔ ∀ (y : β), q y → y = e a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 61,
"column": 37
} | {
"line": 61,
"column": 48
} | {
"line": 61,
"column": 49
} | [
{
"pp": "M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝ : MulOneClass R\nr₁ r₂ : R\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝ : MulOneClass R\nr₁ r₂ : R\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 66,
"column": 37
} | {
"line": 66,
"column": 48
} | {
"line": 66,
"column": 49
} | [
{
"pp": "M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝ : MulOneClass R\nr₁ r₂ : Rᵐᵒᵖ\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝ : MulOneClass R\nr₁ r₂ : Rᵐᵒᵖ\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 71,
"column": 37
} | {
"line": 71,
"column": 48
} | {
"line": 71,
"column": 49
} | [
{
"pp": "M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝¹ : Mul R\ninst✝ : IsRightCancelMul R\nr₁ r₂ : R\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝¹ : Mul R\ninst✝ : IsRightCancelMul R\nr₁ r₂ : R\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 76,
"column": 37
} | {
"line": 76,
"column": 48
} | {
"line": 76,
"column": 49
} | [
{
"pp": "M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝¹ : Mul R\ninst✝ : IsLeftCancelMul R\nr₁ r₂ : Rᵐᵒᵖ\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\nG : Type u_2\nα : Type u_3\nR : Type u_4\ninst✝¹ : Mul R\ninst✝ : IsLeftCancelMul R\nr₁ r₂ : Rᵐᵒᵖ\nh : ∀ (a : R), r₁ • a = r₂ • a\n⊢ r₁ = r₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 100,
"column": 2
} | {
"line": 101,
"column": 60
} | {
"line": 102,
"column": 2
} | [
{
"pp": "case refine_1\nR : Type u_4\nA : Type u_5\ninst✝² : MulOneClass A\ninst✝¹ : SMul R A\ninst✝ : IsScalarTower R A A\nx✝ : FaithfulSMul R A\nr₁ r₂ : R\nhr : (fun r ↦ r • 1) r₁ = (fun r ↦ r • 1) r₂\nh : ∀ {m₁ m₂ : R}, (∀ (a : A), m₁ • a = m₂ • a) → m₁ = m₂\na : A\n⊢ r₁ • a = r₂ • a",
"ppTerm": "?refine... | [
"case refine_2\nR : Type u_4\nA : Type u_5\ninst✝² : MulOneClass A\ninst✝¹ : SMul R A\ninst✝ : IsScalarTower R A A\nh : Injective fun r ↦ r • 1\nr₁ r₂ : R\nhr : ∀ (a : A), r₁ • a = r₂ • a\n⊢ (fun r ↦ r • 1) r₁ = (fun r ↦ r • 1) r₂"
] | · simp only at hr
rw [← one_mul a, ← smul_mul_assoc, ← smul_mul_assoc, hr] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 102,
"column": 4
} | {
"line": 102,
"column": 15
} | {
"line": 102,
"column": 16
} | [
{
"pp": "case refine_2\nR : Type u_4\nA : Type u_5\ninst✝² : MulOneClass A\ninst✝¹ : SMul R A\ninst✝ : IsScalarTower R A A\nh : Injective fun r ↦ r • 1\nr₁ r₂ : R\nhr : ∀ (a : A), r₁ • a = r₂ • a\n⊢ (fun r ↦ r • 1) r₁ = (fun r ↦ r • 1) r₂",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [... | [
"case refine_2\nR : Type u_4\nA : Type u_5\ninst✝² : MulOneClass A\ninst✝¹ : SMul R A\ninst✝ : IsScalarTower R A A\nh : Injective fun r ↦ r • 1\nr₁ r₂ : R\nhr : ∀ (a : A), r₁ • a = r₂ • a\n⊢ r₁ • 1 = r₂ • 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 48
} | {
"line": 110,
"column": 49
} | [
{
"pp": "G : Type u_2\nα : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G α\nh : ∀ (g : G), (∀ (a : α), g • a = a) → g = 1\na₁ a₂ : G\nh' : ∀ (a : α), a₁ • a = a₂ • a\n⊢ ∀ (a : α), (a₂⁻¹ * a₁) • a = a",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toIn... | [
"G : Type u_2\nα : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G α\nh : ∀ (g : G), (∀ (a : α), g • a = a) → g = 1\na₁ a₂ : G\nh' : ∀ (a : α), a₁ • a = a₂ • a\n⊢ ∀ (a : α), a₁ • a = a₂ • a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Faithful | {
"line": 126,
"column": 2
} | {
"line": 126,
"column": 70
} | {
"line": 127,
"column": 4
} | [
{
"pp": "R : Type u_4\nS : Type u_5\nT : Type u_6\ninst✝¹⁰ : Monoid S\ninst✝⁹ : MulOneClass T\ninst✝⁸ : SMul R S\ninst✝⁷ : IsScalarTower R S S\ninst✝⁶ : MulAction S T\ninst✝⁵ : IsScalarTower S T T\ninst✝⁴ : SMul R T\ninst✝³ : IsScalarTower R T T\ninst✝² : IsScalarTower R S T\ninst✝¹ : FaithfulSMul R S\ninst✝ : ... | [
"R : Type u_4\nS : Type u_5\nT : Type u_6\ninst✝¹⁰ : Monoid S\ninst✝⁹ : MulOneClass T\ninst✝⁸ : SMul R S\ninst✝⁷ : IsScalarTower R S S\ninst✝⁶ : MulAction S T\ninst✝⁵ : IsScalarTower S T T\ninst✝⁴ : SMul R T\ninst✝³ : IsScalarTower R T T\ninst✝² : IsScalarTower R S T\ninst✝¹ : FaithfulSMul R S\ninst✝ : FaithfulSMul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sum.Basic | {
"line": 249,
"column": 35
} | {
"line": 249,
"column": 46
} | {
"line": 249,
"column": 47
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Sort u_3\nf : α → γ\ng₁ g₂ : β → γ\nhg : Sum.elim f g₁ = Sum.elim f g₂\nb : β\n⊢ g₁ b = g₂ b",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nγ : Sort u_3\nf : α → γ\ng₁ g₂ : β → γ\nhg : Sum.elim f g₁ = Sum.elim f g₂\nb : β\n⊢ g₁ b = g₂ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Defs | {
"line": 515,
"column": 14
} | {
"line": 515,
"column": 25
} | {
"line": 515,
"column": 26
} | [
{
"pp": "G : Type u_3\nH : Type u_4\ninst✝⁴ : Group G\ninst✝³ : Mul H\ninst✝² : MulAction G H\ninst✝¹ : SMulCommClass G H H\ninst✝ : IsScalarTower G H H\na b x : H\nr : G\nh : SemiconjBy x (r • a) (r • b)\n⊢ SemiconjBy x a b",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"G : Type u_3\nH : Type u_4\ninst✝⁴ : Group G\ninst✝³ : Mul H\ninst✝² : MulAction G H\ninst✝¹ : SMulCommClass G H H\ninst✝ : IsScalarTower G H H\na b x : H\nr : G\nh : SemiconjBy x (r • a) (r • b)\n⊢ SemiconjBy x a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Defs | {
"line": 520,
"column": 14
} | {
"line": 520,
"column": 25
} | {
"line": 520,
"column": 26
} | [
{
"pp": "G : Type u_3\nH : Type u_4\ninst✝⁴ : Group G\ninst✝³ : Mul H\ninst✝² : MulAction G H\ninst✝¹ : SMulCommClass G H H\ninst✝ : IsScalarTower G H H\na b x : H\nr : G\nh : SemiconjBy (r • x) a b\n⊢ SemiconjBy x a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"G : Type u_3\nH : Type u_4\ninst✝⁴ : Group G\ninst✝³ : Mul H\ninst✝² : MulAction G H\ninst✝¹ : SMulCommClass G H H\ninst✝ : IsScalarTower G H H\na b x : H\nr : G\nh : SemiconjBy (r • x) a b\n⊢ SemiconjBy x a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Defs | {
"line": 614,
"column": 22
} | {
"line": 614,
"column": 84
} | {
"line": 616,
"column": 0
} | [
{
"pp": "M : Type u_9\nN : Type u_10\nP : Type u_11\nQ : Type u_12\ninst✝⁹ : SMul M N\ninst✝⁸ : SMul M P\ninst✝⁷ : SMul M Q\ninst✝⁶ : SMul P Q\ninst✝⁵ : Monoid N\ninst✝⁴ : MulAction N P\ninst✝³ : MulAction N Q\ninst✝² : IsScalarTower M N P\ninst✝¹ : IsScalarTower M N Q\ninst✝ : IsScalarTower M P Q\nh : Surjecti... | [] | by obtain ⟨m, rfl⟩ := h n; simp_rw [smul_one_smul, smul_assoc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.Pi.Basic | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 30
} | {
"line": 191,
"column": 31
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝¹ : One β\ninst✝ : One γ\nf : α → β\ng : β → γ\nhg : Injective g\nhg0 : g 1 = 1\n⊢ g ∘ f = 1 ↔ f = 1",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝¹ : One β\ninst✝ : One γ\nf : α → β\ng : β → γ\nhg : Injective g\nhg0 : g 1 = 1\n⊢ g ∘ f = 1 ↔ f = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Prod.Basic | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 60
} | {
"line": 72,
"column": 61
} | [
{
"pp": "α : Type u_5\nβ : Type u_6\na : α\nb₁ b₂ : β\nh : (a, b₁) = (a, b₂)\n⊢ b₁ = b₂",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_5\nβ : Type u_6\na : α\nb₁ b₂ : β\nh : (a, b₁) = (a, b₂)\n⊢ b₁ = b₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Prod.Basic | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 55
} | {
"line": 76,
"column": 56
} | [
{
"pp": "α : Type u_5\nβ : Type u_6\nb : β\nb₁ b₂ : α\nh : (fun a ↦ (a, b)) b₁ = (fun a ↦ (a, b)) b₂\n⊢ b₁ = b₂",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_5\nβ : Type u_6\nb : β\nb₁ b₂ : α\nh : (fun a ↦ (a, b)) b₁ = (fun a ↦ (a, b)) b₂\n⊢ b₁ = b₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 218,
"column": 4
} | {
"line": 218,
"column": 15
} | {
"line": 218,
"column": 16
} | [
{
"pp": "case lt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.lt\n⊢ Ordering.lt ≠ Ordering.gt ↔ a ≤ b",
"ppTerm": "?lt",
"assigned": true,
"usedConstants": [
"Ordering.gt",
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"PartialOrder.toP... | [
"case lt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.lt\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 15
} | {
"line": 219,
"column": 16
} | [
{
"pp": "case eq\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.eq\n⊢ Ordering.eq ≠ Ordering.gt ↔ a ≤ b",
"ppTerm": "?eq",
"assigned": true,
"usedConstants": [
"Ordering.gt",
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"PartialOrder.toP... | [
"case eq\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.eq\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 220,
"column": 4
} | {
"line": 220,
"column": 15
} | {
"line": 220,
"column": 16
} | [
{
"pp": "case gt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.gt\n⊢ Ordering.gt ≠ Ordering.gt ↔ a ≤ b",
"ppTerm": "?gt",
"assigned": true,
"usedConstants": [
"Ordering.gt",
"Eq.mpr",
"False",
"Preorder.toLT",
"congrArg",
"PartialOrder.... | [
"case gt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.gt\n⊢ b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 15
} | {
"line": 224,
"column": 16
} | [
{
"pp": "case lt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.lt\n⊢ Ordering.lt ≠ Ordering.lt ↔ b ≤ a",
"ppTerm": "?lt",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"P... | [
"case lt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.lt\n⊢ a < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 15
} | {
"line": 225,
"column": 16
} | [
{
"pp": "case eq\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.eq\n⊢ Ordering.eq ≠ Ordering.lt ↔ b ≤ a",
"ppTerm": "?eq",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"PartialOrder.toPreorder",
"noCo... | [
"case eq\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.eq\n⊢ b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 226,
"column": 4
} | {
"line": 226,
"column": 15
} | {
"line": 226,
"column": 16
} | [
{
"pp": "case gt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.gt\n⊢ Ordering.gt ≠ Ordering.lt ↔ b ≤ a",
"ppTerm": "?gt",
"assigned": true,
"usedConstants": [
"Ordering.gt",
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"PartialOrder.toP... | [
"case gt\nα : Type u_1\ninst✝ : LinearOrder α\na b : α\nh : compare a b = Ordering.gt\n⊢ b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Max | {
"line": 115,
"column": 29
} | {
"line": 115,
"column": 49
} | {
"line": 115,
"column": 50
} | [
{
"pp": "α : Type u_3\ninst✝¹ : LinearOrder α\ninst✝ : NoBotOrder α\na : α\n⊢ ∃ b, b < a",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_3\ninst✝¹ : LinearOrder α\ninst✝ : NoBotOrder α\na : α\n⊢ ∃ b, b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Basic | {
"line": 413,
"column": 37
} | {
"line": 413,
"column": 55
} | {
"line": 415,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrder α\na b : α\n⊢ (if ¬b ≤ a then a else b) = if a < b then a else b",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Line... | [] | simp only [not_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.Basic | {
"line": 417,
"column": 37
} | {
"line": 417,
"column": 55
} | {
"line": 419,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrder α\na b : α\n⊢ (if ¬b ≤ a then b else a) = if a < b then b else a",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Line... | [] | simp only [not_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.Basic | {
"line": 671,
"column": 61
} | {
"line": 671,
"column": 84
} | {
"line": 671,
"column": 85
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : Preorder α\ninst✝ : Nonempty β\na b : α\n⊢ const β a < const β b ↔ a < b",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.preorder",
"Preorder.toLT",
"Function.const_le_const._simp_1",
"congrArg",
... | [
"α : Type u_2\nβ : Type u_3\ninst✝¹ : Preorder α\ninst✝ : Nonempty β\na b : α\n⊢ a < b → a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Init | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 11
} | {
"line": 347,
"column": 12
} | [
{
"pp": "case self\na b c d e m n k : ℕ\np : ℕ → Prop\nP : ℕ → Sort u_1\nhP : P n\nh : (k : ℕ) → k < n → n ≤ k → P (k + 1) → P k\n⊢ P n",
"ppTerm": "?self",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hP"
],
"usedGoals": []
}
] | [] | | self => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Order.RelClasses | {
"line": 77,
"column": 16
} | {
"line": 77,
"column": 27
} | {
"line": 77,
"column": 28
} | [
{
"pp": "α : Type u\nr : α → α → Prop\ninst✝¹ : Std.Irrefl r\ninst✝ : Subsingleton α\n⊢ ∀ (a b : α), r a b = emptyRelation a b",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"iff_false",
"congrArg",
"eq_iff_iff._simp_1",
"emptyRelation... | [
"α : Type u\nr : α → α → Prop\ninst✝¹ : Std.Irrefl r\ninst✝ : Subsingleton α\n⊢ ∀ (i : α), ¬r i i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Monotone.Defs | {
"line": 548,
"column": 2
} | {
"line": 549,
"column": 80
} | {
"line": 551,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : Preorder γ\ninst✝ : Preorder δ\nf : α → γ\ng : β → δ\nhf : StrictAnti f\nhg : StrictAnti g\na b : α × β\n⊢ a < b → Prod.map f g b < Prod.map f g a",
"ppTerm": "?m.19",
"assigned": true,
... | [] | simp only [Prod.lt_iff]
exact Or.imp (And.imp hf.imp hg.antitone.imp) (And.imp hf.antitone.imp hg.imp) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Monotone.Defs | {
"line": 548,
"column": 2
} | {
"line": 549,
"column": 80
} | {
"line": 551,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : Preorder γ\ninst✝ : Preorder δ\nf : α → γ\ng : β → δ\nhf : StrictAnti f\nhg : StrictAnti g\na b : α × β\n⊢ a < b → Prod.map f g b < Prod.map f g a",
"ppTerm": "?m.19",
"assigned": true,
... | [] | simp only [Prod.lt_iff]
exact Or.imp (And.imp hf.imp hg.antitone.imp) (And.imp hf.antitone.imp hg.imp) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.PropInstances | {
"line": 48,
"column": 17
} | {
"line": 48,
"column": 44
} | {
"line": 48,
"column": 44
} | [
{
"pp": "p q : Prop\n⊢ p ≤ q ∨ q ≤ p",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"true_or",
"Prop.le",
"instInhabitedTrue",
"Classical.propDecidable",
"LE.le",
"dite",
"instNonemptyOfInhabited",... | [] | by_cases h : q <;> simp [h] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Order.PropInstances | {
"line": 48,
"column": 17
} | {
"line": 48,
"column": 44
} | {
"line": 48,
"column": 44
} | [
{
"pp": "p q : Prop\n⊢ p ≤ q ∨ q ≤ p",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"true_or",
"Prop.le",
"instInhabitedTrue",
"Classical.propDecidable",
"LE.le",
"dite",
"instNonemptyOfInhabited",... | [] | by_cases h : q <;> simp [h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.PropInstances | {
"line": 48,
"column": 17
} | {
"line": 48,
"column": 44
} | {
"line": 48,
"column": 44
} | [
{
"pp": "p q : Prop\n⊢ p ≤ q ∨ q ≤ p",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"true_or",
"Prop.le",
"instInhabitedTrue",
"Classical.propDecidable",
"LE.le",
"dite",
"instNonemptyOfInhabited",... | [] | by_cases h : q <;> simp [h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Monotone.Basic | {
"line": 278,
"column": 4
} | {
"line": 278,
"column": 24
} | {
"line": 278,
"column": 25
} | [
{
"pp": "case pos\nα : Type u\nβ : Type v\ninst✝² : Preorder α\ninst✝¹ : Preorder β\nf g : α → β\nhf : StrictMono f\nhg : StrictMono g\np : α → Prop\ninst✝ : DecidablePred p\nhp : ∀ ⦃x y : α⦄, x < y → p y → p x\nhfg : ∀ ⦃x y : α⦄, p x → ¬p y → x < y → f x < g y\nx y : α\nh : x < y\nhy : p y\nhx : p x\n⊢ (fun x ... | [
"case pos\nα : Type u\nβ : Type v\ninst✝² : Preorder α\ninst✝¹ : Preorder β\nf g : α → β\nhf : StrictMono f\nhg : StrictMono g\np : α → Prop\ninst✝ : DecidablePred p\nhp : ∀ ⦃x y : α⦄, x < y → p y → p x\nhfg : ∀ ⦃x y : α⦄, p x → ¬p y → x < y → f x < g y\nx y : α\nh : x < y\nhy : p y\nhx : p x\n⊢ f x < f y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Monotone.Basic | {
"line": 280,
"column": 4
} | {
"line": 280,
"column": 24
} | {
"line": 280,
"column": 25
} | [
{
"pp": "case pos\nα : Type u\nβ : Type v\ninst✝² : Preorder α\ninst✝¹ : Preorder β\nf g : α → β\nhf : StrictMono f\nhg : StrictMono g\np : α → Prop\ninst✝ : DecidablePred p\nhp : ∀ ⦃x y : α⦄, x < y → p y → p x\nhfg : ∀ ⦃x y : α⦄, p x → ¬p y → x < y → f x < g y\nx y : α\nh : x < y\nhy : ¬p y\nhx : p x\n⊢ (fun x... | [
"case pos\nα : Type u\nβ : Type v\ninst✝² : Preorder α\ninst✝¹ : Preorder β\nf g : α → β\nhf : StrictMono f\nhg : StrictMono g\np : α → Prop\ninst✝ : DecidablePred p\nhp : ∀ ⦃x y : α⦄, x < y → p y → p x\nhfg : ∀ ⦃x y : α⦄, p x → ¬p y → x < y → f x < g y\nx y : α\nh : x < y\nhy : ¬p y\nhx : p x\n⊢ f x < g y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Monotone.Basic | {
"line": 281,
"column": 4
} | {
"line": 281,
"column": 24
} | {
"line": 281,
"column": 25
} | [
{
"pp": "case neg\nα : Type u\nβ : Type v\ninst✝² : Preorder α\ninst✝¹ : Preorder β\nf g : α → β\nhf : StrictMono f\nhg : StrictMono g\np : α → Prop\ninst✝ : DecidablePred p\nhp : ∀ ⦃x y : α⦄, x < y → p y → p x\nhfg : ∀ ⦃x y : α⦄, p x → ¬p y → x < y → f x < g y\nx y : α\nh : x < y\nhy : ¬p y\nhx : ¬p x\n⊢ (fun ... | [
"case neg\nα : Type u\nβ : Type v\ninst✝² : Preorder α\ninst✝¹ : Preorder β\nf g : α → β\nhf : StrictMono f\nhg : StrictMono g\np : α → Prop\ninst✝ : DecidablePred p\nhp : ∀ ⦃x y : α⦄, x < y → p y → p x\nhfg : ∀ ⦃x y : α⦄, p x → ¬p y → x < y → f x < g y\nx y : α\nh : x < y\nhy : ¬p y\nhx : ¬p x\n⊢ g x < g y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Monotone.Basic | {
"line": 694,
"column": 61
} | {
"line": 696,
"column": 76
} | {
"line": 698,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝ : Preorder α\nf : ℤ → α\nhf : Antitone f\nn : ℤ\nx : α\nh1 : f (n + 1) < x\nh2 : x < f n\na : ℤ\n⊢ f a ≠ x",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"False",
"Preorder.toLT",
"Int.instLinearOrder",
"Antitone.reflect_lt",
"Parti... | [] | by
rintro rfl
exact (hf.reflect_lt h2).not_ge (Int.le_of_lt_add_one <| hf.reflect_lt h1) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Disjoint | {
"line": 97,
"column": 18
} | {
"line": 97,
"column": 29
} | {
"line": 97,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\na b : α\nh : Disjoint a b\nx : α\nh₁ : x ≤ a\nh₂ : x ≤ b\n⊢ x = ⊥",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\na b : α\nh : Disjoint a b\nx : α\nh₁ : x ≤ a\nh₂ : x ≤ b\n⊢ x = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Basic | {
"line": 460,
"column": 2
} | {
"line": 460,
"column": 13
} | {
"line": 460,
"column": 14
} | [
{
"pp": "α : Type u\ns : Set α\ninst✝ : IsEmpty ↑s\n⊢ s = ∅",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ns : Set α\ninst✝ : IsEmpty ↑s\n⊢ s = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Basic | {
"line": 1077,
"column": 26
} | {
"line": 1077,
"column": 70
} | {
"line": 1078,
"column": 2
} | [
{
"pp": "α : Type u_1\ns✝ t u : Set α\np : α → Prop\ns : Set { a // p a }\na : { a // p a }\n⊢ a ∈ (fun s ↦ {a | ↑a ∈ ↑s}) ((fun s ↦ ⟨{a | ∃ h, ⟨a, h⟩ ∈ s}, ⋯⟩) s) ↔ a ∈ s",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"setOf",
"Membership.mem",
"Exists",
"Subtype"... | [] | exact ⟨fun h ↦ h.2, fun h ↦ ⟨a.property, h⟩⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Set.Insert | {
"line": 268,
"column": 2
} | {
"line": 269,
"column": 41
} | {
"line": 269,
"column": 42
} | [
{
"pp": "α : Type u_1\nl : List α\na : α\n⊢ {x | x ∈ l} = {a} ↔ ∃ n, n > 0 ∧ l = List.replicate n a",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"and_true",
"congrArg",
"_private.Mathlib.Data.Set.Insert.0.Set.setOf_mem_list_eq_re... | [
"α : Type u_1\nl : List α\na : α\n⊢ ((∀ (x : α), x ∈ l → x = a) → a ∈ l → ∃ x, x ∈ l) ∧ ∀ (x : α), x ∈ l → (∀ (x : α), x ∈ l → x = a) → a ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Insert | {
"line": 416,
"column": 17
} | {
"line": 416,
"column": 42
} | {
"line": 416,
"column": 43
} | [
{
"pp": "p q : Prop\n⊢ q ∈ {p}ᶜ ↔ q ∈ {¬p}",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl.compl",
"eq_iff_iff._simp_1",
"Membership.mem",
"Set.instSingletonSet",
"id",
"Set.instCompl",
"Iff",
"Set.mem... | [
"p q : Prop\n⊢ ¬(p ↔ q) ↔ (¬p ↔ q)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Lattice | {
"line": 433,
"column": 4
} | {
"line": 433,
"column": 15
} | {
"line": 433,
"column": 16
} | [
{
"pp": "case refine_1\nα : Type u\ninst✝ : Lattice α\na c : α\nh : a ⊓ a = c ∧ a ⊔ a = c\n⊢ a = c ∧ a = c",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"and_self",
"id",
"And",
"Eq"
],
"usedFVars": [
"α",
"a",
"c"
... | [
"case refine_1\nα : Type u\ninst✝ : Lattice α\na c : α\nh : a ⊓ a = c ∧ a ⊔ a = c\n⊢ a = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Lattice | {
"line": 962,
"column": 4
} | {
"line": 963,
"column": 22
} | {
"line": 964,
"column": 2
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝³ : Max α\ninst✝² : LE α\ninst✝¹ : LT α\ninst✝ : SemilatticeSup β\nf : α → β\nhf_inj : Injective f\nle : ∀ {x y : α}, f x ≤ f y ↔ x ≤ y\nlt : ∀ {x y : α}, f x < f y ↔ x < y\nmap_sup : ∀ (a b : α), f (a ⊔ b) = f a ⊔ f b\na b : α\n⊢ b ≤ a ⊔ b",
"ppTerm": "?m.65",
"ass... | [] | rw [← le, map_sup]
exact le_sup_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Lattice | {
"line": 962,
"column": 4
} | {
"line": 963,
"column": 22
} | {
"line": 964,
"column": 2
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝³ : Max α\ninst✝² : LE α\ninst✝¹ : LT α\ninst✝ : SemilatticeSup β\nf : α → β\nhf_inj : Injective f\nle : ∀ {x y : α}, f x ≤ f y ↔ x ≤ y\nlt : ∀ {x y : α}, f x < f y ↔ x < y\nmap_sup : ∀ (a b : α), f (a ⊔ b) = f a ⊔ f b\na b : α\n⊢ b ≤ a ⊔ b",
"ppTerm": "?m.65",
"ass... | [] | rw [← le, map_sup]
exact le_sup_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Heyting.Basic | {
"line": 243,
"column": 55
} | {
"line": 243,
"column": 67
} | {
"line": 243,
"column": 68
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ a ≤ b ⇨ c ↔ b ⊓ a ≤ c",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"GeneralizedH... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ a ⊓ b ≤ c ↔ b ⊓ a ≤ c"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 246,
"column": 55
} | {
"line": 246,
"column": 67
} | {
"line": 246,
"column": 68
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ a ≤ b ⇨ c ↔ b ≤ a ⇨ c",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"GeneralizedH... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ a ⊓ b ≤ c ↔ b ≤ a ⇨ c"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 253,
"column": 55
} | {
"line": 253,
"column": 67
} | {
"line": 253,
"column": 68
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b : α\n⊢ a ≤ a ⇨ b ↔ a ≤ b",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"GeneralizedHeyting... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b : α\n⊢ a ⊓ a ≤ b ↔ a ≤ b"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 279,
"column": 68
} | {
"line": 279,
"column": 80
} | {
"line": 279,
"column": 81
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b : α\n⊢ ⊤ ≤ a ⇨ b ↔ a ≤ b",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"GeneralizedHeytin... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b : α\n⊢ ⊤ ⊓ a ≤ b ↔ a ≤ b"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 288,
"column": 38
} | {
"line": 288,
"column": 50
} | {
"line": 288,
"column": 51
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b : α\n⊢ b ≤ ⊤ ⇨ a ↔ b ≤ a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toParti... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b : α\n⊢ b ⊓ ⊤ ≤ a ↔ b ≤ a"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 292,
"column": 43
} | {
"line": 292,
"column": 55
} | {
"line": 292,
"column": 56
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ≤ a ⇨ b ⇨ c ↔ d ≤ a ⊓ b ⇨ c",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"le_himp_iff._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semilattice... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ⊓ a ⊓ b ≤ c ↔ d ⊓ (a ⊓ b) ≤ c"
] | le_himp_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.Heyting.Basic | {
"line": 296,
"column": 6
} | {
"line": 296,
"column": 18
} | {
"line": 296,
"column": 19
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ b ⇨ c ≤ (a ⇨ b) ⇨ a ⇨ c",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Generaliz... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ (b ⇨ c) ⊓ (a ⇨ b) ≤ a ⇨ c"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 296,
"column": 19
} | {
"line": 296,
"column": 31
} | {
"line": 296,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ (b ⇨ c) ⊓ (a ⇨ b) ≤ a ⇨ c",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"General... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ (b ⇨ c) ⊓ (a ⇨ b) ⊓ a ≤ c"
] | le_himp_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 13
} | {
"line": 301,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ (b ⇨ c) ⊓ (a ⇨ b) ⊓ a ≤ c",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ (b ⇨ c) ⊓ (a ⇨ b) ⊓ a ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Heyting.Basic | {
"line": 310,
"column": 43
} | {
"line": 310,
"column": 55
} | {
"line": 310,
"column": 56
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ≤ a ⇨ b ⊓ c ↔ d ≤ (a ⇨ b) ⊓ (a ⇨ c)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"le_himp_iff._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Sem... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ⊓ a ≤ b ⊓ c ↔ d ≤ (a ⇨ b) ⊓ (a ⇨ c)"
] | le_himp_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
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