module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Topology.Sets.VietorisTopology | {
"line": 270,
"column": 2
} | {
"line": 290,
"column": 52
} | {
"line": 292,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : TopologicalSpace α\nK : Set α\nhK : IsCompact K\ns : Set (Set α)\nhsK : s ⊆ 𝒫 K\nhs : ∀ L ∈ s, IsCompact L\nS : Set (Set (Set α))\nhS : S ⊆ powerset '' {U | IsOpen[inst✝] U} ∪ (fun V ↦ {s | (s ∩ V).Nonempty}) '' {V | IsOpen[inst✝] V}\nhKS : {t | t ⊆ K ∧ ∀ L ∈ s, (t ∩ L)... | [] | · -- Otherwise, the set `K \ ⋃ Uⱼ` intersects every `Lᵢ`, so it is in one of the covering sets.
simp_rw [← sdiff_nonempty] at hsu
replace hsu L (h : L ∈ s) : (K \ ⋃₀ u ∩ L).Nonempty := (hsu L h).mono <| by grind
obtain ⟨_, hUS, hUu⟩ := mem_sUnion.mp <| hKS ⟨sdiff_subset, hsu⟩
rcases hS hUS with ⟨U, hU, ... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.MetricSpace.HolderNorm | {
"line": 312,
"column": 18
} | {
"line": 312,
"column": 32
} | {
"line": 312,
"column": 33
} | [
{
"pp": "case pos.refine_2\nX : Type u_1\nY : Type u_2\ninst✝⁴ : MetricSpace X\ninst✝³ : NormedAddCommGroup Y\nr : ℝ≥0\nf : X → Y\nα : Type u_3\ninst✝² : NormedRing α\ninst✝¹ : Module α Y\ninst✝ : NormSMulClass α Y\nc : α\nhc : ¬‖c‖₊ = 0\nhf : MemHolder r f\nx₁ x₂ : X\n⊢ ↑‖c‖₊ * edist (f x₁) (f x₂) ≤ ↑(nnHolder... | [
"case pos.refine_2\nX : Type u_1\nY : Type u_2\ninst✝⁴ : MetricSpace X\ninst✝³ : NormedAddCommGroup Y\nr : ℝ≥0\nf : X → Y\nα : Type u_3\ninst✝² : NormedRing α\ninst✝¹ : Module α Y\ninst✝ : NormSMulClass α Y\nc : α\nhc : ¬‖c‖₊ = 0\nhf : MemHolder r f\nx₁ x₂ : X\n⊢ ↑‖c‖₊ • edist (f x₁) (f x₂) ≤ ↑(nnHolderNorm r (c • ... | ← smul_eq_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.MetricSpace.Infsep | {
"line": 58,
"column": 90
} | {
"line": 60,
"column": 66
} | {
"line": 62,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : EDist α\ns : Set α\n⊢ 0 < s.einfsep ↔ ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"Eq.mpr",
"Preorder.toLT",
"Iff.of_eq",
"congrArg",
... | [] | by
rw [pos_iff_ne_zero, Ne, einfsep_zero]
simp only [not_forall, not_exists, not_lt, exists_prop, not_and] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.MetricSpace.Infsep | {
"line": 255,
"column": 2
} | {
"line": 256,
"column": 29
} | {
"line": 258,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : EMetricSpace α\ns : Set α\ninst✝ : Finite ↑s\n⊢ ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Membership.mem",... | [] | rw [← einfsep_pos]
exact einfsep_pos_of_finite | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.MetricSpace.Infsep | {
"line": 255,
"column": 2
} | {
"line": 256,
"column": 29
} | {
"line": 258,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : EMetricSpace α\ns : Set α\ninst✝ : Finite ↑s\n⊢ ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Membership.mem",... | [] | rw [← einfsep_pos]
exact einfsep_pos_of_finite | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.MetricSpace.Infsep | {
"line": 376,
"column": 6
} | {
"line": 376,
"column": 31
} | {
"line": 377,
"column": 6
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PseudoMetricSpace α\ns : Set α\ninst✝ : Decidable s.Nontrivial\nhs : s.Nontrivial\n⊢ BddBelow (uncurry dist '' s.offDiag)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Real.instLE",
"Real",
"Real.instZero",
"lowerBounds",
"Se... | [
"α : Type u_1\ninst✝¹ : PseudoMetricSpace α\ns : Set α\ninst✝ : Decidable s.Nontrivial\nhs : s.Nontrivial\nd : ℝ\nh : d ∈ uncurry dist '' s.offDiag\n⊢ 0 ≤ d"
] | refine ⟨0, fun d h => ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.MetricSpace.Snowflaking | {
"line": 400,
"column": 2
} | {
"line": 401,
"column": 75
} | {
"line": 403,
"column": 0
} | [
{
"pp": "X : Type u_1\nα : ℝ\nhα₀ : 0 < α\nhα₁ : α ≤ 1\ninst✝ : PseudoEMetricSpace X\ns : Set X\n⊢ ediam (⇑ofSnowflaking ⁻¹' s) = ediam s ^ α",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Equiv.instEquivLike",
"ENNReal.rpow_inv_rpow",
"Met... | [] | rw [← ENNReal.rpow_inv_rpow hα₀.ne' (ediam _), ← ediam_preimage_toSnowflaking,
← Set.preimage_comp, ofSnowflaking_comp_toSnowflaking, Set.preimage_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.MetricSpace.Snowflaking | {
"line": 400,
"column": 2
} | {
"line": 401,
"column": 75
} | {
"line": 403,
"column": 0
} | [
{
"pp": "X : Type u_1\nα : ℝ\nhα₀ : 0 < α\nhα₁ : α ≤ 1\ninst✝ : PseudoEMetricSpace X\ns : Set X\n⊢ ediam (⇑ofSnowflaking ⁻¹' s) = ediam s ^ α",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Equiv.instEquivLike",
"ENNReal.rpow_inv_rpow",
"Met... | [] | rw [← ENNReal.rpow_inv_rpow hα₀.ne' (ediam _), ← ediam_preimage_toSnowflaking,
← Set.preimage_comp, ofSnowflaking_comp_toSnowflaking, Set.preimage_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.MetricSpace.Snowflaking | {
"line": 400,
"column": 2
} | {
"line": 401,
"column": 75
} | {
"line": 403,
"column": 0
} | [
{
"pp": "X : Type u_1\nα : ℝ\nhα₀ : 0 < α\nhα₁ : α ≤ 1\ninst✝ : PseudoEMetricSpace X\ns : Set X\n⊢ ediam (⇑ofSnowflaking ⁻¹' s) = ediam s ^ α",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Equiv.instEquivLike",
"ENNReal.rpow_inv_rpow",
"Met... | [] | rw [← ENNReal.rpow_inv_rpow hα₀.ne' (ediam _), ← ediam_preimage_toSnowflaking,
← Set.preimage_comp, ofSnowflaking_comp_toSnowflaking, Set.preimage_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sets.VietorisTopology | {
"line": 476,
"column": 4
} | {
"line": 476,
"column": 79
} | {
"line": 477,
"column": 4
} | [
{
"pp": "case inr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nU : Set (α × β)\nhU : U ∈ {V | IsOpen[instTopologicalSpaceProd] V}\nK : Compacts α\nL : Compacts β\nx : α\ny : β\nhx : x ∈ K\nhy : y ∈ L\nhxy : (x, y) ∈ U\nV : Set α\nW : Set β\nhV : IsOpen[inst✝¹] V\nhW : Is... | [
"case inr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nU : Set (α × β)\nhU : U ∈ {V | IsOpen[instTopologicalSpaceProd] V}\nK : Compacts α\nL : Compacts β\nx : α\ny : β\nhx : x ∈ K\nhy : y ∈ L\nhxy : (x, y) ∈ U\nV : Set α\nW : Set β\nhV : IsOpen[inst✝¹] V\nhW : IsOpen[inst✝] ... | simp_rw [Function.comp_apply, coe_prod, prod_inter_prod, prod_nonempty_iff] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Topology.NatEmbedding | {
"line": 40,
"column": 6
} | {
"line": 40,
"column": 16
} | {
"line": 41,
"column": 2
} | [
{
"pp": "case refine_2\nX : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : T2Space X\ninst✝ : Infinite X\nU : ℕ → Set X\nhne✝ : ∀ (n : ℕ), (U n).Nonempty\nho : ∀ (n : ℕ), IsOpen[inst✝²] (U n)\nhd : Pairwise (Disjoint on U)\nn n' : ℕ\nhne : n ≠ n'\nm m' : ℕ\n⊢ Nat.pair n m ≠ Nat.pair n' m'",
"ppTerm": "?ref... | [] | simp [hne] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.Order.PartialSups | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 77
} | {
"line": 51,
"column": 0
} | [
{
"pp": "L : Type u_1\ninst✝³ : SemilatticeSup L\ninst✝² : TopologicalSpace L\ninst✝¹ : ContinuousSup L\nX : Type u_2\ninst✝ : TopologicalSpace X\nf : ℕ → X → L\nn : ℕ\nx : X\nhf : ∀ k ≤ n, ContinuousAt (f k) x\n⊢ ContinuousAt ((partialSups f) n) x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstan... | [] | simpa only [← Pi.partialSups_apply] using ContinuousAt.partialSups_apply hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Topology.Order.PartialSups | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 77
} | {
"line": 51,
"column": 0
} | [
{
"pp": "L : Type u_1\ninst✝³ : SemilatticeSup L\ninst✝² : TopologicalSpace L\ninst✝¹ : ContinuousSup L\nX : Type u_2\ninst✝ : TopologicalSpace X\nf : ℕ → X → L\nn : ℕ\nx : X\nhf : ∀ k ≤ n, ContinuousAt (f k) x\n⊢ ContinuousAt ((partialSups f) n) x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstan... | [] | simpa only [← Pi.partialSups_apply] using ContinuousAt.partialSups_apply hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.PartialSups | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 77
} | {
"line": 51,
"column": 0
} | [
{
"pp": "L : Type u_1\ninst✝³ : SemilatticeSup L\ninst✝² : TopologicalSpace L\ninst✝¹ : ContinuousSup L\nX : Type u_2\ninst✝ : TopologicalSpace X\nf : ℕ → X → L\nn : ℕ\nx : X\nhf : ∀ k ≤ n, ContinuousAt (f k) x\n⊢ ContinuousAt ((partialSups f) n) x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstan... | [] | simpa only [← Pi.partialSups_apply] using ContinuousAt.partialSups_apply hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sheaves.Skyscraper | {
"line": 79,
"column": 2
} | {
"line": 81,
"column": 25
} | {
"line": 83,
"column": 0
} | [
{
"pp": "X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{w, v} C\ninst✝ : HasTerminal C\nA : C\nhd : (U : Opens ↑(of PUnit.{u + 1})) → Decidable (PUnit.unit ∈ U)\n⊢ skyscraperPresheaf p₀ A =\n (Presheaf.pushforward C (ofHom (ContinuousMap.const (↑(of PUnit.{u... | [] | convert_to @skyscraperPresheaf X p₀ (fun U => hd <| (Opens.map <| ofHom <|
ContinuousMap.const _ p₀).obj U)
C _ _ A = _ <;> congr | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Topology.Sheaves.Skyscraper | {
"line": 79,
"column": 2
} | {
"line": 81,
"column": 25
} | {
"line": 83,
"column": 0
} | [
{
"pp": "X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{w, v} C\ninst✝ : HasTerminal C\nA : C\nhd : (U : Opens ↑(of PUnit.{u + 1})) → Decidable (PUnit.unit ∈ U)\n⊢ skyscraperPresheaf p₀ A =\n (Presheaf.pushforward C (ofHom (ContinuousMap.const (↑(of PUnit.{u... | [] | convert_to @skyscraperPresheaf X p₀ (fun U => hd <| (Opens.map <| ofHom <|
ContinuousMap.const _ p₀).obj U)
C _ _ A = _ <;> congr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Sheaves.Skyscraper | {
"line": 79,
"column": 2
} | {
"line": 81,
"column": 25
} | {
"line": 83,
"column": 0
} | [
{
"pp": "X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{w, v} C\ninst✝ : HasTerminal C\nA : C\nhd : (U : Opens ↑(of PUnit.{u + 1})) → Decidable (PUnit.unit ∈ U)\n⊢ skyscraperPresheaf p₀ A =\n (Presheaf.pushforward C (ofHom (ContinuousMap.const (↑(of PUnit.{u... | [] | convert_to @skyscraperPresheaf X p₀ (fun U => hd <| (Opens.map <| ofHom <|
ContinuousMap.const _ p₀).obj U)
C _ _ A = _ <;> congr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sheaves.Skyscraper | {
"line": 171,
"column": 58
} | {
"line": 171,
"column": 78
} | {
"line": 171,
"column": 79
} | [
{
"pp": "X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{u, v} C\nA : C\ninst✝ : HasTerminal C\ny : ↑X\nh✝ : p₀ ⤳ y\nc : Cocone ((OpenNhds.inclusion y).op ⋙ skyscraperPresheaf p₀ A)\nf : (skyscraperPresheafCoconeOfSpecializes p₀ A h✝).pt ⟶ c.pt\nh : ∀ (j : (Open... | [
"X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{u, v} C\nA : C\ninst✝ : HasTerminal C\ny : ↑X\nh✝ : p₀ ⤳ y\nc : Cocone ((OpenNhds.inclusion y).op ⋙ skyscraperPresheaf p₀ A)\nf : (skyscraperPresheafCoconeOfSpecializes p₀ A h✝).pt ⟶ c.pt\nh : ∀ (j : (OpenNhds y)ᵒᵖ), ... | eqToHom_trans_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 263,
"column": 8
} | {
"line": 263,
"column": 86
} | {
"line": 264,
"column": 8
} | [
{
"pp": "case op.op\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nc : Cone (SheafConditionEqualizerProducts.diagram F U)\nx y : CategoryTheory.Pairwise ι\nf' : unop (op y) ⟶ unop (op x)\n⊢ ((Functor.const (CategoryTheory.Pairwise ι)ᵒ... | [
"case op.op.single.single.id_single\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nc : Cone (SheafConditionEqualizerProducts.diagram F U)\ni : ι\n⊢ ((Functor.const (CategoryTheory.Pairwise ι)ᵒᵖ).obj c.pt).map (Quiver.Hom.op (id_single i))... | rcases x with (⟨i⟩ | ⟨⟩) <;> rcases y with (⟨⟩ | ⟨j, j⟩) <;> rcases f' with ⟨⟩ | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 398,
"column": 12
} | {
"line": 398,
"column": 28
} | {
"line": 399,
"column": 12
} | [
{
"pp": "case op\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nP : IsLimit (SheafConditionEqualizerProducts.fork F U)\nx : CategoryTheory.Pairwise ι\n⊢ 𝟙 ((coneEquiv F U).symm.functor.obj (SheafConditionEqualizerProducts.fork F U)).... | [
"case op.single\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nP : IsLimit (SheafConditionEqualizerProducts.fork F U)\na✝ : ι\n⊢ 𝟙 ((coneEquiv F U).symm.functor.obj (SheafConditionEqualizerProducts.fork F U)).pt ≫\n (Functor.mapCone... | rcases x with ⟨⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Topology.SmallInductiveDimension | {
"line": 74,
"column": 8
} | {
"line": 74,
"column": 37
} | {
"line": 74,
"column": 37
} | [
{
"pp": "case mp\nX : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (Set X)\nhs : IsTopologicalBasis s\nh : ∀ U ∈ s, HasSmallInductiveDimensionLT (↑(frontier U)) 0\nU : Set X\nhU : U ∈ s\n⊢ IsClosed U",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"cl... | [
"case mp\nX : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (Set X)\nhs : IsTopologicalBasis s\nh : ∀ U ∈ s, HasSmallInductiveDimensionLT (↑(frontier U)) 0\nU : Set X\nhU : U ∈ s\n⊢ closure U ⊆ U"
] | ← closure_subset_iff_isClosed | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Spectral.ConstructibleTopology | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 51
} | {
"line": 63,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set X\nhs : IsCompact s\nho : IsOpen[inst✝] s\n⊢ IsOpen[constructibleTopology X] s",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"TopologicalSpace.isOpen_generateFrom_of_mem",
"constructibleTopologySubbasis"
],
"us... | [
"X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set X\nhs : IsCompact s\nho : IsOpen[inst✝] s\n⊢ s ∈ constructibleTopologySubbasis X"
] | apply TopologicalSpace.isOpen_generateFrom_of_mem | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Topology.Spectral.ConstructibleTopology | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 51
} | {
"line": 68,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set X\nhs : IsCompact sᶜ\nho : IsClosed[inst✝] s\n⊢ IsOpen[constructibleTopology X] s",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"TopologicalSpace.isOpen_generateFrom_of_mem",
"constructibleTopologySubbasis"
],
... | [
"X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set X\nhs : IsCompact sᶜ\nho : IsClosed[inst✝] s\n⊢ s ∈ constructibleTopologySubbasis X"
] | apply TopologicalSpace.isOpen_generateFrom_of_mem | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Topology.Spectral.ConstructibleTopology | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 24
} | {
"line": 78,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ns : Set X\nhs : s ∈ constructibleTopologySubbasis X\n⊢ IsCompact s",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Compl.compl",
"setOf",
"Membership.mem",
"Set.instCompl",
"Or.casesOn... | [
"case inl\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ns : Set X\nhs : s ∈ {s | IsOpen[inst✝¹] s ∧ IsCompact s}\n⊢ IsCompact s",
"case inr\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ns : Set X\nhs : s ∈ {s | IsClosed[inst✝¹] s ∧ IsCompact sᶜ}\n⊢ IsCompact s"
] | obtain (hs | hs) := hs | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 412,
"column": 12
} | {
"line": 412,
"column": 28
} | {
"line": 413,
"column": 12
} | [
{
"pp": "case op\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nP : IsLimit (SheafConditionEqualizerProducts.fork F U)\nx : CategoryTheory.Pairwise ι\n⊢ 𝟙 (Functor.mapCone F (cocone U).op).pt ≫\n ((coneEquiv F U).symm.functor.ob... | [
"case op.single\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nP : IsLimit (SheafConditionEqualizerProducts.fork F U)\na✝ : ι\n⊢ 𝟙 (Functor.mapCone F (cocone U).op).pt ≫\n ((coneEquiv F U).symm.functor.obj (SheafConditionEqualizerPr... | rcases x with ⟨⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Topology.UniformSpace.CompareReals | {
"line": 63,
"column": 2
} | {
"line": 66,
"column": 24
} | {
"line": 68,
"column": 0
} | [
{
"pp": "⊢ AbsoluteValue.abs.uniformSpace = PseudoMetricSpace.toUniformSpace",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Rat.instOfNat",
"Rat.instSub",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Rea... | [] | ext s
rw [(AbsoluteValue.hasBasis_uniformity _).mem_iff, Metric.uniformity_basis_dist_rat.mem_iff]
simp only [Rat.dist_eq, AbsoluteValue.abs_apply, ← Rat.cast_sub, ← Rat.cast_abs, Rat.cast_lt,
_root_.abs_sub_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.UniformSpace.CompareReals | {
"line": 63,
"column": 2
} | {
"line": 66,
"column": 24
} | {
"line": 68,
"column": 0
} | [
{
"pp": "⊢ AbsoluteValue.abs.uniformSpace = PseudoMetricSpace.toUniformSpace",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Rat.instOfNat",
"Rat.instSub",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Rea... | [] | ext s
rw [(AbsoluteValue.hasBasis_uniformity _).mem_iff, Metric.uniformity_basis_dist_rat.mem_iff]
simp only [Rat.dist_eq, AbsoluteValue.abs_apply, ← Rat.cast_sub, ← Rat.cast_abs, Rat.cast_lt,
_root_.abs_sub_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.UniformSpace.Dini | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 23
} | {
"line": 62,
"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... | [] | exact hF_mono hnm x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.UniformSpace.Ultra.Basic | {
"line": 99,
"column": 2
} | {
"line": 106,
"column": 26
} | {
"line": 108,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝¹ : UniformSpace X\ninst✝ : IsUltraUniformity X\nx : X\ns : Set X\n⊢ s ∈ 𝓝 x ↔ ∃ V ∈ 𝓤 X, SetRel.IsSymm V ∧ SetRel.IsTrans V ∧ ball x V ⊆ s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"SetRel",
"co... | [] | rw [UniformSpace.mem_nhds_iff]
constructor
· rintro ⟨V, V_in, V_sub⟩
rw [IsUltraUniformity.hasBasis.mem_iff'] at V_in
obtain ⟨U, ⟨U_in, U_sym, U_trans⟩, U_sub⟩ := V_in
refine ⟨U, U_in, U_sym, U_trans, (UniformSpace.ball_mono U_sub _).trans V_sub⟩
· rintro ⟨V, V_in, _, _, V_sub⟩
exact ⟨V, V_in, V_s... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.UniformSpace.Ultra.Basic | {
"line": 99,
"column": 2
} | {
"line": 106,
"column": 26
} | {
"line": 108,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝¹ : UniformSpace X\ninst✝ : IsUltraUniformity X\nx : X\ns : Set X\n⊢ s ∈ 𝓝 x ↔ ∃ V ∈ 𝓤 X, SetRel.IsSymm V ∧ SetRel.IsTrans V ∧ ball x V ⊆ s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"SetRel",
"co... | [] | rw [UniformSpace.mem_nhds_iff]
constructor
· rintro ⟨V, V_in, V_sub⟩
rw [IsUltraUniformity.hasBasis.mem_iff'] at V_in
obtain ⟨U, ⟨U_in, U_sym, U_trans⟩, U_sub⟩ := V_in
refine ⟨U, U_in, U_sym, U_trans, (UniformSpace.ball_mono U_sub _).trans V_sub⟩
· rintro ⟨V, V_in, _, _, V_sub⟩
exact ⟨V, V_in, V_s... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sion | {
"line": 412,
"column": 2
} | {
"line": 412,
"column": 95
} | {
"line": 413,
"column": 2
} | [
{
"pp": "case right\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\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\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈... | [
"case right\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\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\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSem... | obtain ⟨b, hb, hb'⟩ : ∃ b ∈ Y, IsMaxOn (fun y ↦ f (ξ y) y) Y b := husc.exists_isMaxOn ne_Y kY | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Data.Nat.BinaryRec | {
"line": 60,
"column": 82
} | {
"line": 61,
"column": 66
} | {
"line": 63,
"column": 0
} | [
{
"pp": "n : Nat\nb : Bool\n⊢ bit b n = 0 ↔ n = 0 ∧ b = false",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"cond",
"Nat.bit",
"False",
"HMul.hMul",
"and_true",
"congrArg",
"and_self",
"Nat.add_eq_zero_iff._simp_1",
"false_and",
... | [] | by
cases n <;> cases b <;> simp [bit, Nat.two_mul, ← Nat.add_assoc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.BinaryRec | {
"line": 81,
"column": 76
} | {
"line": 81,
"column": 82
} | {
"line": 81,
"column": 82
} | [
{
"pp": "n : Nat\nhn : n >>> 1 ≠ 0\n⊢ 0 < 2",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.BinaryRec | {
"line": 81,
"column": 76
} | {
"line": 81,
"column": 82
} | {
"line": 81,
"column": 82
} | [
{
"pp": "n : Nat\nhn : n >>> 1 ≠ 0\n⊢ 0 < 2",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.BinaryRec | {
"line": 81,
"column": 76
} | {
"line": 81,
"column": 82
} | {
"line": 81,
"column": 82
} | [
{
"pp": "n : Nat\nhn : n >>> 1 ≠ 0\n⊢ 0 < 2",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.BinaryRec | {
"line": 98,
"column": 62
} | {
"line": 98,
"column": 68
} | {
"line": 98,
"column": 68
} | [
{
"pp": "n : Nat\nn0 : ¬n + 1 + 1 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.BinaryRec | {
"line": 98,
"column": 62
} | {
"line": 98,
"column": 68
} | {
"line": 98,
"column": 68
} | [
{
"pp": "n : Nat\nn0 : ¬n + 1 + 1 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.BinaryRec | {
"line": 98,
"column": 62
} | {
"line": 98,
"column": 68
} | {
"line": 98,
"column": 68
} | [
{
"pp": "n : Nat\nn0 : ¬n + 1 + 1 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.BinaryRec | {
"line": 133,
"column": 16
} | {
"line": 133,
"column": 22
} | {
"line": 134,
"column": 2
} | [
{
"pp": "case false\nn : Nat\n⊢ false.toNat < 2",
"ppTerm": "?false",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Bool.toNat",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNa... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.BinaryRec | {
"line": 133,
"column": 16
} | {
"line": 133,
"column": 22
} | {
"line": 134,
"column": 2
} | [
{
"pp": "case true\nn : Nat\n⊢ true.toNat < 2",
"ppTerm": "?true",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Bool.toNat",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.BinaryRec | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 10
} | {
"line": 136,
"column": 0
} | [
{
"pp": "case H\nb : Bool\nn : Nat\n⊢ 0 < 2",
"ppTerm": "?H",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.BinaryRec | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 10
} | {
"line": 136,
"column": 0
} | [
{
"pp": "case H\nb : Bool\nn : Nat\n⊢ 0 < 2",
"ppTerm": "?H",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.BinaryRec | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 10
} | {
"line": 136,
"column": 0
} | [
{
"pp": "case H\nb : Bool\nn : Nat\n⊢ 0 < 2",
"ppTerm": "?H",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Defs | {
"line": 781,
"column": 4
} | {
"line": 781,
"column": 76
} | {
"line": 783,
"column": 0
} | [
{
"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 * x = 1",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Semigroup.toMul",
"HMul.hMul",
"Monoid.... | [] | rwa [show y = z by simpa [mul_assoc, h] using congr_arg (· * y) hz.symm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Logic.Relation | {
"line": 905,
"column": 6
} | {
"line": 905,
"column": 24
} | {
"line": 906,
"column": 6
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\na b✝ c : α\nh : ∀ (a b c : α), r a b → r a c → ∃ d, ReflGen r b d ∧ ReflTransGen r c d\nhac : ReflTransGen r a c\nd e : α\na✝ : ReflTransGen r a d\nhde : r d e\nb : α\nhdb : ReflTransGen r d b\n⊢ ∃ a, ReflTransGen r e a ∧ ReflGen r b a",
"ppTerm": "?m.59",
"assig... | [] | induction hdb with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Logic.Function.Iterate | {
"line": 179,
"column": 22
} | {
"line": 179,
"column": 48
} | {
"line": 179,
"column": 48
} | [
{
"pp": "α : Type u\nf : α → α\nn : ℕ\nhn : 0 < n\n⊢ f^[n.pred.succ] = f^[n]",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.succ_pred_eq_of_pos",
"congrArg",
"id",
"Nat.iterate",
"Nat",
"Nat.succ",
"Eq",
"Nat.pred"
]... | [
"α : Type u\nf : α → α\nn : ℕ\nhn : 0 < n\n⊢ f^[n] = f^[n]"
] | Nat.succ_pred_eq_of_pos hn | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Function.Iterate | {
"line": 182,
"column": 23
} | {
"line": 182,
"column": 49
} | {
"line": 182,
"column": 49
} | [
{
"pp": "α : Type u\nf : α → α\nn : ℕ\nhn : 0 < n\n⊢ f^[n.pred.succ] = f^[n]",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.succ_pred_eq_of_pos",
"congrArg",
"id",
"Nat.iterate",
"Nat",
"Nat.succ",
"Eq",
"Nat.pred"
]... | [
"α : Type u\nf : α → α\nn : ℕ\nhn : 0 < n\n⊢ f^[n] = f^[n]"
] | Nat.succ_pred_eq_of_pos hn | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Action.Defs | {
"line": 717,
"column": 29
} | {
"line": 717,
"column": 71
} | {
"line": 719,
"column": 0
} | [
{
"pp": "M : Type u_1\nN : Type u_2\nG✝ : Type u_3\nH : Type u_4\nα : Type u_5\nβ : Type u_6\nγ : Type u_7\nδ : Type u_8\nG : Type u_9\nP : Type u_10\ninst✝¹ : Group G\ninst✝ : MulAction G P\na : G\nb c : P\nh : a • b = a • c\n⊢ b = c",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"... | [] | rw [← inv_smul_smul a b, h, inv_smul_smul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Group.Action.Defs | {
"line": 717,
"column": 29
} | {
"line": 717,
"column": 71
} | {
"line": 719,
"column": 0
} | [
{
"pp": "M : Type u_1\nN : Type u_2\nG✝ : Type u_3\nH : Type u_4\nα : Type u_5\nβ : Type u_6\nγ : Type u_7\nδ : Type u_8\nG : Type u_9\nP : Type u_10\ninst✝¹ : Group G\ninst✝ : MulAction G P\na : G\nb c : P\nh : a • b = a • c\n⊢ b = c",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"... | [] | rw [← inv_smul_smul a b, h, inv_smul_smul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Action.Defs | {
"line": 717,
"column": 29
} | {
"line": 717,
"column": 71
} | {
"line": 719,
"column": 0
} | [
{
"pp": "M : Type u_1\nN : Type u_2\nG✝ : Type u_3\nH : Type u_4\nα : Type u_5\nβ : Type u_6\nγ : Type u_7\nδ : Type u_8\nG : Type u_9\nP : Type u_10\ninst✝¹ : Group G\ninst✝ : MulAction G P\na : G\nb c : P\nh : a • b = a • c\n⊢ b = c",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"... | [] | rw [← inv_smul_smul a b, h, inv_smul_smul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Basic | {
"line": 550,
"column": 2
} | {
"line": 550,
"column": 23
} | {
"line": 551,
"column": 2
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\nπ : ι → Type u_4\n⊢ IsEquiv α (fun x1 x2 ↦ x1 ≠ x2)ᶜ",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HEq.refl",
"Compl.compl",
"eq_isEquiv",
"Prop.instCompl",
"Pi.instCompl",
"IsEquiv",
... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\nπ : ι → Type u_4\nx✝¹ x✝ : α\n⊢ (fun x1 x2 ↦ x1 ≠ x2)ᶜ = Eq"
] | convert! eq_isEquiv α | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Data.Bool.Basic | {
"line": 33,
"column": 55
} | {
"line": 33,
"column": 61
} | {
"line": 35,
"column": 0
} | [
{
"pp": "⊢ ¬true = false",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 33,
"column": 55
} | {
"line": 33,
"column": 61
} | {
"line": 35,
"column": 0
} | [
{
"pp": "⊢ ¬true = false",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 33,
"column": 55
} | {
"line": 33,
"column": 61
} | {
"line": 35,
"column": 0
} | [
{
"pp": "⊢ ¬true = false",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 35,
"column": 55
} | {
"line": 35,
"column": 61
} | {
"line": 37,
"column": 0
} | [
{
"pp": "⊢ ¬false = true",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 35,
"column": 55
} | {
"line": 35,
"column": 61
} | {
"line": 37,
"column": 0
} | [
{
"pp": "⊢ ¬false = true",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 35,
"column": 55
} | {
"line": 35,
"column": 61
} | {
"line": 37,
"column": 0
} | [
{
"pp": "⊢ ¬false = true",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 108,
"column": 57
} | {
"line": 108,
"column": 63
} | {
"line": 110,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (a && b) = true → a = true",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 108,
"column": 57
} | {
"line": 108,
"column": 63
} | {
"line": 110,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (a && b) = true → a = true",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 108,
"column": 57
} | {
"line": 108,
"column": 63
} | {
"line": 110,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (a && b) = true → a = true",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 110,
"column": 57
} | {
"line": 110,
"column": 63
} | {
"line": 112,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, a = true → b = true → (a && b) = true",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 110,
"column": 57
} | {
"line": 110,
"column": 63
} | {
"line": 112,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, a = true → b = true → (a && b) = true",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 110,
"column": 57
} | {
"line": 110,
"column": 63
} | {
"line": 112,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, a = true → b = true → (a && b) = true",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 112,
"column": 58
} | {
"line": 112,
"column": 64
} | {
"line": 114,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (a && b) = true → b = true",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 112,
"column": 58
} | {
"line": 112,
"column": 64
} | {
"line": 114,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (a && b) = true → b = true",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 112,
"column": 58
} | {
"line": 112,
"column": 64
} | {
"line": 114,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (a && b) = true → b = true",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"instDecidableEqBool",
"forall_prop_decidable",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 62
} | {
"line": 116,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, a = !b ↔ a ≠ b",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"If... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 62
} | {
"line": 116,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, a = !b ↔ a ≠ b",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"If... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 62
} | {
"line": 116,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, a = !b ↔ a ≠ b",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"If... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 116,
"column": 58
} | {
"line": 116,
"column": 64
} | {
"line": 118,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (!a) = b ↔ a ≠ b",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 116,
"column": 58
} | {
"line": 116,
"column": 64
} | {
"line": 118,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (!a) = b ↔ a ≠ b",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 116,
"column": 58
} | {
"line": 116,
"column": 64
} | {
"line": 118,
"column": 0
} | [
{
"pp": "⊢ ∀ {a b : Bool}, (!a) = b ↔ a ≠ b",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 121,
"column": 47
} | {
"line": 121,
"column": 53
} | {
"line": 123,
"column": 0
} | [
{
"pp": "⊢ ∀ (b : Bool), (!b) ≠ b",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 121,
"column": 47
} | {
"line": 121,
"column": 53
} | {
"line": 123,
"column": 0
} | [
{
"pp": "⊢ ∀ (b : Bool), (!b) ≠ b",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 121,
"column": 47
} | {
"line": 121,
"column": 53
} | {
"line": 123,
"column": 0
} | [
{
"pp": "⊢ ∀ (b : Bool), (!b) ≠ b",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 123,
"column": 45
} | {
"line": 123,
"column": 51
} | {
"line": 125,
"column": 0
} | [
{
"pp": "⊢ ∀ (b : Bool), b ≠ !b",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 123,
"column": 45
} | {
"line": 123,
"column": 51
} | {
"line": 125,
"column": 0
} | [
{
"pp": "⊢ ∀ (b : Bool), b ≠ !b",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 123,
"column": 45
} | {
"line": 123,
"column": 51
} | {
"line": 125,
"column": 0
} | [
{
"pp": "⊢ ∀ (b : Bool), b ≠ !b",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 125,
"column": 49
} | {
"line": 125,
"column": 55
} | {
"line": 128,
"column": 0
} | [
{
"pp": "⊢ ∀ (a b : Bool), a = b ∨ a = !b",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Or",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 125,
"column": 49
} | {
"line": 125,
"column": 55
} | {
"line": 128,
"column": 0
} | [
{
"pp": "⊢ ∀ (a b : Bool), a = b ∨ a = !b",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Or",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 125,
"column": 49
} | {
"line": 125,
"column": 55
} | {
"line": 128,
"column": 0
} | [
{
"pp": "⊢ ∀ (a b : Bool), a = b ∨ a = !b",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"Bool.not",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Eq.refl",
"Or",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 138,
"column": 66
} | {
"line": 138,
"column": 72
} | {
"line": 140,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, (x ^^ y) = true ↔ x ≠ y",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Iff",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 138,
"column": 66
} | {
"line": 138,
"column": 72
} | {
"line": 140,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, (x ^^ y) = true ↔ x ≠ y",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Iff",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 138,
"column": 66
} | {
"line": 138,
"column": 72
} | {
"line": 140,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, (x ^^ y) = true ↔ x ≠ y",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Ne",
"Bool.true",
"Iff",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 143,
"column": 16
} | {
"line": 143,
"column": 22
} | {
"line": 144,
"column": 2
} | [
{
"pp": "⊢ ∀ (a : Bool), a ≤ a",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool.instDecidableLe",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 143,
"column": 16
} | {
"line": 143,
"column": 22
} | {
"line": 144,
"column": 2
} | [
{
"pp": "⊢ ∀ (a : Bool), a ≤ a",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool.instDecidableLe",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 143,
"column": 16
} | {
"line": 143,
"column": 22
} | {
"line": 144,
"column": 2
} | [
{
"pp": "⊢ ∀ (a : Bool), a ≤ a",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool.instDecidableLe",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 144,
"column": 17
} | {
"line": 144,
"column": 23
} | {
"line": 145,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b c : Bool), a ≤ b → b ≤ c → a ≤ c",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 144,
"column": 17
} | {
"line": 144,
"column": 23
} | {
"line": 145,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b c : Bool), a ≤ b → b ≤ c → a ≤ c",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 144,
"column": 17
} | {
"line": 144,
"column": 23
} | {
"line": 145,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b c : Bool), a ≤ b → b ≤ c → a ≤ c",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 150,
"column": 25
} | {
"line": 150,
"column": 31
} | {
"line": 151,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a < b ↔ a ≤ b ∧ ¬b ≤ a",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.instLT",
"Bool.true",
"Bool.instDecidab... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 150,
"column": 25
} | {
"line": 150,
"column": 31
} | {
"line": 151,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a < b ↔ a ≤ b ∧ ¬b ≤ a",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.instLT",
"Bool.true",
"Bool.instDecidab... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 150,
"column": 25
} | {
"line": 150,
"column": 31
} | {
"line": 151,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a < b ↔ a ≤ b ∧ ¬b ≤ a",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.instLT",
"Bool.true",
"Bool.instDecidab... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 145,
"column": 20
} | {
"line": 145,
"column": 26
} | {
"line": 146,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a ≤ b → b ≤ a → a = b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 145,
"column": 20
} | {
"line": 145,
"column": 26
} | {
"line": 146,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a ≤ b → b ≤ a → a = b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 145,
"column": 20
} | {
"line": 145,
"column": 26
} | {
"line": 146,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a ≤ b → b ≤ a → a = b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 146,
"column": 17
} | {
"line": 146,
"column": 23
} | {
"line": 147,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a ≤ b ∨ b ≤ a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Or",
"Bool.ins... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 146,
"column": 17
} | {
"line": 146,
"column": 23
} | {
"line": 147,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a ≤ b ∨ b ≤ a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Or",
"Bool.ins... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 146,
"column": 17
} | {
"line": 146,
"column": 23
} | {
"line": 147,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), a ≤ b ∨ b ≤ a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Or",
"Bool.ins... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 152,
"column": 16
} | {
"line": 152,
"column": 22
} | {
"line": 154,
"column": 0
} | [
{
"pp": "⊢ ∀ (a b : Bool), min a b = if a ≤ b then a else b",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"Bool.instMin",
"of_decide_eq_true",
"inferInstance",
"id",
"instDecidableEqBool",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
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