module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 748,
"column": 4
} | {
"line": 748,
"column": 27
} | {
"line": 748,
"column": 28
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nS : Finset G\nε : ℝ\nhε₀ : 0 < ε\nhε₁ : ε ≤ 1\nhS : S.Nonempty\nK : ℝ := 1 - ε / 2\nhK : K < 1\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nH : Subgroup G\nw✝ : Fintype ↥H\nhH : IsAtom K S (↑H).toFinset\nZ : Finset G\nhZS : Z ⊆ S... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nS : Finset G\nε : ℝ\nhε₀ : 0 < ε\nhε₁ : ε ≤ 1\nhS : S.Nonempty\nK : ℝ := 1 - ε / 2\nhK : K < 1\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nH : Subgroup G\nw✝ : Fintype ↥H\nhH : IsAtom K S (↑H).toFinset\nZ : Finset G\nhZS : Z ⊆ S\nhHZS : ↑H ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Pentagonal.PowerSeries | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 13
} | {
"line": 164,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nthis✝ : TopologicalSpace R := ⊥\nthis : DiscreteTopology R\nh :\n ∀ (d : ℕ),\n Tendsto (fun i ↦ (coeff d) (∏ b ∈ i, (1 - X ^ (b + 1)))) (SummationFilter.unconditional ℕ).filter\n (𝓝 ((coeff d) (pentagonalSeries R)))\n⊢ ∀ᶠ (s : Finset ℕ) in atTop, (coef... | [
"R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nthis✝ : TopologicalSpace R := ⊥\nthis : DiscreteTopology R\nh :\n ∀ (d : ℕ),\n Tendsto (fun i ↦ (coeff d) (∏ b ∈ i, (1 - X ^ (b + 1)))) (SummationFilter.unconditional ℕ).filter\n (𝓝 ((coeff d) (pentagonalSeries R)))\n⊢ ∃ a, ∀ (b : Finset ℕ), a ⊆ b → (coeff n) (∏ n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Pentagonal.PowerSeries | {
"line": 160,
"column": 2
} | {
"line": 164,
"column": 17
} | {
"line": 166,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\n⊢ ∀ᶠ (s : Finset ℕ) in atTop, (coeff n) (∏ n ∈ s, (1 - X ^ (n + 1))) = (coeff n) (pentagonalSeries R)",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Pure.pure",
"IsSemitopologicalRing.toIsTopologicalAddGroup",
"Eq.mpr",
... | [] | let : TopologicalSpace R := ⊥
have : DiscreteTopology R := ⟨rfl⟩
have h := (multipliable_one_sub_X_pow R).hasProd
rw [tprod_one_sub_X_pow' R, HasProd, tendsto_iff_coeff_tendsto] at h
simpa using h n | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Enumerative.Pentagonal.PowerSeries | {
"line": 160,
"column": 2
} | {
"line": 164,
"column": 17
} | {
"line": 166,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\n⊢ ∀ᶠ (s : Finset ℕ) in atTop, (coeff n) (∏ n ∈ s, (1 - X ^ (n + 1))) = (coeff n) (pentagonalSeries R)",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Pure.pure",
"IsSemitopologicalRing.toIsTopologicalAddGroup",
"Eq.mpr",
... | [] | let : TopologicalSpace R := ⊥
have : DiscreteTopology R := ⟨rfl⟩
have h := (multipliable_one_sub_X_pow R).hasProd
rw [tprod_one_sub_X_pow' R, HasProd, tendsto_iff_coeff_tendsto] at h
simpa using h n | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Enumerative.Pentagonal.PowerSeries | {
"line": 177,
"column": 2
} | {
"line": 177,
"column": 13
} | {
"line": 177,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : TopologicalSpace R\nn : ℕ\n⊢ ∀ᶠ (x' : Finset ℕ) in (SummationFilter.unconditional ℕ).filter,\n (coeff n) (∏ b ∈ x', (1 - X ^ (b + 1))) = (coeff n) (pentagonalSeries R)",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : TopologicalSpace R\nn : ℕ\n⊢ ∃ a, ∀ (b : Finset ℕ), a ⊆ b → (coeff n) (∏ b ∈ b, (1 - X ^ (b + 1))) = (coeff n) (pentagonalSeries R)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 768,
"column": 17
} | {
"line": 768,
"column": 28
} | {
"line": 768,
"column": 29
} | [
{
"pp": "case e_a\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nS : Finset G\nε : ℝ\nhε₀ : 0 < ε\nhε₁ : ε ≤ 1\nhS : S.Nonempty\nK : ℝ := 1 - ε / 2\nhK : K < 1\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nH : Subgroup G\nw✝ : Fintype ↥H\nhH : IsAtom K S (↑H).toFinset\nZ : Finset G\nh... | [
"case e_a\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nS : Finset G\nε : ℝ\nhε₀ : 0 < ε\nhε₁ : ε ≤ 1\nhS : S.Nonempty\nK : ℝ := 1 - ε / 2\nhK : K < 1\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nH : Subgroup G\nw✝ : Fintype ↥H\nhH : IsAtom K S (↑H).toFinset\nZ : Finset G\nhZS : Z ⊆ S\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Pentagonal.Ring | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 35
} | {
"line": 162,
"column": 36
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommRing R\ninst✝² : TopologicalSpace R\ninst✝¹ : IsTopologicalRing R\ninst✝ : T2Space R\nx : R\nhx : IsTopologicallyNilpotent x\nhsum : ∀ (k : ℕ), Summable fun n ↦ x ^ ((k + 1) * n) * ∏ i ∈ Finset.range (n + 1), (1 - x ^ (k + i + 1))\nhlhs : ∀ (k : ℕ), Multipliable fun n ↦ 1 - x... | [
"R : Type u_1\ninst✝³ : CommRing R\ninst✝² : TopologicalSpace R\ninst✝¹ : IsTopologicalRing R\ninst✝ : T2Space R\nx : R\nhx : IsTopologicallyNilpotent x\nhsum : ∀ (k : ℕ), Summable fun n ↦ x ^ ((k + 1) * n) * ∏ i ∈ Finset.range (n + 1), (1 - x ^ (k + i + 1))\nhlhs : ∀ (k : ℕ), Multipliable fun n ↦ 1 - x ^ (n + k + ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 258,
"column": 6
} | {
"line": 258,
"column": 53
} | {
"line": 259,
"column": 8
} | [
{
"pp": "⊢ (fun n ↦ 2) =o[atTop] fun n ↦ ↑n / 3",
"ppTerm": "?m.167",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"False",
"Real.partialOrder",
"Real",
"instHDiv",
"GroupWithZero.toDivisionMonoid",... | [
"⊢ Tendsto (fun x ↦ 3⁻¹ * ↑x) atTop atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 54
} | {
"line": 276,
"column": 55
} | [
{
"pp": "n : ℕ\nhn : 6 ≤ n\nthis : 0 ≤ ↑n / 3 - 2\n⊢ ‖(↑n / 3 - 2) * ↑((n - 3) / 6) * rexp (-4 * √(Real.log ↑((n - 3) / 6)))‖ ≤ ↑(ruzsaSzemerediNumberNat n)",
"ppTerm": "?m.307",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
"instHDi... | [
"n : ℕ\nhn : 6 ≤ n\nthis : 0 ≤ ↑n / 3 - 2\n⊢ (↑n / 3 - 2) * ↑((n - 3) / 6) * rexp (-(4 * √(Real.log ↑((n - 3) / 6)))) ≤ ↑(ruzsaSzemerediNumberNat n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 192,
"column": 36
} | {
"line": 192,
"column": 51
} | {
"line": 192,
"column": 52
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nX : Set α\nh : V(G) ⊆ X ∧ E(G) = ∅\ne : β\nx y : α\nhe : G.IsLink e x y\n⊢ (noEdge X β).IsLink e x y",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",... | [
"α : Type u_1\nβ : Type u_2\nG : Graph α β\nX : Set α\nh : V(G) ⊆ X ∧ E(G) = ∅\ne : β\nx y : α\nhe : G.IsLink e x y\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Delete | {
"line": 54,
"column": 14
} | {
"line": 54,
"column": 25
} | {
"line": 54,
"column": 26
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nE₀ : Set β\nh : G.restrict E₀ = G\n⊢ E(G) ⊆ E₀",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nG : Graph α β\nE₀ : Set β\nh : G.restrict E₀ = G\n⊢ E(G) ⊆ E₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 393,
"column": 19
} | {
"line": 393,
"column": 35
} | {
"line": 393,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nhe : V(G) = ∅\ne : β\nx y : α\nh : G.IsLink e x y\n⊢ False",
"ppTerm": "?m.40",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nG : Graph α β\nhe : V(G) = ∅\ne : β\nx y : α\nh : G.IsLink e x y\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Delete | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 15
} | {
"line": 73,
"column": 16
} | [
{
"pp": "case refine_1\nα : Type u_1\nβ : Type u_2\nG H : Graph α β\nh : H ≤ G\nF : Set β\n⊢ V(H.restrict F) ⊆ V(G.restrict F)",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"LE.le",
"Set.instLE",
"congr",
"Graph.ve... | [
"case refine_1\nα : Type u_1\nβ : Type u_2\nG H : Graph α β\nh : H ≤ G\nF : Set β\n⊢ V(H) ⊆ V(G)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 17
} | {
"line": 397,
"column": 18
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nh : V(G) = ∅\ne : β\nx y : α\nhe : G.IsLink e x y\n⊢ ⊥.IsLink e x y",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"OrderBot.toBot",
"P... | [
"α : Type u_1\nβ : Type u_2\nG : Graph α β\nh : V(G) = ∅\ne : β\nx y : α\nhe : G.IsLink e x y\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Basic | {
"line": 346,
"column": 8
} | {
"line": 347,
"column": 11
} | {
"line": 347,
"column": 12
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [
"α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E(G) → Std.Symm (G.IsLink e)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Basic | {
"line": 346,
"column": 8
} | {
"line": 347,
"column": 25
} | {
"line": 347,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [] | simpa [show E = E(G) by simp [Set.ext_iff, hE, G.edge_mem_iff_exists_isLink]]
using G.isLink_symm | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.Graph.Basic | {
"line": 346,
"column": 8
} | {
"line": 347,
"column": 25
} | {
"line": 347,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [] | simpa [show E = E(G) by simp [Set.ext_iff, hE, G.edge_mem_iff_exists_isLink]]
using G.isLink_symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Graph.Basic | {
"line": 346,
"column": 8
} | {
"line": 347,
"column": 25
} | {
"line": 347,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [] | simpa [show E = E(G) by simp [Set.ext_iff, hE, G.edge_mem_iff_exists_isLink]]
using G.isLink_symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.HalesJewett | {
"line": 121,
"column": 30
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 72
} | [
{
"pp": "case inl.inl\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\na : α\nhl : l.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\nval✝ : α\nhm : m.idxFun i = Sum.inl val✝\n⊢ Sum.inl a = Sum.inl val✝",
"ppTerm": "?i... | [
"case inl.inl\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\na : α\nhl : l.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\nval✝ : α\nhm : m.idxFun i = Sum.inl val✝\n⊢ a = val✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 121,
"column": 30
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 72
} | [
{
"pp": "case inl.inr\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\na : α\nhl : l.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\nval✝ : η\nhm : m.idxFun i = Sum.inr val✝\n⊢ Sum.inl a = Sum.inr val✝",
"ppTerm": "?i... | [
"case inl.inr\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\na : α\nhl : l.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\nval✝ : η\nhm : m.idxFun i = Sum.inr val✝\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 126,
"column": 6
} | {
"line": 126,
"column": 42
} | {
"line": 126,
"column": 43
} | [
{
"pp": "case inr.inl\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\ne : η\nhl : l.idxFun i = Sum.inr e\na : α\nhm : m.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\n⊢ Sum.inr e = Sum.inl a",
"ppTerm": "?inr.inl",
... | [
"case inr.inl\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\ne : η\nhl : l.idxFun i = Sum.inr e\na : α\nhm : m.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 131,
"column": 6
} | {
"line": 131,
"column": 47
} | {
"line": 131,
"column": 48
} | [
{
"pp": "case inr.inr\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\ne : η\nhl : l.idxFun i = Sum.inr e\nf : η\nhm : m.idxFun i = Sum.inr f\na b : α\nhab : a ≠ b\nhef : e ≠ f\n⊢ False",
"ppTerm": "?inr.inr",
... | [
"case inr.inr\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\ne : η\nhl : l.idxFun i = Sum.inr e\nf : η\nhm : m.idxFun i = Sum.inr f\na b : α\nhab : a ≠ b\nhef : e ≠ f\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 201,
"column": 30
} | {
"line": 201,
"column": 68
} | {
"line": 201,
"column": 69
} | [
{
"pp": "case refine_1.none\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : l.idxFun i = some a\nhi : m.idxFun i = none\n⊢ none = some a",
"ppTerm": "?refine_1.none",
"assigned": true,
"usedConstants"... | [
"case refine_1.none\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : l.idxFun i = some a\nhi : m.idxFun i = none\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 201,
"column": 30
} | {
"line": 201,
"column": 68
} | {
"line": 201,
"column": 69
} | [
{
"pp": "case refine_1.some\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : l.idxFun i = some a\nval✝ : α\nhi : m.idxFun i = some val✝\n⊢ some val✝ = some a",
"ppTerm": "?refine_1.some",
"assigned": true,... | [
"case refine_1.some\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : l.idxFun i = some a\nval✝ : α\nhi : m.idxFun i = some val✝\n⊢ val✝ = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 202,
"column": 30
} | {
"line": 202,
"column": 68
} | {
"line": 202,
"column": 69
} | [
{
"pp": "case refine_2.none\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : m.idxFun i = some a\nhi : l.idxFun i = none\n⊢ none = some a",
"ppTerm": "?refine_2.none",
"assigned": true,
"usedConstants"... | [
"case refine_2.none\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : m.idxFun i = some a\nhi : l.idxFun i = none\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 202,
"column": 30
} | {
"line": 202,
"column": 68
} | {
"line": 202,
"column": 69
} | [
{
"pp": "case refine_2.some\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : m.idxFun i = some a\nval✝ : α\nhi : l.idxFun i = some val✝\n⊢ some val✝ = some a",
"ppTerm": "?refine_2.some",
"assigned": true,... | [
"case refine_2.some\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : m.idxFun i = some a\nval✝ : α\nhi : l.idxFun i = some val✝\n⊢ val✝ = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Hindman | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 50
} | {
"line": 175,
"column": 51
} | [
{
"pp": "M : Type u_1\ninst✝ : Semigroup M\na : Stream' M\nS : Set (Ultrafilter M) := ⋯\nU : Ultrafilter M\nhU : ∀ (i : ℕ), U ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nV : Ultrafilter M\nhV : ∀ (i : ℕ), V ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nn : ℕ\nm : M\nhm : m ∈ FP (Stream'.drop n a... | [
"M : Type u_1\ninst✝ : Semigroup M\na : Stream' M\nS : Set (Ultrafilter M) := ⋂ n, {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop n a)}\nU : Ultrafilter M\nhU : ∀ (i : ℕ), U ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nV : Ultrafilter M\nhV : ∀ (i : ℕ), V ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nn ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Hindman | {
"line": 210,
"column": 4
} | {
"line": 210,
"column": 51
} | {
"line": 211,
"column": 4
} | [
{
"pp": "case h.cons'\nM : Type u_1\ninst✝ : Semigroup M\nU : Ultrafilter M\nU_idem : U * U = U\nexists_elem : ∀ {s : Set M}, s ∈ U → (s ∩ {m | ∀ᶠ (m' : M) in ↑U, m * m' ∈ s}).Nonempty\nelem : { s // s ∈ U } → M := fun p ↦ ⋯.some\nsucc : { s // s ∈ U } → { s // s ∈ U } := fun p ↦ ⟨↑p ∩ {m | elem p * m ∈ ↑p}, ⋯⟩... | [
"case h.cons'.refine_2\nM : Type u_1\ninst✝ : Semigroup M\nU : Ultrafilter M\nU_idem : U * U = U\nexists_elem : ∀ {s : Set M}, s ∈ U → (s ∩ {m | ∀ᶠ (m' : M) in ↑U, m * m' ∈ s}).Nonempty\nelem : { s // s ∈ U } → M := fun p ↦ ⋯.some\nsucc : { s // s ∈ U } → { s // s ∈ U } := fun p ↦ ⟨↑p ∩ {m | elem p * m ∈ ↑p}, ⋯⟩\na... | have := Set.inter_subset_right (ih (succ p) ?_) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.KatonaCircle | {
"line": 59,
"column": 41
} | {
"line": 59,
"column": 52
} | {
"line": 59,
"column": 53
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ Fintype.card ↥s ≤ Fintype.card X",
"ppTerm": "?m.273",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Fins... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ #s ≤ Fintype.card X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 60,
"column": 35
} | {
"line": 60,
"column": 46
} | {
"line": 60,
"column": 47
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ ↑(↑f ((Equiv.symm ↑f) ⟨↑n, ⋯⟩)) < #s",
"ppTerm": "?m.293",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.apply_symm_a... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ ↑n < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 68,
"column": 54
} | {
"line": 68,
"column": 65
} | {
"line": 68,
"column": 66
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥sᶜ)\n⊢ ↑n < Fintype.card X - #s",
"ppTerm": "?m.344",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥sᶜ)\n⊢ ↑n < Fintype.card X - #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 83,
"column": 24
} | {
"line": 83,
"column": 35
} | {
"line": 83,
"column": 36
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nn : Fin (Fintype.card X)\nhn : ↑n < #s\n⊢ ↑n < Fintype.card ↥s",
"ppTerm": "?m.424",
"assigned": true,
"usedConst... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nn : Fin (Fintype.card X)\nhn : ↑n < #s\n⊢ ↑n < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 88,
"column": 38
} | {
"line": 88,
"column": 49
} | {
"line": 88,
"column": 50
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑(g ⟨x, hx⟩) < #s",
"ppTerm": "?m.458",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑(g ⟨x, hx⟩) < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 98,
"column": 10
} | {
"line": 98,
"column": 38
} | {
"line": 98,
"column": 39
} | [
{
"pp": "case mp\nX : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑({ toFun := fun x ↦ if hx : x ∈ s then Fin.castLE ⋯ (g ⟨x, hx⟩) else Fin.cast ⋯ ((g' ⟨x, ⋯⟩).a... | [
"case mp\nX : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑(g ⟨x, ⋯⟩) < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 95,
"column": 26
} | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 38
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nC : Set α\n⊢ (M✶ ＼ C)✶ = M ↔ Disjoint C M.E",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Matro... | [
"α : Type u_1\nM : Matroid α\nC : Set α\n⊢ (M✶ ＼ C)✶✶ = M✶ ↔ Disjoint C M.E"
] | ← dual_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 109,
"column": 2
} | {
"line": 109,
"column": 29
} | {
"line": 109,
"column": 30
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\ninst✝ : DecidableEq X\ns : Finset X\n⊢ #(prefixed s) = (#s)! * (Fintype.card X - #s)!",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝¹ : Fintype X\ninst✝ : DecidableEq X\ns : Finset X\n⊢ #(prefixed s) = (#s)! * (Fintype.card X - #s)!"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 173,
"column": 47
} | {
"line": 173,
"column": 58
} | {
"line": 173,
"column": 59
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\n⊢ M ／ (X \\ I ∪ I) = M ／ I ＼ (X \\ I)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Matroid.dual",
"Set.instUnion",
"id",
"SDiff.sdiff",
"propext",
... | [
"α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\n⊢ (M ／ (X \\ I ∪ I))✶ = (M ／ I ＼ (X \\ I))✶"
] | ← dual_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 178,
"column": 41
} | {
"line": 178,
"column": 52
} | {
"line": 178,
"column": 53
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\nJ : Set α\nhJ : J ⊆ (M✶ ＼ I ＼ (X \\ I)).E\ne : α\nhe : e ∈ X \\ I\n⊢ Disjoint {e} I",
"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Complet... | [
"α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\nJ : Set α\nhJ : J ⊆ (M✶ ＼ I ＼ (X \\ I)).E\ne : α\nhe : e ∈ X \\ I\n⊢ e ∉ I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 67,
"column": 38
} | {
"line": 67,
"column": 49
} | {
"line": 67,
"column": 50
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nM✝ M : (i : ι) → Matroid (α i)\nI : Set ((i : ι) × α i)\nh : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nBs : (i : ι) → Set (α i)\nhBs : ∀ (i : ι), (M i).IsBase (Bs i) ∧ Sigma.mk i ⁻¹' I ⊆ Bs i\ni : ι\n⊢ (M i).IsBase (Sigma.mk i ⁻¹' univ.sigma Bs)",
"ppTerm": "?m.102"... | [
"ι : Type u_1\nα : ι → Type u_2\nM✝ M : (i : ι) → Matroid (α i)\nI : Set ((i : ι) × α i)\nh : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nBs : (i : ι) → Set (α i)\nhBs : ∀ (i : ι), (M i).IsBase (Bs i) ∧ Sigma.mk i ⁻¹' I ⊆ Bs i\ni : ι\n⊢ (M i).IsBase (Bs i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 202,
"column": 2
} | {
"line": 203,
"column": 85
} | {
"line": 205,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI J X : Set α\nhIX : M.IsBasis' I X\nhJI : J ⊆ I\n⊢ ∀ ⦃K : Set α⦄, Disjoint K J → M.Indep (K ∪ J) → K ⊆ X → I ⊆ K ∪ J → K ⊆ I",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBoolea... | [] | exact fun K hJK hKJi hKX hIJK ↦ by
simp [hIX.eq_of_subset_indep hKJi hIJK (union_subset hKX (hJI.trans hIX.subset))] | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 97
} | {
"line": 212,
"column": 4
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI J X : Set α\nhIX : M.IsBasis' I X\nhJI : J ⊆ I\n⊢ (M ／ J).IsBasis' (I \\ J) X",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_of_subset._simp_1_1",... | [
"α : Type u_1\nM : Matroid α\nI J X : Set α\nhIX : M.IsBasis' I X\nhJI : J ⊆ I\n⊢ (M ／ J).IsBasis (I \\ J) (X ∩ (M.E \\ J))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 52
} | {
"line": 240,
"column": 4
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI J X : Set α\nh : M.IsBasis' (J ∪ I) (X ∪ I)\nhJI : Disjoint J I\nhXI : Disjoint X I\n⊢ (M ／ I).IsBasis' J X",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nM : Matroid α\nI J X : Set α\nh : M.IsBasis' (J ∪ I) (X ∪ I)\nhJI : Disjoint J I\nhXI : Disjoint X I\n⊢ (M ／ I).IsBasis' J X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 512,
"column": 2
} | {
"line": 512,
"column": 13
} | {
"line": 512,
"column": 14
} | [
{
"pp": "case h\nα : Type u_5\nκ : Type u_6\nη : Type u_7\ninst✝² : Finite α\ninst✝¹ : Finite κ\ninst✝ : Finite η\nι : Type\nιfin : Fintype ι\nhι : ∀ (C : (ι → α) → κ), ∃ l, IsMono C l\nC : (Fin (Fintype.card ι) → α) → κ\nl : Subspace η α ι\nc : κ\ncl : ∀ (x : η → α), (fun v ↦ C (v ∘ ⇑(Fintype.equivFin ι).symm)... | [
"case h\nα : Type u_5\nκ : Type u_6\nη : Type u_7\ninst✝² : Finite α\ninst✝¹ : Finite κ\ninst✝ : Finite η\nι : Type\nιfin : Fintype ι\nhι : ∀ (C : (ι → α) → κ), ∃ l, IsMono C l\nC : (Fin (Fintype.card ι) → α) → κ\nl : Subspace η α ι\nc : κ\ncl : ∀ (x : η → α), (fun v ↦ C (v ∘ ⇑(Fintype.equivFin ι).symm)) (↑l x) = c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Groebner | {
"line": 164,
"column": 6
} | {
"line": 164,
"column": 24
} | {
"line": 164,
"column": 25
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nι : Type u_3\nb : ι → MvPolynomial σ R\nhb : ∀ (i : ι), IsUnit (m.leadingCoeff (b i))\nf : MvPolynomial σ R\nhb' : ∀ (i : ι), m.degree (b i) ≠ 0\nhf0 : ¬f = 0\ni : ι\nhf : m.degree (b i) ≤ m.degree f\nhf0' : m.degree f = 0\n⊢ m.degree... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nι : Type u_3\nb : ι → MvPolynomial σ R\nhb : ∀ (i : ι), IsUnit (m.leadingCoeff (b i))\nf : MvPolynomial σ R\nhb' : ∀ (i : ι), m.degree (b i) ≠ 0\nhf0 : ¬f = 0\ni : ι\nhf : m.degree (b i) ≤ m.degree f\nhf0' : m.degree f = 0\n⊢ m.degree (b i) = 0"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 367,
"column": 6
} | {
"line": 367,
"column": 17
} | {
"line": 367,
"column": 18
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nX : Set α\nhX : X ⊆ M.coloops\n⊢ M ／ X = M ＼ X",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Matroid.dual",
"id",
"propext",
"Eq.symm",
"Eq",
"Matroid",
"Matroid.contract",
... | [
"α : Type u_1\nM : Matroid α\nX : Set α\nhX : X ⊆ M.coloops\n⊢ (M ／ X)✶ = (M ＼ X)✶"
] | ← dual_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 134,
"column": 21
} | {
"line": 134,
"column": 32
} | {
"line": 134,
"column": 33
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝ :\n I ⊆ X ∧\n (∀ ⦃t : Set ((i : ι) × α i)⦄, (∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' t)) → t ⊆ X → I ⊆ t → I = t) ∧\n X ⊆ univ.sigma fun i ↦ (M i).E\nhIX : ... | [
"ι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝ :\n I ⊆ X ∧\n (∀ ⦃t : Set ((i : ι) × α i)⦄, (∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' t)) → t ⊆ X → I ⊆ t → I = t) ∧\n X ⊆ univ.sigma fun i ↦ (M i).E\nhIX : I ⊆ X\nh : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 490,
"column": 2
} | {
"line": 490,
"column": 49
} | {
"line": 490,
"column": 50
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nK C : Set α\nhC : M.IsCircuit C\nhK : K.Nonempty\nhKC : K ⊆ C\n⊢ (M ／ (C \\ K)).IsCircuit K",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nM : Matroid α\nK C : Set α\nhC : M.IsCircuit C\nhK : K.Nonempty\nhKC : K ⊆ C\n⊢ (M ／ (C \\ K)).IsCircuit K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 135,
"column": 29
} | {
"line": 135,
"column": 40
} | {
"line": 135,
"column": 41
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝¹ :\n (∀ (x : ι), Sigma.mk x ⁻¹' I ⊆ Sigma.mk x ⁻¹' X) ∧\n (∀ (x : ι) ⦃t : Set (α x)⦄, (M x).Indep t → t ⊆ Sigma.mk x ⁻¹' X → Sigma.mk x ⁻¹' I ⊆ t → Sigma.mk x ⁻... | [
"ι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝¹ :\n (∀ (x : ι), Sigma.mk x ⁻¹' I ⊆ Sigma.mk x ⁻¹' X) ∧\n (∀ (x : ι) ⦃t : Set (α x)⦄, (M x).Indep t → t ⊆ Sigma.mk x ⁻¹' X → Sigma.mk x ⁻¹' I ⊆ t → Sigma.mk x ⁻¹' I = t) ∧\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 15
} | {
"line": 137,
"column": 16
} | [
{
"pp": "case refine_4\nι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝¹ :\n (∀ (x : ι), Sigma.mk x ⁻¹' I ⊆ Sigma.mk x ⁻¹' X) ∧\n (∀ (x : ι) ⦃t : Set (α x)⦄, (M x).Indep t → t ⊆ Sigma.mk x ⁻¹' X → Sigma.mk x ⁻¹' I ⊆ t... | [
"case refine_4\nι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝¹ :\n (∀ (x : ι), Sigma.mk x ⁻¹' I ⊆ Sigma.mk x ⁻¹' X) ∧\n (∀ (x : ι) ⦃t : Set (α x)⦄, (M x).Indep t → t ⊆ Sigma.mk x ⁻¹' X → Sigma.mk x ⁻¹' I ⊆ t → Sigma.mk ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 541,
"column": 2
} | {
"line": 541,
"column": 51
} | {
"line": 542,
"column": 2
} | [
{
"pp": "α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\n⊢ (M ／ C ↾ R).Indep I ↔ ((M ↾ (R ∪ C)) ／ C).Indep I",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Matroid.IsBasis'",
"Exists",
"Set.instUnion",
"Matroid.Indep",
"Iff... | [
"α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\nJ : Set α\nhJ : (M ↾ (R ∪ C)).IsBasis' J C\n⊢ (M ／ C ↾ R).Indep I ↔ ((M ↾ (R ∪ C)) ／ C).Indep I"
] | obtain ⟨J, hJ⟩ := (M ↾ (R ∪ C)).exists_isBasis' C | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 138,
"column": 26
} | {
"line": 138,
"column": 37
} | {
"line": 138,
"column": 38
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝¹ :\n (∀ (x : ι), Sigma.mk x ⁻¹' I ⊆ Sigma.mk x ⁻¹' X) ∧\n (∀ (x : ι) ⦃t : Set (α x)⦄, (M x).Indep t → t ⊆ Sigma.mk x ⁻¹' X → Sigma.mk x ⁻¹' I ⊆ t → Sigma.mk x ⁻... | [
"ι : Type u_1\nα : ι → Type u_2\nM : (i : ι) → Matroid (α i)\nI X : Set ((i : ι) × α i)\nhI : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nx✝¹ :\n (∀ (x : ι), Sigma.mk x ⁻¹' I ⊆ Sigma.mk x ⁻¹' X) ∧\n (∀ (x : ι) ⦃t : Set (α x)⦄, (M x).Indep t → t ⊆ Sigma.mk x ⁻¹' X → Sigma.mk x ⁻¹' I ⊆ t → Sigma.mk x ⁻¹' I = t) ∧\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 543,
"column": 4
} | {
"line": 543,
"column": 65
} | {
"line": 543,
"column": 66
} | [
{
"pp": "α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\nJ : Set α\nhJ : (M ↾ (R ∪ C)).IsBasis' J C\n⊢ M.IsBasis' J C",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\nJ : Set α\nhJ : (M ↾ (R ∪ C)).IsBasis' J C\n⊢ M.IsBasis' J C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Groebner | {
"line": 205,
"column": 10
} | {
"line": 205,
"column": 49
} | {
"line": 205,
"column": 50
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nι : Type u_3\nb : ι → MvPolynomial σ R\nhb : ∀ (i : ι), IsUnit (m.leadingCoeff (b i))\nf : MvPolynomial σ R\nhb' : ∀ (i : ι), m.degree (b i) ≠ 0\nhf0 : ¬f = 0\nhf : ∀ (i : ι), ¬m.degree (b i) ≤ m.degree f\ng' : ι →₀ MvPolynomial σ R\n... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nι : Type u_3\nb : ι → MvPolynomial σ R\nhb : ∀ (i : ι), IsUnit (m.leadingCoeff (b i))\nf : MvPolynomial σ R\nhb' : ∀ (i : ι), m.degree (b i) ≠ 0\nhf0 : ¬f = 0\nhf : ∀ (i : ι), ¬m.degree (b i) ≤ m.degree f\ng' : ι →₀ MvPolynomial σ R\nr' : MvPolyn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 295,
"column": 9
} | {
"line": 295,
"column": 33
} | {
"line": 295,
"column": 34
} | [
{
"pp": "case h\nα : Type u_1\nM N : Matroid α\nh : Disjoint M.E N.E\nI✝ : Set α\na✝ : I✝ ⊆ (M.disjointSum N h).E\n⊢ (M.disjointSum N h).Indep I✝ ↔ (N.disjointSum M ⋯).Indep I✝",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLatti... | [
"case h\nα : Type u_1\nM N : Matroid α\nh : Disjoint M.E N.E\nI✝ : Set α\na✝ : I✝ ⊆ (M.disjointSum N h).E\n⊢ M.Indep (I✝ ∩ M.E) ∧ N.Indep (I✝ ∩ N.E) ∧ I✝ ⊆ M.E ∪ N.E ↔ N.Indep (I✝ ∩ N.E) ∧ M.Indep (I✝ ∩ M.E) ∧ I✝ ⊆ M.E ∪ N.E"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Arborescence | {
"line": 71,
"column": 16
} | {
"line": 71,
"column": 55
} | {
"line": 72,
"column": 6
} | [
{
"pp": "case zero\nV : Type u\ninst✝ : Quiver V\nr : V\nheight : V → ℕ\nheight_lt : ∀ ⦃a b : V⦄ (a_1 : a ⟶ b), height a < height b\nunique_arrow : ∀ ⦃a b c : V⦄ (e : a ⟶ c) (f : b ⟶ c), a = b ∧ e ≍ f\nroot_or_arrow : ∀ (b : V), b = r ∨ ∃ a, Nonempty (a ⟶ b)\nb : V\nhn : height b < 0\n⊢ Nonempty (Path r b)",
... | [] | exact False.elim (Nat.not_lt_zero _ hn) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.Quiver.Arborescence | {
"line": 71,
"column": 16
} | {
"line": 71,
"column": 55
} | {
"line": 72,
"column": 6
} | [
{
"pp": "case zero\nV : Type u\ninst✝ : Quiver V\nr : V\nheight : V → ℕ\nheight_lt : ∀ ⦃a b : V⦄ (a_1 : a ⟶ b), height a < height b\nunique_arrow : ∀ ⦃a b c : V⦄ (e : a ⟶ c) (f : b ⟶ c), a = b ∧ e ≍ f\nroot_or_arrow : ∀ (b : V), b = r ∨ ∃ a, Nonempty (a ⟶ b)\nb : V\nhn : height b < 0\n⊢ Nonempty (Path r b)",
... | [] | exact False.elim (Nat.not_lt_zero _ hn) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Quiver.Arborescence | {
"line": 71,
"column": 16
} | {
"line": 71,
"column": 55
} | {
"line": 72,
"column": 6
} | [
{
"pp": "case zero\nV : Type u\ninst✝ : Quiver V\nr : V\nheight : V → ℕ\nheight_lt : ∀ ⦃a b : V⦄ (a_1 : a ⟶ b), height a < height b\nunique_arrow : ∀ ⦃a b c : V⦄ (e : a ⟶ c) (f : b ⟶ c), a = b ∧ e ≍ f\nroot_or_arrow : ∀ (b : V), b = r ∨ ∃ a, Nonempty (a ⟶ b)\nb : V\nhn : height b < 0\n⊢ Nonempty (Path r b)",
... | [] | exact False.elim (Nat.not_lt_zero _ hn) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Quiver.ConnectedComponent | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 85
} | {
"line": 201,
"column": 6
} | [
{
"pp": "V : Type u_2\ninst✝ : Quiver V\nh_sc : IsStronglyConnected V\ni₀ j₀ : V\ne₀ : i₀ ⟶ j₀\ni j : V\np₁ : Path i i₀\np₂ : Path j₀ j\np : Path i j := p₁.comp (e₀.toPath.comp p₂)\n⊢ 0 < p.length",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",... | [
"V : Type u_2\ninst✝ : Quiver V\nh_sc : IsStronglyConnected V\ni₀ j₀ : V\ne₀ : i₀ ⟶ j₀\ni j : V\np₁ : Path i i₀\np₂ : Path j₀ j\np : Path i j := p₁.comp (e₀.toPath.comp p₂)\n⊢ 0 < 1 + (p₂.length + p₁.length)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Nullstellensatz | {
"line": 142,
"column": 6
} | {
"line": 142,
"column": 68
} | {
"line": 142,
"column": 69
} | [
{
"pp": "case h_option.Heval\nR : Type u_1\ninst✝³ : CommRing R\nσ✝ : Type u_2\ninst✝² : Finite σ✝\ninst✝¹ : IsDomain R\nσ : Type u_2\ninst✝ : Fintype σ\nh :\n ∀ (P : MvPolynomial σ R) (S : σ → Finset R),\n (∀ (i : σ), degreeOf i P < #(S i)) → (∀ (x : σ → R), (∀ (i : σ), x i ∈ S i) → (eval x) P = 0) → P = 0... | [
"case h_option.Heval\nR : Type u_1\ninst✝³ : CommRing R\nσ✝ : Type u_2\ninst✝² : Finite σ✝\ninst✝¹ : IsDomain R\nσ : Type u_2\ninst✝ : Fintype σ\nh :\n ∀ (P : MvPolynomial σ R) (S : σ → Finset R),\n (∀ (i : σ), degreeOf i P < #(S i)) → (∀ (x : σ → R), (∀ (i : σ), x i ∈ S i) → (eval x) P = 0) → P = 0\nP : MvPoly... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Nullstellensatz | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 54
} | {
"line": 73,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nσ : Type u_2\ninst✝¹ : Finite σ\ninst✝ : IsDomain R\nP : MvPolynomial σ R\nS : σ → Finset R\nHdeg : ∀ (i : σ), degreeOf i P < #(S i)\nHeval : ∀ (x : σ → R), (∀ (i : σ), x i ∈ S i) → (eval x) P = 0\n⊢ P = 0",
"ppTerm": "?m.24",
"assigned": true,
"usedConsta... | [] | induction σ using Finite.induction_empty_option with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Combinatorics.Nullstellensatz | {
"line": 183,
"column": 6
} | {
"line": 183,
"column": 54
} | {
"line": 183,
"column": 55
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nι : Type u_3\ni : ι\nS : Finset R\nm : ι →₀ ℕ\nhP : P S i = (rename fun x ↦ i) (P S ())\ne : Unit →₀ ℕ\nhe : ¬coeff e (P S ()) = 0\nhm : mapDomain (fun x ↦ i) e = m\nthis✝ : Nontrivial R\nthis : lex.toSyn e ≤ lex.toSyn (single () #S)\n⊢ e () ≤ #S",
"ppTerm": "?m.11... | [
"R : Type u_1\ninst✝ : CommRing R\nι : Type u_3\ni : ι\nS : Finset R\nm : ι →₀ ℕ\nhP : P S i = (rename fun x ↦ i) (P S ())\ne : Unit →₀ ℕ\nhe : ¬coeff e (P S ()) = 0\nhm : mapDomain (fun x ↦ i) e = m\nthis✝ : Nontrivial R\nthis : lex.toSyn e ≤ lex.toSyn (single () #S)\n⊢ e () ≤ #S"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Covering | {
"line": 109,
"column": 73
} | {
"line": 109,
"column": 84
} | {
"line": 109,
"column": 85
} | [
{
"pp": "U : Type u_1\ninst✝¹ : Quiver U\nV : Type u_2\ninst✝ : Quiver V\nφ : U ⥤q V\nhφ : φ.IsCovering\nu v : U\nf g : u ⟶ v\nhe : (fun f ↦ φ.map f) f = (fun f ↦ φ.map f) g\n⊢ φ.star u (Star.mk f) = φ.star u (Star.mk g)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"U : Type u_1\ninst✝¹ : Quiver U\nV : Type u_2\ninst✝ : Quiver V\nφ : U ⥤q V\nhφ : φ.IsCovering\nu v : U\nf g : u ⟶ v\nhe : (fun f ↦ φ.map f) f = (fun f ↦ φ.map f) g\n⊢ φ.map f = φ.map g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Covering | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 13
} | {
"line": 110,
"column": 14
} | [
{
"pp": "U : Type u_1\ninst✝¹ : Quiver U\nV : Type u_2\ninst✝ : Quiver V\nφ : U ⥤q V\nhφ : φ.IsCovering\nu v : U\nf g : u ⟶ v\nhe : (fun f ↦ φ.map f) f = (fun f ↦ φ.map f) g\nthis : φ.star u (Star.mk f) = φ.star u (Star.mk g)\n⊢ f = g",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
... | [
"U : Type u_1\ninst✝¹ : Quiver U\nV : Type u_2\ninst✝ : Quiver V\nφ : U ⥤q V\nhφ : φ.IsCovering\nu v : U\nf g : u ⟶ v\nhe : (fun f ↦ φ.map f) f = (fun f ↦ φ.map f) g\nthis : φ.star u (Star.mk f) = φ.star u (Star.mk g)\n⊢ f = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 141,
"column": 4
} | {
"line": 141,
"column": 15
} | {
"line": 141,
"column": 16
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\n⊢ (p.comp q).length = 0",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Nat.add_eq_zero_iff._simp_1",
"id",
"instOfNatNat",
"instHAdd... | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\n⊢ p.length = 0 ∧ q.length = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 143,
"column": 4
} | {
"line": 143,
"column": 29
} | {
"line": 143,
"column": 30
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\nhlen : (p.comp q).length = 0\n⊢ p.length + q.length = 0",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.add_eq_zero_iff._simp_1",
"id",
"instOfNatNat",
... | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\nhlen : (p.comp q).length = 0\n⊢ p.length = 0 ∧ q.length = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 15
} | {
"line": 150,
"column": 16
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\n⊢ (p.comp q).length = 0",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Nat.add_eq_zero_iff._simp_1",
"id",
"instOfNatNat",
"instHAdd... | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\n⊢ p.length = 0 ∧ q.length = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 152,
"column": 4
} | {
"line": 152,
"column": 29
} | {
"line": 152,
"column": 30
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\nhlen : (p.comp q).length = 0\n⊢ p.length + q.length = 0",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.add_eq_zero_iff._simp_1",
"id",
"instOfNatNat",
... | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nq : Path b a\nh : p.comp q = nil\nhlen : (p.comp q).length = 0\n⊢ p.length = 0 ∧ q.length = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 159,
"column": 11
} | {
"line": 159,
"column": 22
} | {
"line": 159,
"column": 23
} | [
{
"pp": "case nil\nV : Type u_1\ninst✝ : Quiver V\na b : V\nq : Path a a\nx✝ : nil.length = 0 ∧ q.length = 0\nhp : nil.length = 0\nhq : q.length = 0\n⊢ nil.comp q = nil",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Quiver.Path.nil",
"congrArg",
"id",
... | [
"case nil\nV : Type u_1\ninst✝ : Quiver V\na b : V\nq : Path a a\nx✝ : nil.length = 0 ∧ q.length = 0\nhp : nil.length = 0\nhq : q.length = 0\n⊢ q = nil"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 18
} | {
"line": 167,
"column": 19
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nh₁ : p.vertices.getLast ⋯ = b\nh₂ : p.vertices.getLast ⋯ ∈ p.vertices\n⊢ b ∈ p.vertices",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nh₁ : p.vertices.getLast ⋯ = b\nh₂ : p.vertices.getLast ⋯ ∈ p.vertices\n⊢ b ∈ p.vertices"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 183,
"column": 31
} | {
"line": 183,
"column": 42
} | {
"line": 183,
"column": 43
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nn : ℕ\nhn : n ≤ nil.length\n⊢ n = 0",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nn : ℕ\nhn : n ≤ nil.length\n⊢ n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Weight | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 31
} | {
"line": 105,
"column": 32
} | [
{
"pp": "case cons\nV : Type u_1\ninst✝³ : Quiver V\nR : Type u_2\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nw : {i j : V} → (i ⟶ j) → R\nhw : ∀ {i j : V} (e : i ⟶ j), 0 < w e\ni j b✝ c✝ : V\np : Path i b✝\ne : b✝ ⟶ c✝\nih : 0 < weight (fun {i j} ↦ w) p\nhe : 0 < w e\n⊢ 0 < wei... | [
"case cons\nV : Type u_1\ninst✝³ : Quiver V\nR : Type u_2\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nw : {i j : V} → (i ⟶ j) → R\nhw : ∀ {i j : V} (e : i ⟶ j), 0 < w e\ni j b✝ c✝ : V\np : Path i b✝\ne : b✝ ⟶ c✝\nih : 0 < weight (fun {i j} ↦ w) p\nhe : 0 < w e\n⊢ 0 < weight (fun {i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Weight | {
"line": 116,
"column": 6
} | {
"line": 116,
"column": 31
} | {
"line": 116,
"column": 32
} | [
{
"pp": "case cons\nV : Type u_1\ninst✝³ : Quiver V\nR : Type u_2\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nw : {i j : V} → (i ⟶ j) → R\nhw : ∀ {i j : V} (e : i ⟶ j), 0 ≤ w e\ni j b✝ c✝ : V\np : Path i b✝\ne : b✝ ⟶ c✝\nih : 0 ≤ weight (fun {i j} ↦ w) p\nhe : 0 ≤ w e\n⊢ 0 ≤ wei... | [
"case cons\nV : Type u_1\ninst✝³ : Quiver V\nR : Type u_2\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nw : {i j : V} → (i ⟶ j) → R\nhw : ∀ {i j : V} (e : i ⟶ j), 0 ≤ w e\ni j b✝ c✝ : V\np : Path i b✝\ne : b✝ ⟶ c✝\nih : 0 ≤ weight (fun {i j} ↦ w) p\nhe : 0 ≤ w e\n⊢ 0 ≤ weight (fun {i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 219,
"column": 6
} | {
"line": 219,
"column": 52
} | {
"line": 219,
"column": 53
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nv : V\nhv : v ∈ nil.vertices\n⊢ v = a",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nv : V\nhv : v ∈ nil.vertices\n⊢ v = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 222,
"column": 6
} | {
"line": 222,
"column": 76
} | {
"line": 222,
"column": 76
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\nb v : V\np : Path v b\nhv : v ∈ nil.vertices\n⊢ ¬v ∈ nil.vertices.tail",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"False",
"Quiver.Path.nil",
"congrArg",
"Membership.mem",
"List.tail",
"List",
"_private... | [] | by simp only [vertices_nil, tail_cons, not_mem_nil, not_false_eq_true] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Quiver.Path.Vertices | {
"line": 225,
"column": 6
} | {
"line": 225,
"column": 17
} | {
"line": 225,
"column": 18
} | [
{
"pp": "V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nv b✝ c✝ : V\npPrev : Path a b✝\ne : b✝ ⟶ c✝\nih : v ∈ pPrev.vertices → ∃ p₁ p₂, pPrev = p₁.comp p₂ ∧ ¬v ∈ p₂.vertices.tail\nhv : v ∈ (pPrev.cons e).vertices\n⊢ v ∈ pPrev.vertices ∨ v = (pPrev.cons e).end",
"ppTerm": "?m.104",
"assigned": tr... | [
"V : Type u_1\ninst✝ : Quiver V\na b : V\np : Path a b\nv b✝ c✝ : V\npPrev : Path a b✝\ne : b✝ ⟶ c✝\nih : v ∈ pPrev.vertices → ∃ p₁ p₂, pPrev = p₁.comp p₂ ∧ ¬v ∈ p₂.vertices.tail\nhv : v ∈ (pPrev.cons e).vertices\n⊢ v ∈ pPrev.vertices ∨ v = c✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Schnirelmann | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 15
} | {
"line": 100,
"column": 16
} | [
{
"pp": "case inl\nA : Set ℕ\ninst✝ : DecidablePred fun x ↦ x ∈ A\nhk : 0 ∉ A\n⊢ schnirelmannDensity A ≤ 1 - (↑0)⁻¹",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Real.instLE",
"Real",
"congrArg",
"Real.instIn... | [
"case inl\nA : Set ℕ\ninst✝ : DecidablePred fun x ↦ x ∈ A\nhk : 0 ∉ A\n⊢ schnirelmannDensity A ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Schnirelmann | {
"line": 102,
"column": 6
} | {
"line": 102,
"column": 16
} | {
"line": 102,
"column": 17
} | [
{
"pp": "case inr\nA : Set ℕ\ninst✝ : DecidablePred fun x ↦ x ∈ A\nk : ℕ\nhk : k ∉ A\nhk' : k > 0\n⊢ ↑(#({a ∈ Ioc 0 k | a ∈ A})) / ↑k ≤ 1 - (↑k)⁻¹",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Real.instLE",
"Real",
"DivInvMonoid.toI... | [
"case inr\nA : Set ℕ\ninst✝ : DecidablePred fun x ↦ x ∈ A\nk : ℕ\nhk : k ∉ A\nhk' : k > 0\n⊢ ↑(#({a ∈ Ioc 0 k | a ∈ A})) / ↑k ≤ 1 - 1 / ↑k"
] | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Schnirelmann | {
"line": 212,
"column": 36
} | {
"line": 212,
"column": 47
} | {
"line": 212,
"column": 48
} | [
{
"pp": "A : Set ℕ\ninst✝ : DecidablePred fun x ↦ x ∈ A\nhA : A.Finite\n⊢ schnirelmannDensity A = 0",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Set ℕ\ninst✝ : DecidablePred fun x ↦ x ∈ A\nhA : A.Finite\n⊢ schnirelmannDensity A = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Schnirelmann | {
"line": 242,
"column": 8
} | {
"line": 242,
"column": 18
} | {
"line": 242,
"column": 19
} | [
{
"pp": "m : ℕ\nhm : m ≠ 1\nhm' : m > 0\n⊢ ↑(#({a ∈ Ioc 0 m | a ∈ {n | n % m = 1}})) / ↑m ≤ (↑m)⁻¹",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Real.instLE",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Monoid.toMulOneCl... | [
"m : ℕ\nhm : m ≠ 1\nhm' : m > 0\n⊢ ↑(#({a ∈ Ioc 0 m | a ∈ {n | n % m = 1}})) / ↑m ≤ 1 / ↑m"
] | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SetFamily.AhlswedeZhang | {
"line": 169,
"column": 2
} | {
"line": 169,
"column": 87
} | {
"line": 170,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝³ : SemilatticeSup α\ns t : Finset α\na : α\ninst✝² : DecidableLE α\ninst✝¹ : OrderTop α\ninst✝ : DecidableEq α\nhs : a ∈ lowerClosure ↑s\nht : a ∈ lowerClosure ↑t\n⊢ (s ∪ t).truncatedSup a = s.truncatedSup a ⊔ t.truncatedSup a",
"ppTerm": "?m.33",
"assigned": true,
"used... | [
"α : Type u_1\ninst✝³ : SemilatticeSup α\ns t : Finset α\na : α\ninst✝² : DecidableLE α\ninst✝¹ : OrderTop α\ninst✝ : DecidableEq α\nhs : a ∈ lowerClosure ↑s\nht : a ∈ lowerClosure ↑t\n⊢ (({b ∈ s | a ≤ b} ∪ {b ∈ t | a ≤ b}).sup' ⋯ fun x ↦ id x) = {b ∈ s | a ≤ b}.sup' ⋯ id ⊔ {b ∈ t | a ≤ b}.sup' ⋯ id"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sups | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 28
} | {
"line": 159,
"column": 29
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq β\ninst✝³ : SemilatticeSup α\ninst✝² : SemilatticeSup β\ninst✝¹ : FunLike F α β\ninst✝ : SupHomClass F α β\nf : F\nhf : Injective ⇑f\ns t : Finset α\n⊢ map { toFun := ⇑f, inj' := hf } (s ⊻ t) = map { toFun := ⇑f, inj... | [
"F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq β\ninst✝³ : SemilatticeSup α\ninst✝² : SemilatticeSup β\ninst✝¹ : FunLike F α β\ninst✝ : SupHomClass F α β\nf : F\nhf : Injective ⇑f\ns t : Finset α\n⊢ image (⇑f) (s ⊻ t) = image (⇑f) s ⊻ image (⇑f) t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sups | {
"line": 304,
"column": 2
} | {
"line": 304,
"column": 28
} | {
"line": 304,
"column": 29
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq β\ninst✝³ : SemilatticeInf α\ninst✝² : SemilatticeInf β\ninst✝¹ : FunLike F α β\ninst✝ : InfHomClass F α β\nf : F\nhf : Injective ⇑f\ns t : Finset α\n⊢ map { toFun := ⇑f, inj' := hf } (s ⊼ t) = map { toFun := ⇑f, inj... | [
"F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq β\ninst✝³ : SemilatticeInf α\ninst✝² : SemilatticeInf β\ninst✝¹ : FunLike F α β\ninst✝ : InfHomClass F α β\nf : F\nhf : Injective ⇑f\ns t : Finset α\n⊢ image (⇑f) (s ⊼ t) = image (⇑f) s ⊼ image (⇑f) t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sups | {
"line": 466,
"column": 2
} | {
"line": 466,
"column": 66
} | {
"line": 466,
"column": 67
} | [
{
"pp": "α : Type u_2\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns₁ s₂ t : Finset α\n⊢ (s₁ ∩ s₂) ○ t ⊆ s₁ ○ t ∩ s₂ ○ t",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableEqProd",
"SProd.spro... | [
"α : Type u_2\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns₁ s₂ t : Finset α\n⊢ image (fun ab ↦ ab.1 ⊔ ab.2) ({ab ∈ s₁ ×ˢ t | Disjoint ab.1 ab.2} ∩ {ab ∈ s₂ ×ˢ t | Disjoint ab.1 ab.2}) ⊆\n image (fun ab ↦ ab.1 ⊔ ab.2) ({ab ∈ s₁ ×ˢ t | Disjoint ab.1 ab.2... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sups | {
"line": 469,
"column": 2
} | {
"line": 469,
"column": 66
} | {
"line": 469,
"column": 67
} | [
{
"pp": "α : Type u_2\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns t₁ t₂ : Finset α\n⊢ s ○ (t₁ ∩ t₂) ⊆ s ○ t₁ ∩ s ○ t₂",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableEqProd",
"SProd.spro... | [
"α : Type u_2\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns t₁ t₂ : Finset α\n⊢ image (fun ab ↦ ab.1 ⊔ ab.2) ({ab ∈ s ×ˢ t₁ | Disjoint ab.1 ab.2} ∩ {ab ∈ s ×ˢ t₂ | Disjoint ab.1 ab.2}) ⊆\n image (fun ab ↦ ab.1 ⊔ ab.2) ({ab ∈ s ×ˢ t₁ | Disjoint ab.1 ab.2... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.AhlswedeZhang | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 87
} | {
"line": 247,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝³ : SemilatticeInf α\ns t : Finset α\na : α\ninst✝² : DecidableLE α\ninst✝¹ : BoundedOrder α\ninst✝ : DecidableEq α\nhs : a ∈ upperClosure ↑s\nht : a ∈ upperClosure ↑t\n⊢ (s ∪ t).truncatedInf a = s.truncatedInf a ⊓ t.truncatedInf a",
"ppTerm": "?m.34",
"assigned": true,
"... | [
"α : Type u_1\ninst✝³ : SemilatticeInf α\ns t : Finset α\na : α\ninst✝² : DecidableLE α\ninst✝¹ : BoundedOrder α\ninst✝ : DecidableEq α\nhs : a ∈ upperClosure ↑s\nht : a ∈ upperClosure ↑t\n⊢ (({b ∈ s | b ≤ a} ∪ {b ∈ t | b ≤ a}).inf' ⋯ fun x ↦ id x) = {b ∈ s | b ≤ a}.inf' ⋯ id ⊓ {b ∈ t | b ≤ a}.inf' ⋯ id"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sups | {
"line": 660,
"column": 14
} | {
"line": 660,
"column": 25
} | {
"line": 660,
"column": 26
} | [
{
"pp": "α : Type u_4\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\nn : ℕ\nhn : n ≤ Fintype.card α\nh𝒜 : Set.Sized n ↑𝒜ᶜˢ\n⊢ Set.Sized (Fintype.card α - n) ↑𝒜",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_4\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\nn : ℕ\nhn : n ≤ Fintype.card α\nh𝒜 : Set.Sized n ↑𝒜ᶜˢ\n⊢ Set.Sized (Fintype.card α - n) ↑𝒜"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sups | {
"line": 661,
"column": 15
} | {
"line": 661,
"column": 53
} | {
"line": 661,
"column": 54
} | [
{
"pp": "α : Type u_4\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\nn : ℕ\nhn : n ≤ Fintype.card α\nh𝒜 : Set.Sized (Fintype.card α - n) ↑𝒜\n⊢ Set.Sized n ↑𝒜ᶜˢ",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_4\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\nn : ℕ\nhn : n ≤ Fintype.card α\nh𝒜 : Set.Sized (Fintype.card α - n) ↑𝒜\n⊢ Set.Sized n ↑𝒜ᶜˢ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Irreducible | {
"line": 79,
"column": 35
} | {
"line": 79,
"column": 53
} | {
"line": 79,
"column": 54
} | [
{
"pp": "α : Type u_2\ninst✝ : SemilatticeSup α\na : α\nh : ∀ ⦃b c : α⦄, a ≤ b ⊔ c → a ≤ b ∨ a ≤ c\nb c : α\nha : b ⊔ c = a\n⊢ b = a ∨ c = a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semi... | [
"α : Type u_2\ninst✝ : SemilatticeSup α\na : α\nh : ∀ ⦃b c : α⦄, a ≤ b ⊔ c → a ≤ b ∨ a ≤ c\nb c : α\nha : b ⊔ c = a\n⊢ c ≤ b ∨ b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Irreducible | {
"line": 101,
"column": 13
} | {
"line": 101,
"column": 36
} | {
"line": 101,
"column": 37
} | [
{
"pp": "case empty\nι : Type u_1\nα : Type u_2\ninst✝¹ : SemilatticeSup α\na : α\ninst✝ : OrderBot α\ns : Finset ι\nf : ι → α\nha : SupIrred a\nh : ∅.sup f = a\n⊢ ∃ i ∈ ∅, f i = a",
"ppTerm": "?empty",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"congrArg",
"Fins... | [
"case empty\nι : Type u_1\nα : Type u_2\ninst✝¹ : SemilatticeSup α\na : α\ninst✝ : OrderBot α\ns : Finset ι\nf : ι → α\nha : SupIrred a\nh : ∅.sup f = a\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Irreducible | {
"line": 162,
"column": 35
} | {
"line": 162,
"column": 53
} | {
"line": 162,
"column": 54
} | [
{
"pp": "α : Type u_2\ninst✝ : SemilatticeInf α\na : α\nh : ∀ ⦃b c : α⦄, b ⊓ c ≤ a → b ≤ a ∨ c ≤ a\nb c : α\nha : b ⊓ c = a\n⊢ b = a ∨ c = a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"left_eq_inf._simp_1",
"PartialOrder.toPreorder",
... | [
"α : Type u_2\ninst✝ : SemilatticeInf α\na : α\nh : ∀ ⦃b c : α⦄, b ⊓ c ≤ a → b ≤ a ∨ c ≤ a\nb c : α\nha : b ⊓ c = a\n⊢ b ≤ c ∨ c ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Irreducible | {
"line": 286,
"column": 29
} | {
"line": 286,
"column": 58
} | {
"line": 286,
"column": 59
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrder α\na x✝¹ x✝ : α\n⊢ max x✝¹ x✝ = a → x✝¹ = a ∨ x✝ = a",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"_pri... | [
"α : Type u_2\ninst✝ : LinearOrder α\na x✝¹ x✝ : α\n⊢ x✝¹ = a ∧ x✝ ≤ x✝¹ ∨ x✝ = a ∧ x✝¹ ≤ x✝ → x✝¹ = a ∨ x✝ = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Irreducible | {
"line": 290,
"column": 29
} | {
"line": 290,
"column": 58
} | {
"line": 290,
"column": 59
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrder α\na x✝¹ x✝ : α\n⊢ min x✝¹ x✝ = a → x✝¹ = a ∨ x✝ = a",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
... | [
"α : Type u_2\ninst✝ : LinearOrder α\na x✝¹ x✝ : α\n⊢ x✝¹ = a ∧ x✝¹ ≤ x✝ ∨ x✝ = a ∧ x✝ ≤ x✝¹ → x✝¹ = a ∨ x✝ = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Birkhoff | {
"line": 286,
"column": 2
} | {
"line": 287,
"column": 89
} | {
"line": 289,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝¹ : Finite α\ninst✝ : DistribLattice α\n⊢ ∃ β x x_1 f, Injective ⇑f",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
"Finset",
"Classical.propDecidable",
"Exists",
"Subtype.fintype",
"inferInstance",
... | [] | cases nonempty_fintype α
exact ⟨{a : α // SupIrred a}, _, inferInstance, _, LatticeHom.birkhoffFinset_injective⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Birkhoff | {
"line": 286,
"column": 2
} | {
"line": 287,
"column": 89
} | {
"line": 289,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝¹ : Finite α\ninst✝ : DistribLattice α\n⊢ ∃ β x x_1 f, Injective ⇑f",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
"Finset",
"Classical.propDecidable",
"Exists",
"Subtype.fintype",
"inferInstance",
... | [] | cases nonempty_fintype α
exact ⟨{a : α // SupIrred a}, _, inferInstance, _, LatticeHom.birkhoffFinset_injective⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SetFamily.Compression.UV | {
"line": 254,
"column": 2
} | {
"line": 254,
"column": 16
} | {
"line": 255,
"column": 2
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : DecidableRel Disjoint\ninst✝¹ : DecidableLE α\ns : Finset α\nu v a : α\ninst✝ : DecidableEq α\nhva : v ≤ a\nhvu : v = ⊥ → u = ⊥\nleft✝ : a ∉ s\nb : α\nhb : b ∈ s\nh : (if Disjoint u b ∧ v ≤ b then (b ⊔ u) \\ v else b) = a\n⊢ a ∈ s",... | [
"case pos\nα : Type u_1\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : DecidableRel Disjoint\ninst✝¹ : DecidableLE α\ns : Finset α\nu v a : α\ninst✝ : DecidableEq α\nhva : v ≤ a\nhvu : v = ⊥ → u = ⊥\nleft✝ : a ∉ s\nb : α\nhb : b ∈ s\nh✝ : Disjoint u b ∧ v ≤ b\nh : (b ⊔ u) \\ v = a\n⊢ a ∈ s",
"case neg\nα : Type ... | split_ifs at h | Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1 | Mathlib.Tactic.splitIfs |
Mathlib.Combinatorics.SetFamily.AhlswedeZhang | {
"line": 418,
"column": 4
} | {
"line": 418,
"column": 25
} | {
"line": 418,
"column": 26
} | [
{
"pp": "case ind.inl\nα : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\ninst✝ : Nonempty α\nm : ℕ\nih : ∀ (𝒜 : Finset (Finset α)), #𝒜 < m → 𝒜.Nonempty → univ ∉ 𝒜 → supSum 𝒜 = ↑(card α) * ∑ k ∈ range (card α), (↑k)⁻¹\na : Finset α\nh𝒜₁ : {a}.Nonempty\nh𝒜₂ : univ ∉ {a}\nhm : m = #{a}\n⊢ a ≠ univ",... | [
"case ind.inl\nα : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\ninst✝ : Nonempty α\nm : ℕ\nih : ∀ (𝒜 : Finset (Finset α)), #𝒜 < m → 𝒜.Nonempty → univ ∉ 𝒜 → supSum 𝒜 = ↑(card α) * ∑ k ∈ range (card α), (↑k)⁻¹\na : Finset α\nh𝒜₁ : {a}.Nonempty\nh𝒜₂ : univ ∉ {a}\nhm : m = #{a}\n⊢ ¬a = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.AhlswedeZhang | {
"line": 427,
"column": 4
} | {
"line": 427,
"column": 15
} | {
"line": 427,
"column": 16
} | [
{
"pp": "case ind.inr.succ.h𝒜₂\nα : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\ninst✝ : Nonempty α\ns : Finset α\n𝒜 : Finset (Finset α)\nhs : s ∉ 𝒜\nh𝒜₁ : (insert s 𝒜).Nonempty\nh𝒜₂ : univ ∉ insert s 𝒜\nh𝒜₃ : (insert s 𝒜).Nontrivial\nih :\n ∀ (𝒜_1 : Finset (Finset α)),\n #𝒜_1 < #𝒜 + 1 ... | [
"case ind.inr.succ.h𝒜₂\nα : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\ninst✝ : Nonempty α\ns : Finset α\n𝒜 : Finset (Finset α)\nhs : s ∉ 𝒜\nh𝒜₁ : (insert s 𝒜).Nonempty\nh𝒜₂ : univ ∉ insert s 𝒜\nh𝒜₃ : (insert s 𝒜).Nontrivial\nih :\n ∀ (𝒜_1 : Finset (Finset α)),\n #𝒜_1 < #𝒜 + 1 → 𝒜_1.Nonem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.KruskalKatona | {
"line": 68,
"column": 6
} | {
"line": 68,
"column": 22
} | {
"line": 68,
"column": 23
} | [
{
"pp": "case mp.right\nα : Type u_1\ninst✝¹ : LinearOrder α\ns : Finset α\ninst✝ : Fintype α\nhs : s.Nonempty\nt : Finset α\na : α\nha : a ∉ t\nhst : #s = #(insert a t)\nhts : toColex (insert a t) ≤ toColex s\n⊢ toColex t ≤ toColex (s.erase (s.min' hs))",
"ppTerm": "?mp.right",
"assigned": false,
"... | [
"case mp.right\nα : Type u_1\ninst✝¹ : LinearOrder α\ns : Finset α\ninst✝ : Fintype α\nhs : s.Nonempty\nt : Finset α\na : α\nha : a ∉ t\nhst : #s = #(insert a t)\nhts : toColex (insert a t) ≤ toColex s\n⊢ toColex t ≤ toColex (s.erase (s.min' hs))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 174,
"column": 8
} | {
"line": 174,
"column": 23
} | {
"line": 174,
"column": 24
} | [
{
"pp": "case pos.refine_1\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\na : α\nf₁ f₂ f₃ f₄ : Finset α → β\nu : Finset α\ninst✝ : ExistsAddOfLE β\nhu : a ∉ u\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Fi... | [
"case pos.refine_1\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\na : α\nf₁ f₂ f₃ f₄ : Finset α → β\nu : Finset α\ninst✝ : ExistsAddOfLE β\nhu : a ∉ u\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α⦄, s ⊆... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.KruskalKatona | {
"line": 90,
"column": 4
} | {
"line": 91,
"column": 34
} | {
"line": 91,
"column": 35
} | [
{
"pp": "case mpr.inr.inl\nα : Type u_1\ninst✝¹ : LinearOrder α\ns : Finset α\ninst✝ : Fintype α\nhs : s.Nonempty\nt : Finset α\ncards' : #(s.erase (s.min' hs)) = #t\nk : α\nhks : k ∈ s.erase (s.min' hs)\nhkt : k ∉ t\nz : ∀ ⦃a : α⦄, k < a → (a ∈ t ↔ a ∈ s.erase (s.min' hs))\nj : α := tᶜ.min' ⋯\nhjk✝ : j ≤ k\nth... | [
"case mpr.inr.inl\nα : Type u_1\ninst✝¹ : LinearOrder α\ns : Finset α\ninst✝ : Fintype α\nhs : s.Nonempty\nt : Finset α\ncards' : #(s.erase (s.min' hs)) = #t\nk : α\nhks : k ∈ s.erase (s.min' hs)\nhkt : k ∉ t\nz : ∀ ⦃a : α⦄, k < a → (a ∈ t ↔ a ∈ s.erase (s.min' hs))\nj : α := tᶜ.min' ⋯\nhjk✝ : j ≤ k\nthis : j ∉ t\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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