module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 18
} | {
"line": 112,
"column": 19
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nH : G.Subgraph\nh : H.Preconnected\nv : ↑H.verts\ninst✝ : Fintype ↑(H.neighborSet ↑v)\nhv : H.degree ↑v = 0\nhn : H.verts.Nontrivial\nthis : Nontrivial ↑H.verts\n⊢ False",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"V : Type u\nG : SimpleGraph V\nH : G.Subgraph\nh : H.Preconnected\nv : ↑H.verts\ninst✝ : Fintype ↑(H.neighborSet ↑v)\nhv : H.degree ↑v = 0\nhn : H.verts.Nontrivial\nthis : Nontrivial ↑H.verts\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 131,
"column": 21
} | {
"line": 131,
"column": 32
} | {
"line": 131,
"column": 33
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nH : G.Subgraph\nhc : H.Connected\nh : ∀ v ∈ H.verts, ∀ (w : V), G.Adj v w → H.Adj v w\nv : V\nhv : v ∈ H.verts\nw : V\nhw : w ∈ H.verts\n⊢ G.Reachable w v",
"ppTerm": "?m.55",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"V : Type u\nG : SimpleGraph V\nH : G.Subgraph\nhc : H.Connected\nh : ∀ v ∈ H.verts, ∀ (w : V), G.Adj v w → H.Adj v w\nv : V\nhv : v ∈ H.verts\nw : V\nhw : w ∈ H.verts\n⊢ G.Reachable w v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 351,
"column": 8
} | {
"line": 351,
"column": 33
} | {
"line": 351,
"column": 34
} | [
{
"pp": "case inl\nV : Type u_1\nv w : V\nG : SimpleGraph V\ns t : Set V\nα : Type u_2\nβ : Type u_3\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nleft right : Finset V\ncard_left : #left = Fintype.card α\ncard_right : #right = Fintype.card β\nh : G.IsCompleteBetween ↑left ↑right\nthis✝ : Nonempty (α ↪ ↥left)\nfα : α... | [
"case inl\nV : Type u_1\nv w : V\nG : SimpleGraph V\ns t : Set V\nα : Type u_2\nβ : Type u_3\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nleft right : Finset V\ncard_left : #left = Fintype.card α\ncard_right : #right = Fintype.card β\nh : G.IsCompleteBetween ↑left ↑right\nthis✝ : Nonempty (α ↪ ↥left)\nfα : α ↪ ↥left := ... | ← Sum.inl_getLeft s₁ hs₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 280,
"column": 47
} | {
"line": 280,
"column": 58
} | {
"line": 280,
"column": 59
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : ExistsAddOfLE β\na : α\nu : Finset α\nhu : a ∉ u\nf₁ f₂ f₃ f₄ : Finset α → β\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α⦄, s ⊆ insert... | [
"α : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : ExistsAddOfLE β\na : α\nu : Finset α\nhu : a ∉ u\nf₁ f₂ f₃ f₄ : Finset α → β\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α⦄, s ⊆ insert a u → ∀ ⦃t ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 281,
"column": 47
} | {
"line": 281,
"column": 58
} | {
"line": 281,
"column": 59
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : ExistsAddOfLE β\na : α\nu : Finset α\nhu : a ∉ u\nf₁ f₂ f₃ f₄ : Finset α → β\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α⦄, s ⊆ insert... | [
"α : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : ExistsAddOfLE β\na : α\nu : Finset α\nhu : a ∉ u\nf₁ f₂ f₃ f₄ : Finset α → β\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α⦄, s ⊆ insert a u → ∀ ⦃t ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 282,
"column": 4
} | {
"line": 283,
"column": 33
} | {
"line": 283,
"column": 34
} | [
{
"pp": "case insert\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : ExistsAddOfLE β\na : α\nu : Finset α\nhu : a ∉ u\nf₁ f₂ f₃ f₄ : Finset α → β\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α... | [
"case insert\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : DecidableEq α\ninst✝³ : CommSemiring β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : ExistsAddOfLE β\na : α\nu : Finset α\nhu : a ∉ u\nf₁ f₂ f₃ f₄ : Finset α → β\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ ⦃s : Finset α⦄, s ⊆ inser... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 440,
"column": 2
} | {
"line": 440,
"column": 34
} | {
"line": 440,
"column": 35
} | [
{
"pp": "V : Type u_1\nv : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhv : v ∈ s\n⊢ G.neighborFinset v ⊆ (between (↑s) (↑s)ᶜ G).neighborFinset v ∪ s",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finse... | [
"V : Type u_1\nv : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhv : v ∈ s\n⊢ G.neighborSet v ⊆ (between (↑s) (↑s)ᶜ G).neighborSet v ∪ ↑s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 447,
"column": 4
} | {
"line": 447,
"column": 15
} | {
"line": 447,
"column": 16
} | [
{
"pp": "V : Type u_1\nv : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhv : v ∈ s\n⊢ (between (↑s) (↑s)ᶜ G).IsBipartiteWith ↑s ↑sᶜ",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl.... | [
"V : Type u_1\nv : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhv : v ∈ s\n⊢ (between (↑s) (↑s)ᶜ G).IsBipartiteWith (↑s) (↑s)ᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 276,
"column": 2
} | {
"line": 276,
"column": 13
} | {
"line": 276,
"column": 14
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v : V\nw : G.Walk u v\nh : ¬w.Nil\n⊢ w.toSubgraph.Adj u w.snd",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u\nG : SimpleGraph V\nu v : V\nw : G.Walk u v\nh : ¬w.Nil\n⊢ w.toSubgraph.Adj u w.snd"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 34
} | {
"line": 456,
"column": 35
} | [
{
"pp": "V : Type u_1\nw : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhw : w ∈ sᶜ\n⊢ G.neighborFinset w ⊆ (between (↑s) (↑s)ᶜ G).neighborFinset w ∪ sᶜ",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin... | [
"V : Type u_1\nw : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhw : w ∈ sᶜ\n⊢ G.neighborSet w ⊆ (between (↑s) (↑s)ᶜ G).neighborSet w ∪ (↑s)ᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 281,
"column": 2
} | {
"line": 282,
"column": 9
} | {
"line": 282,
"column": 10
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v : V\nw : G.Walk u v\nh : 0 < w.length\n⊢ w.toSubgraph.Adj w.penultimate v",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u\nG : SimpleGraph V\nu v : V\nw : G.Walk u v\nh : 0 < w.length\n⊢ w.toSubgraph.Adj w.penultimate v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 456,
"column": 80
} | {
"line": 456,
"column": 91
} | {
"line": 456,
"column": 92
} | [
{
"pp": "V : Type u_1\nw : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhw : w ∈ sᶜ\n⊢ w ∈ (↑s)ᶜ",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"congrArg",
"Compl.co... | [
"V : Type u_1\nw : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhw : w ∈ sᶜ\n⊢ w ∉ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 463,
"column": 4
} | {
"line": 463,
"column": 15
} | {
"line": 463,
"column": 16
} | [
{
"pp": "V : Type u_1\nw : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhw : w ∈ sᶜ\n⊢ (between (↑s) (↑s)ᶜ G).IsBipartiteWith ↑s ↑sᶜ",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl... | [
"V : Type u_1\nw : V\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ns : Finset V\ninst✝ : DecidableRel G.Adj\nhw : w ∈ sᶜ\n⊢ (between (↑s) (↑s)ᶜ G).IsBipartiteWith (↑s) (↑s)ᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 101,
"column": 15
} | {
"line": 101,
"column": 25
} | {
"line": 102,
"column": 2
} | [
{
"pp": "case inl\nV : Type u_1\nG : SimpleGraph V\nu v w : V\nhuv : G.edist u v = ⊤\n⊢ G.edist u w ≤ G.edist u v + G.edist v w",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"instTopENat",
"congrArg",
"le_top._simp_2",
"PartialOrder.toPreorder",
"LinearOrdere... | [] | simp [huv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 101,
"column": 15
} | {
"line": 101,
"column": 25
} | {
"line": 102,
"column": 2
} | [
{
"pp": "case inl\nV : Type u_1\nG : SimpleGraph V\nu v w : V\nhuv : G.edist u v = ⊤\n⊢ G.edist u w ≤ G.edist u v + G.edist v w",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"instTopENat",
"congrArg",
"le_top._simp_2",
"PartialOrder.toPreorder",
"LinearOrdere... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 101,
"column": 15
} | {
"line": 101,
"column": 25
} | {
"line": 102,
"column": 2
} | [
{
"pp": "case inl\nV : Type u_1\nG : SimpleGraph V\nu v w : V\nhuv : G.edist u v = ⊤\n⊢ G.edist u w ≤ G.edist u v + G.edist v w",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"instTopENat",
"congrArg",
"le_top._simp_2",
"PartialOrder.toPreorder",
"LinearOrdere... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 549,
"column": 18
} | {
"line": 549,
"column": 29
} | {
"line": 549,
"column": 30
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nx✝ : V × V\nh :\n x✝ ∈\n {x |\n match x with\n | (x, y) => G.Adj x y}\n⊢ (match x✝, h with\n | (v, w), x => s(Sum.inl v, Sum.inr w)) ∈\n G.bipartiteDoubleCover.edgeFinset",
"ppTerm": "?m.38",
"a... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nx✝ : V × V\nh :\n x✝ ∈\n {x |\n match x with\n | (x, y) => G.Adj x y}\n⊢ G.Adj x✝.1 x✝.2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 14
} | {
"line": 141,
"column": 2
} | [
{
"pp": "case pos\nV : Type u_1\nG : SimpleGraph V\nu v : V\nhuv : u = v\n⊢ G.edist u v ≤ 1 ↔ G.Adj u v ∨ u = v",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"False",
"instAddMonoidWithOneENat",
"congrArg",
"CommSemiring.toSemiring",
"instIsBotZeroClass",
... | [] | simp [huv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 14
} | {
"line": 141,
"column": 2
} | [
{
"pp": "case pos\nV : Type u_1\nG : SimpleGraph V\nu v : V\nhuv : u = v\n⊢ G.edist u v ≤ 1 ↔ G.Adj u v ∨ u = v",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"False",
"instAddMonoidWithOneENat",
"congrArg",
"CommSemiring.toSemiring",
"instIsBotZeroClass",
... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 14
} | {
"line": 141,
"column": 2
} | [
{
"pp": "case pos\nV : Type u_1\nG : SimpleGraph V\nu v : V\nhuv : u = v\n⊢ G.edist u v ≤ 1 ↔ G.Adj u v ∨ u = v",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"False",
"instAddMonoidWithOneENat",
"congrArg",
"CommSemiring.toSemiring",
"instIsBotZeroClass",
... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 553,
"column": 22
} | {
"line": 553,
"column": 33
} | {
"line": 553,
"column": 34
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nv w : V ⊕ V\nval✝¹ val✝ : V\nhe : G.bipartiteDoubleCover.Adj (Sum.inl val✝¹) (Sum.inr val✝)\n⊢ ∃ a,\n ∃ (ha :\n a ∈\n {x |\n match x with\n | (x, y) => G.Adj x y}),\n (match a, ha with... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nv w : V ⊕ V\nval✝¹ val✝ : V\nhe : G.bipartiteDoubleCover.Adj (Sum.inl val✝¹) (Sum.inr val✝)\n⊢ G.Adj val✝¹ val✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 554,
"column": 22
} | {
"line": 554,
"column": 33
} | {
"line": 554,
"column": 34
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nv w : V ⊕ V\nval✝¹ val✝ : V\nhe : G.bipartiteDoubleCover.Adj (Sum.inr val✝¹) (Sum.inl val✝)\n⊢ ∃ a,\n ∃ (ha :\n a ∈\n {x |\n match x with\n | (x, y) => G.Adj x y}),\n (match a, ha with... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nv w : V ⊕ V\nval✝¹ val✝ : V\nhe : G.bipartiteDoubleCover.Adj (Sum.inr val✝¹) (Sum.inl val✝)\n⊢ G.Adj val✝ val✝¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 387,
"column": 2
} | {
"line": 387,
"column": 13
} | {
"line": 387,
"column": 14
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.IsPath\nhnp : ¬p.Nil\n⊢ p.toSubgraph.neighborSet v = {p.penultimate}",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.IsPath\nhnp : ¬p.Nil\n⊢ p.toSubgraph.neighborSet v = {p.penultimate}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 267,
"column": 2
} | {
"line": 267,
"column": 79
} | {
"line": 268,
"column": 4
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nu v : V\nh : 0 < sInf (Set.range Walk.length)\n⊢ Set.univ.Nonempty",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nG : SimpleGraph V\nu v : V\nh : 0 < sInf (Set.range Walk.length)\n⊢ Set.univ.Nonempty"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 13
} | {
"line": 338,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ #s * #t ≤ #(s ⊼ t) * #(s ⊻ t)",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ #s * #t ≤ #(s ⊼ t) * #(s ⊻ t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 347,
"column": 12
} | {
"line": 347,
"column": 23
} | {
"line": 347,
"column": 24
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁵ : DistribLattice α\ninst✝⁴ : CommSemiring β\ninst✝³ : LinearOrder β\ninst✝² : IsStrictOrderedRing β\ninst✝¹ : ExistsAddOfLE β\nf₁ f₂ f₃ f₄ : α → β\ninst✝ : Fintype α\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a... | [
"α : Type u_1\nβ : Type u_2\ninst✝⁵ : DistribLattice α\ninst✝⁴ : CommSemiring β\ninst✝³ : LinearOrder β\ninst✝² : IsStrictOrderedRing β\ninst✝¹ : ExistsAddOfLE β\nf₁ f₂ f₃ f₄ : α → β\ninst✝ : Fintype α\nh₁ : 0 ≤ f₁\nh₂ : 0 ≤ f₂\nh₃ : 0 ≤ f₃\nh₄ : 0 ≤ f₄\nh : ∀ (a b : α), f₁ a * f₂ b ≤ f₃ (a ⊓ b) * f₄ (a ⊔ b)\n⊢ (∑ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 365,
"column": 59
} | {
"line": 365,
"column": 67
} | {
"line": 366,
"column": 2
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nu v u' v' : V\np₁ : G.Walk u v\np₂ : G.Walk u' v'\nh₁ : p₁.length = G.dist u v\nhh : G.dist u' v' < p₂.length\nru : G.Walk u u'\nrv : G.Walk v' v\nh : p₁ = (ru.append p₂).append rv\ns : G.Walk u' v'\nh✝ : s.IsPath ∧ s.length = G.dist u' v'\nr : G.Walk u v := (ru.append ... | [] | simp [r] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 384,
"column": 38
} | {
"line": 386,
"column": 9
} | {
"line": 386,
"column": 9
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : p.length = G.dist v w\nhl : 1 < G.dist v w\nhnp : ¬p.Nil\n⊢ ¬p.tail.Nil",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.Walk.exists_adj_adj_not_adj... | [] | by
simp only [not_nil_iff_lt_length, ← p.length_tail_add_one hnp] at hp ⊢
lia | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 42
} | {
"line": 573,
"column": 43
} | [
{
"pp": "case inl.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inl.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 391,
"column": 6
} | {
"line": 391,
"column": 38
} | {
"line": 391,
"column": 39
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : p.length = G.dist v w\nhl : 1 < G.dist v w\nhnp : ¬p.Nil\nthis✝ : p.tail.tail.length < p.tail.length\nthis : p.tail.length < p.length\nhv : v = p.getVert 2\n⊢ G.dist v w ≤ p.tail.tail.length",
"ppTerm": "?m.155",
"assigned": true,
... | [
"V : Type u_1\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : p.length = G.dist v w\nhl : 1 < G.dist v w\nhnp : ¬p.Nil\nthis✝ : p.tail.tail.length < p.tail.length\nthis : p.tail.length < p.length\nhv : v = p.getVert 2\n⊢ G.dist (p.getVert 2) w ≤ p.tail.tail.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 390,
"column": 4
} | {
"line": 392,
"column": 7
} | {
"line": 393,
"column": 2
} | [
{
"pp": "case pos\nV : Type u_1\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : p.length = G.dist v w\nhl : 1 < G.dist v w\nhnp : ¬p.Nil\nthis✝ : p.tail.tail.length < p.tail.length\nthis : p.tail.length < p.length\nhv : v = p.getVert 2\n⊢ G.Adj v (p.getVert 1) ∧ G.Adj (p.getVert 1) (p.getVert 2) ∧ ¬G.Adj v (p... | [] | have : G.dist v w ≤ p.tail.tail.length := by
simpa [hv, p.getVert_tail] using dist_le p.tail.tail
lia | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Metric | {
"line": 390,
"column": 4
} | {
"line": 392,
"column": 7
} | {
"line": 393,
"column": 2
} | [
{
"pp": "case pos\nV : Type u_1\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : p.length = G.dist v w\nhl : 1 < G.dist v w\nhnp : ¬p.Nil\nthis✝ : p.tail.tail.length < p.tail.length\nthis : p.tail.length < p.length\nhv : v = p.getVert 2\n⊢ G.Adj v (p.getVert 1) ∧ G.Adj (p.getVert 1) (p.getVert 2) ∧ ¬G.Adj v (p... | [] | have : G.dist v w ≤ p.tail.tail.length := by
simpa [hv, p.getVert_tail] using dist_le p.tail.tail
lia | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 42
} | {
"line": 573,
"column": 43
} | [
{
"pp": "case inl.inr.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inl.inr.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 53
} | {
"line": 573,
"column": 64
} | {
"line": 573,
"column": 65
} | [
{
"pp": "case inl.inr.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inl.inr.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 42
} | {
"line": 573,
"column": 43
} | [
{
"pp": "case inr.inl.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inr.inl.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 362,
"column": 4
} | {
"line": 362,
"column": 33
} | {
"line": 362,
"column": 34
} | [
{
"pp": "case inr.inr.refine_2\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : DistribLattice α\ninst✝⁴ : CommSemiring β\ninst✝³ : LinearOrder β\ninst✝² : IsStrictOrderedRing β\ninst✝¹ : ExistsAddOfLE β\nf g μ : α → β\ninst✝ : Fintype α\nhμ₀ : 0 ≤ μ\nhf✝ : 0 ≤ f\nhg✝ : 0 ≤ g\nhμ : Monotone μ\nhfg : ∑ a, f a = ∑ a, g a\nh... | [
"case inr.inr.refine_2\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : DistribLattice α\ninst✝⁴ : CommSemiring β\ninst✝³ : LinearOrder β\ninst✝² : IsStrictOrderedRing β\ninst✝¹ : ExistsAddOfLE β\nf g μ : α → β\ninst✝ : Fintype α\nhμ₀ : 0 ≤ μ\nhf✝ : 0 ≤ f\nhg✝ : 0 ≤ g\nhμ : Monotone μ\nhfg : ∑ a, f a = ∑ a, g a\nh : ∀ (a b : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 53
} | {
"line": 573,
"column": 64
} | {
"line": 573,
"column": 65
} | [
{
"pp": "case inr.inl.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inr.inl.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 42
} | {
"line": 573,
"column": 43
} | [
{
"pp": "case inr.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inr.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 392,
"column": 2
} | {
"line": 392,
"column": 67
} | {
"line": 393,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : GeneralizedBooleanAlgebra α\ns t : Finset α\nthis :\n ∀ (s t : Finset α),\n map { toFun := ⇑liftLatticeHom, inj' := ⋯ } (s \\\\ t) =\n map { toFun := ⇑liftLatticeHom, inj' := ⋯ } s \\\\ map { toFun := ⇑liftLatticeHom, inj' := ⋯ } t\n⊢ #s * #t ≤ #(s... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : GeneralizedBooleanAlgebra α\ns t : Finset α\nthis :\n ∀ (s t : Finset α),\n map { toFun := ⇑liftLatticeHom, inj' := ⋯ } (s \\\\ t) =\n map { toFun := ⇑liftLatticeHom, inj' := ⋯ } s \\\\ map { toFun := ⇑liftLatticeHom, inj' := ⋯ } t\n⊢ #s * #t ≤ #(s \\\\ t) * #... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SetFamily.FourFunctions | {
"line": 399,
"column": 4
} | {
"line": 399,
"column": 22
} | {
"line": 399,
"column": 23
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : GeneralizedBooleanAlgebra α\ns : Finset α\n⊢ #s ^ 2 ≤ #(s \\\\ s) ^ 2",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : GeneralizedBooleanAlgebra α\ns : Finset α\n⊢ #s ^ 2 ≤ #(s \\\\ s) ^ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 472,
"column": 2
} | {
"line": 472,
"column": 47
} | {
"line": 473,
"column": 2
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv w : V\np : G.Walk v v\nh : p.IsCycle\nhadj : p.toSubgraph.Adj v w\n⊢ ∃ p', p'.IsCycle ∧ p'.snd = w ∧ p'.toSubgraph.verts = p.toSubgraph.verts",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Membership.mem",
"SimpleGraph.Walk.toSubgraph... | [
"V : Type u\nG : SimpleGraph V\nv w : V\np : G.Walk v v\nh : p.IsCycle\nhadj : p.toSubgraph.Adj v w\nthis : w ∈ p.toSubgraph.neighborSet v\n⊢ ∃ p', p'.IsCycle ∧ p'.snd = w ∧ p'.toSubgraph.verts = p.toSubgraph.verts"
] | have : w ∈ p.toSubgraph.neighborSet v := hadj | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 42
} | {
"line": 577,
"column": 43
} | [
{
"pp": "case inl.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inl.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 42
} | {
"line": 577,
"column": 43
} | [
{
"pp": "case inl.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inl.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 53
} | {
"line": 577,
"column": 64
} | {
"line": 577,
"column": 65
} | [
{
"pp": "case inl.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inl.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 42
} | {
"line": 577,
"column": 43
} | [
{
"pp": "case inr.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inr.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 53
} | {
"line": 577,
"column": 64
} | {
"line": 577,
"column": 65
} | [
{
"pp": "case inr.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inr.inl.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Sum | {
"line": 250,
"column": 2
} | {
"line": 250,
"column": 12
} | {
"line": 251,
"column": 4
} | [
{
"pp": "case coe\nV : Type u_3\nW : Type u_5\nG : SimpleGraph V\nH : SimpleGraph W\nn : ℕ\nhG : G.chromaticNumber ≤ ↑n\nhH : H.chromaticNumber ≤ ↑n\n⊢ (G ⊕g H).chromaticNumber ≤ ↑n",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"ENat.instNatCast",
"SimpleGraph... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 42
} | {
"line": 577,
"column": 43
} | [
{
"pp": "case inr.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBe... | [
"case inr.inr.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 520,
"column": 61
} | {
"line": 520,
"column": 92
} | {
"line": 520,
"column": 93
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v : V\np : G.Walk u v\ns : Finset V\nh✝ : {x ∈ s | x ∈ p.support}.Nonempty\nx : V\nhxs : x ∈ s\nhx : x ∈ p.support\nh : {t ∈ s.erase x | t ∈ (p.takeUntil x hx).support} = ∅\nthis : {t ∈ s | t ∈ (p.takeUntil x hx).support} ⊆ {x}\n⊢ ∀ t ∈ s, t ∈ (p.... | [
"V : Type u\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v : V\np : G.Walk u v\ns : Finset V\nh✝ : {x ∈ s | x ∈ p.support}.Nonempty\nx : V\nhxs : x ∈ s\nhx : x ∈ p.support\nh : {t ∈ s.erase x | t ∈ (p.takeUntil x hx).support} = ∅\nthis : {t ∈ s | t ∈ (p.takeUntil x hx).support} ⊆ {x}\n⊢ ∀ t ∈ s, t ∈ (p.takeUntil x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 579,
"column": 6
} | {
"line": 579,
"column": 17
} | {
"line": 579,
"column": 18
} | [
{
"pp": "case refine_1.inl.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompl... | [
"case refine_1.inl.inl\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Hasse | {
"line": 131,
"column": 22
} | {
"line": 133,
"column": 24
} | {
"line": 135,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nV : Type u_3\ninst✝ : DecidableEq V\nG : SimpleGraph V\nu v : V\nw : G.Walk u v\na b : Fin (w.length + 1)\nh : (pathGraph (w.length + 1)).Adj a b\n⊢ w.toSubgraph.coe.Adj ⟨w.support[a], ⋯⟩ ⟨w.support[b], ⋯⟩",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [... | [] | by
grind [support_getElem_eq_getVert, Subgraph.coe_adj, pathGraph_adj, toSubgraph_adj_getVert,
Subgraph.Adj.symm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 581,
"column": 57
} | {
"line": 581,
"column": 68
} | {
"line": 581,
"column": 69
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right... | [
"V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right\nleft right... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 659,
"column": 4
} | {
"line": 659,
"column": 75
} | {
"line": 660,
"column": 4
} | [
{
"pp": "case refine_2.patches\nV : Type u\nG : SimpleGraph V\nGpc : G.Preconnected\nt : Finset V\nu : V\nut : u ∈ t\nv : V\nhv : v ∈ ↑(t.biUnion fun v ↦ (Nonempty.some ⋯).support.toFinset)\n⊢ ∃ s' ⊆ ↑(t.biUnion fun v ↦ (Nonempty.some ⋯).support.toFinset),\n ∃ (hu' : u ∈ s') (hv' : v ∈ s'), (induce s' G).Rea... | [
"case refine_2.patches\nV : Type u\nG : SimpleGraph V\nGpc : G.Preconnected\nt : Finset V\nu : V\nut : u ∈ t\nv : V\nhv : ∃ a ∈ t, v ∈ (Nonempty.some ⋯).support\n⊢ ∃ s' ⊆ ↑(t.biUnion fun v ↦ (Nonempty.some ⋯).support.toFinset),\n ∃ (hu' : u ∈ s') (hv' : v ∈ s'), (induce s' G).Reachable ⟨u, hu'⟩ ⟨v, hv'⟩"
] | simp only [Finset.mem_coe, Finset.mem_biUnion, List.mem_toFinset] at hv | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 583,
"column": 58
} | {
"line": 583,
"column": 69
} | {
"line": 583,
"column": 70
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right... | [
"V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right\nleft right... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.CycleGraph | {
"line": 192,
"column": 8
} | {
"line": 192,
"column": 98
} | {
"line": 193,
"column": 8
} | [
{
"pp": "case inr\nV✝ : Type u_1\nG✝ : SimpleGraph V✝\nV : Type u_1\nG : SimpleGraph V\nn : ℕ\nhn : 2 < n\na : V\np : G.Walk a a\nhp₁ : p.IsCycle\nhp₂ : p.length = n\nx : ℕ\nhx : x < n\ny : ℕ\nhy : y < n\nhab✝ : (cycleGraph n).Adj ⟨x, hx⟩ ⟨y, hy⟩\nhne : x ≠ y\nhle : x > y\nhab : n + ↑⟨y, hy⟩ - ↑⟨x, hx⟩ = 1\n⊢ G... | [
"case inr\nV✝ : Type u_1\nG✝ : SimpleGraph V✝\nV : Type u_1\nG : SimpleGraph V\nn : ℕ\nhn : 2 < n\na : V\np : G.Walk a a\nhp₁ : p.IsCycle\nhp₂ : p.length = n\nx : ℕ\nhx : x < n\ny : ℕ\nhy : y < n\nhab✝ : (cycleGraph n).Adj ⟨x, hx⟩ ⟨y, hy⟩\nhne : x ≠ y\nhle : x > y\nhab : n + ↑⟨y, hy⟩ - ↑⟨x, hx⟩ = 1\n⊢ G.Adj p.suppo... | simp_rw [show x = n - 1 by lia, show y = 0 by lia, Fin.succ_mk, show n - 1 + 1 = n by lia] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 703,
"column": 18
} | {
"line": 703,
"column": 23
} | {
"line": 703,
"column": 23
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nG' : G.Subgraph\nG'' : G'.coe.Subgraph\nf : G'.coe →g G\nhpreconn : G''.Preconnected\nu' : V\nu : ↑G'.verts\nhu : u ∈ G''.verts\nhfu : f u = u'\nv' : V\nv : ↑G'.verts\nhv : v ∈ G''.verts\nhfv : f v = v'\n⊢ (Subgraph.map f G'').coe.Reachable ⟨f u, ⋯⟩ ⟨v', ⋯⟩",
"ppTerm"... | [
"V : Type u\nG : SimpleGraph V\nG' : G.Subgraph\nG'' : G'.coe.Subgraph\nf : G'.coe →g G\nhpreconn : G''.Preconnected\nu' : V\nu : ↑G'.verts\nhu : u ∈ G''.verts\nhfu : f u = u'\nv' : V\nv : ↑G'.verts\nhv : v ∈ G''.verts\nhfv : f v = v'\n⊢ (Subgraph.map f G'').coe.Reachable ⟨f u, ⋯⟩ ⟨f v, ⋯⟩"
] | ← hfv | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 587,
"column": 8
} | {
"line": 587,
"column": 19
} | {
"line": 587,
"column": 20
} | [
{
"pp": "case refine_1.inl.inr.refine_3\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCove... | [
"case refine_1.inl.inr.refine_3\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsComplete... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 589,
"column": 57
} | {
"line": 589,
"column": 68
} | {
"line": 589,
"column": 69
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right... | [
"V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right\nleft right... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 591,
"column": 58
} | {
"line": 591,
"column": 69
} | {
"line": 591,
"column": 70
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right... | [
"V : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑left ↑right\nleft right... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 595,
"column": 8
} | {
"line": 595,
"column": 19
} | {
"line": 595,
"column": 20
} | [
{
"pp": "case refine_1.inr.inl.refine_3\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCove... | [
"case refine_1.inr.inl.refine_3\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsComplete... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 596,
"column": 6
} | {
"line": 596,
"column": 17
} | {
"line": 596,
"column": 18
} | [
{
"pp": "case refine_1.inr.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompl... | [
"case refine_1.inr.inr\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ :\n ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.bipartiteDoubleCover.IsCompleteBetween ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 603,
"column": 4
} | {
"line": 603,
"column": 28
} | {
"line": 603,
"column": 29
} | [
{
"pp": "case refine_2\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ : ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.IsCompleteBetween ↑left ↑right\nleft ri... | [
"case refine_2\nV : Type u_1\nG : SimpleGraph V\nα : Type u_2\nβ : Type u_3\ninst✝³ : Finite α\ninst✝² : Finite β\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nthis✝ : Fintype α\nthis : Fintype β\nx✝ : ∃ left right, #left = Fintype.card α ∧ #right = Fintype.card β ∧ G.IsCompleteBetween ↑left ↑right\nleft right : Finset... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Cayley | {
"line": 127,
"column": 2
} | {
"line": 128,
"column": 27
} | {
"line": 130,
"column": 0
} | [
{
"pp": "M : Type u_1\ns : Set M\ninst✝ : Group M\nu v : M\n⊢ (mulCayley s).Adj u v ↔ u ≠ v ∧ (u⁻¹ * v ∈ s ∨ v⁻¹ * u ∈ s)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"and_true",
"Monoid.toMulOneClass",
"congrAr... | [] | simp [mulCayley_adj', ← eq_inv_mul_iff_mul_eq (b := u), ← inv_mul_eq_iff_eq_mul (a := v),
and_or_left, exists_or] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Cayley | {
"line": 127,
"column": 2
} | {
"line": 128,
"column": 27
} | {
"line": 130,
"column": 0
} | [
{
"pp": "M : Type u_1\ns : Set M\ninst✝ : Group M\nu v : M\n⊢ (mulCayley s).Adj u v ↔ u ≠ v ∧ (u⁻¹ * v ∈ s ∨ v⁻¹ * u ∈ s)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"and_true",
"Monoid.toMulOneClass",
"congrAr... | [] | simp [mulCayley_adj', ← eq_inv_mul_iff_mul_eq (b := u), ← inv_mul_eq_iff_eq_mul (a := v),
and_or_left, exists_or] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Cayley | {
"line": 127,
"column": 2
} | {
"line": 128,
"column": 27
} | {
"line": 130,
"column": 0
} | [
{
"pp": "M : Type u_1\ns : Set M\ninst✝ : Group M\nu v : M\n⊢ (mulCayley s).Adj u v ↔ u ≠ v ∧ (u⁻¹ * v ∈ s ∨ v⁻¹ * u ∈ s)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"and_true",
"Monoid.toMulOneClass",
"congrAr... | [] | simp [mulCayley_adj', ← eq_inv_mul_iff_mul_eq (b := u), ← inv_mul_eq_iff_eq_mul (a := v),
and_or_left, exists_or] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic | {
"line": 53,
"column": 14
} | {
"line": 53,
"column": 25
} | {
"line": 53,
"column": 26
} | [
{
"pp": "V : Type u_1\ninst✝ : Fintype V\np : SimpleGraph V → Prop\nx✝ : ∃ G, p G\nG : SimpleGraph V\nhp : p G\n⊢ G ∈ {G | p G}",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"instFintypeSimpleGraphOfDecidableEq",
"Eq.mpr",
"Finset.mem_filter._simp_1",
"Finset.univ... | [
"V : Type u_1\ninst✝ : Fintype V\np : SimpleGraph V → Prop\nx✝ : ∃ G, p G\nG : SimpleGraph V\nhp : p G\n⊢ p G"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic | {
"line": 55,
"column": 12
} | {
"line": 55,
"column": 23
} | {
"line": 55,
"column": 24
} | [
{
"pp": "V : Type u_1\ninst✝ : Fintype V\np : SimpleGraph V → Prop\nx✝ : ∃ G, p G\nG : SimpleGraph V\nhp : p G\nG' : SimpleGraph V\nhp' : G' ∈ {G | p G}\nh : ∀ x' ∈ {G | p G}, #x'.edgeFinset ≤ #G'.edgeFinset\n⊢ p G'",
"ppTerm": "?m.133",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"V : Type u_1\ninst✝ : Fintype V\np : SimpleGraph V → Prop\nx✝ : ∃ G, p G\nG : SimpleGraph V\nhp : p G\nG' : SimpleGraph V\nhp' : G' ∈ {G | p G}\nh : ∀ x' ∈ {G | p G}, #x'.edgeFinset ≤ #G'.edgeFinset\n⊢ p G'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic | {
"line": 55,
"column": 62
} | {
"line": 55,
"column": 73
} | {
"line": 55,
"column": 74
} | [
{
"pp": "V : Type u_1\ninst✝ : Fintype V\np : SimpleGraph V → Prop\nx✝² : ∃ G, p G\nG : SimpleGraph V\nhp✝ : p G\nG' : SimpleGraph V\nhp' : G' ∈ {G | p G}\nh : ∀ x' ∈ {G | p G}, #x'.edgeFinset ≤ #G'.edgeFinset\nx✝¹ : SimpleGraph V\nx✝ : DecidableRel x✝¹.Adj\nhp : p x✝¹\n⊢ ?m.149 ∈ {G | p G}",
"ppTerm": "?m.... | [
"V : Type u_1\ninst✝ : Fintype V\np : SimpleGraph V → Prop\nx✝² : ∃ G, p G\nG : SimpleGraph V\nhp✝ : p G\nG' : SimpleGraph V\nhp' : G' ∈ {G | p G}\nh : ∀ x' ∈ {G | p G}, #x'.edgeFinset ≤ #G'.edgeFinset\nx✝¹ : SimpleGraph V\nx✝ : DecidableRel x✝¹.Adj\nhp : p x✝¹\n⊢ p ?m.149"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 15
} | {
"line": 96,
"column": 16
} | [
{
"pp": "n : ℕ\nV : Type u_1\nW : Type u_2\nH : SimpleGraph W\ninst✝ : Fintype V\nhc : Fintype.card V = n\ne : Fin n ≃ V\nG : SimpleGraph (Fin n)\nh : G ∈ {G | H.Free G}\n⊢ SimpleGraph.map (⇑e) G ∈ univ ∧ H.Free G",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"instFintypeSimpleGrap... | [
"n : ℕ\nV : Type u_1\nW : Type u_2\nH : SimpleGraph W\ninst✝ : Fintype V\nhc : Fintype.card V = n\ne : Fin n ≃ V\nG : SimpleGraph (Fin n)\nh : G ∈ {G | H.Free G}\n⊢ IsEmpty (H.Copy G)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 15
} | {
"line": 96,
"column": 16
} | [
{
"pp": "n : ℕ\nV : Type u_1\nW : Type u_2\nH : SimpleGraph W\ninst✝ : Fintype V\nhc : Fintype.card V = n\ne : V ≃ Fin n := Fintype.equivFinOfCardEq hc\nG : SimpleGraph V\nh : G ∈ {G | H.Free G}\n⊢ SimpleGraph.map (⇑e) G ∈ univ ∧ H.Free G",
"ppTerm": "?m.339",
"assigned": true,
"usedConstants": [
... | [
"n : ℕ\nV : Type u_1\nW : Type u_2\nH : SimpleGraph W\ninst✝ : Fintype V\nhc : Fintype.card V = n\ne : V ≃ Fin n := Fintype.equivFinOfCardEq hc\nG : SimpleGraph V\nh : G ∈ {G | H.Free G}\n⊢ IsEmpty (H.Copy G)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic | {
"line": 106,
"column": 64
} | {
"line": 106,
"column": 75
} | {
"line": 106,
"column": 76
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nh : H.Free G\n⊢ G ∈ {G | H.Free G}",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"SimpleGraph.Free",
"Eq.mpr",
"Finset.mem_filter._simp_1",
"... | [
"V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nh : H.Free G\n⊢ IsEmpty (H.Copy G)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 15
} | {
"line": 116,
"column": 16
} | [
{
"pp": "case cons\nV : Type u_1\nHs : Set (SimpleGraph V)\nhHs : Hs.Nonempty\nh_dir : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) Hs\nu✝ v✝ u v w : V\np : (sSup Hs).Walk v w\nH₁ : SimpleGraph V\nhH₁ : H₁ ∈ Hs\nih : ∀ e ∈ p.edges, e ∈ H₁.edgeSet\nH₂ : SimpleGraph V\nhH₂ : H₂ ∈ Hs\nh_adj : H₂.Adj u v\nH : SimpleGraph V\nhH... | [
"case cons\nV : Type u_1\nHs : Set (SimpleGraph V)\nhHs : Hs.Nonempty\nh_dir : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) Hs\nu✝ v✝ u v w : V\np : (sSup Hs).Walk v w\nH₁ : SimpleGraph V\nhH₁ : H₁ ∈ Hs\nih : ∀ e ∈ p.edges, e ∈ H₁.edgeSet\nH₂ : SimpleGraph V\nhH₂ : H₂ ∈ Hs\nh_adj : H₂.Adj u v\nH : SimpleGraph V\nhH : H ∈ Hs\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 217,
"column": 86
} | {
"line": 220,
"column": 7
} | {
"line": 222,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nh : G.IsAcyclic\nu v w : V\np : G.Walk u v\nhp : p.IsPath\nhadj : G.Adj v w\nhsupp : w ∈ p.support\n⊢ w = p.penultimate",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"List.mem_reverse._simp_1",
"Eq.mpr",
"congrArg",
"Simpl... | [] | by
rw [← snd_reverse]
apply h.eq_snd_of_adj_start hp.reverse hadj
simpa | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 289,
"column": 6
} | {
"line": 289,
"column": 73
} | {
"line": 290,
"column": 6
} | [
{
"pp": "case cons.inr\nV : Type u_1\nG : SimpleGraph V\nhG : G.IsAcyclic\nv w u' v' w✝ : V\nhead : G.Adj u' v'\ntail : G.Walk v' w✝\nih : List.IsChain (fun x1 x2 ↦ x1 ≠ x2) tail.edges → tail.IsPath\nh : List.IsChain (fun x1 x2 ↦ x1 ≠ x2) (cons head tail).edges\nhcc : (∀ y ∈ tail.edges.head?, s(u', v') ≠ y) ∧ L... | [
"case cons.inr\nV : Type u_1\nG : SimpleGraph V\nhG : G.IsAcyclic\nv w u' v' w✝ : V\nhead : G.Adj u' v'\ntail : G.Walk v' w✝\nih : List.IsChain (fun x1 x2 ↦ x1 ≠ x2) tail.edges → tail.IsPath\nh : List.IsChain (fun x1 x2 ↦ x1 ≠ x2) (cons head tail).edges\nhcc : (∀ y ∈ tail.edges.head?, s(u', v') ≠ y) ∧ List.IsChain ... | have := IsPath.mk' this |>.eq_snd_of_mem_edges (Sym2.eq_swap ▸ hhh) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 100,
"column": 4
} | {
"line": 101,
"column": 42
} | {
"line": 101,
"column": 43
} | [
{
"pp": "V : Type u_1\ninst✝¹ : Fintype V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nK : Finset V\nleft✝ : K ⊆ univ\nhn : #K ≤ Fintype.card V\nhG : G.IsTuranMaximal #K\nh : G.CliqueFree #K\n⊢ ∃ a ∈ K, ∃ b ∈ K, a ≠ b ∧ ¬G.Adj a b",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"F... | [
"V : Type u_1\ninst✝¹ : Fintype V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nK : Finset V\nleft✝ : K ⊆ univ\nhn : #K ≤ Fintype.card V\nhG : G.IsTuranMaximal #K\nh : G.CliqueFree #K\n⊢ ∃ a ∈ K, ∃ b ∈ K, ¬a = b ∧ ¬G.Adj a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 308,
"column": 41
} | {
"line": 308,
"column": 52
} | {
"line": 308,
"column": 53
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (fun p ↦ p.Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 60
} | {
"line": 107,
"column": 61
} | [
{
"pp": "V : Type u_1\ninst✝ : Fintype V\nr : ℕ\nhr : 0 < r\n⊢ ∃ H x, H.IsTuranMaximal r",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Adj",
"DecidableRel",
"Exists",
"id",
"instOfNatNat",
"_private.Mathlib.Combinatorics.Si... | [
"V : Type u_1\ninst✝ : Fintype V\nr : ℕ\nhr : 0 < r\n⊢ ∃ x, x.CliqueFree (r + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 317,
"column": 54
} | {
"line": 317,
"column": 65
} | {
"line": 317,
"column": 66
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (fun p ↦ p.Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 321,
"column": 49
} | {
"line": 321,
"column": 60
} | {
"line": 321,
"column": 61
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (fun p ↦ p.Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 329,
"column": 4
} | {
"line": 330,
"column": 45
} | {
"line": 331,
"column": 4
} | [
{
"pp": "case inr\nV : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝¹ : Nonempty V\ninhabited_h : Inhabited V\nthis✝ : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (fun p ↦ p.Is... | · rw [Sym2.eq_swap]
exact this y x h.symm (le_of_not_ge h') | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 334,
"column": 56
} | {
"line": 334,
"column": 67
} | {
"line": 334,
"column": 68
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : Fintype ↑G.edgeSet\nhG : G.IsTree\nthis✝ : Nonempty V\ninhabited_h : Inhabited V\nthis : {default}ᶜ.card + 1 = Fintype.card V\nf : (x : V) → G.Walk x default\nhf : ∀ (x : V), (fun p ↦ p.IsPath) (f x)\nhf' : ∀ (x : V) (y : G.Walk x default), (fun p ↦ p.Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 214,
"column": 31
} | {
"line": 214,
"column": 42
} | {
"line": 214,
"column": 43
} | [
{
"pp": "V : Type u_1\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\nr : ℕ\nh : G.IsTuranMaximal r\ninst✝ : DecidableEq V\nfp : Finpartition univ := h.finpartition\nlarge : Finset V\nhl : large ∈ fp.parts\nsmall : Finset V\nhs : small ∈ fp.parts\nineq : #small + 1 < #large\nw : V\nhw : w ∈... | [
"V : Type u_1\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\nr : ℕ\nh : G.IsTuranMaximal r\ninst✝ : DecidableEq V\nfp : Finpartition univ := h.finpartition\nlarge : Finset V\nhl : large ∈ fp.parts\nsmall : Finset V\nhs : small ∈ fp.parts\nineq : #small + 1 < #large\nw : V\nhw : w ∈ large\nv : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 386,
"column": 67
} | {
"line": 386,
"column": 77
} | {
"line": 386,
"column": 77
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nu v : V\nhuv : ¬u = v\nhadj : ¬G.Adj u v\nhacyc : (G ⊔ edge u v).IsAcyclic\nhreach : G.Reachable u v\n⊢ s(u, v) ∈ (G ⊔ edge u v).edgeSet",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"False",
"SimpleGraph.edge",
"eq_false",
... | [] | simp [huv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 386,
"column": 67
} | {
"line": 386,
"column": 77
} | {
"line": 386,
"column": 77
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nu v : V\nhuv : ¬u = v\nhadj : ¬G.Adj u v\nhacyc : (G ⊔ edge u v).IsAcyclic\nhreach : G.Reachable u v\n⊢ s(u, v) ∈ (G ⊔ edge u v).edgeSet",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"False",
"SimpleGraph.edge",
"eq_false",
... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 386,
"column": 67
} | {
"line": 386,
"column": 77
} | {
"line": 386,
"column": 77
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nu v : V\nhuv : ¬u = v\nhadj : ¬G.Adj u v\nhacyc : (G ⊔ edge u v).IsAcyclic\nhreach : G.Reachable u v\n⊢ s(u, v) ∈ (G ⊔ edge u v).edgeSet",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"False",
"SimpleGraph.edge",
"eq_false",
... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling | {
"line": 202,
"column": 56
} | {
"line": 202,
"column": 79
} | {
"line": 202,
"column": 80
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nx y : V\n⊢ (EdgeLabeling.labelGraph G.toTopEdgeLabeling 1).Adj x y ↔ G.Adj x y",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Iff.of_eq",
"congrArg",
"SimpleGraph.Adj",
... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nx y : V\n⊢ G.Adj x y → ¬x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 417,
"column": 57
} | {
"line": 417,
"column": 68
} | {
"line": 417,
"column": 69
} | [
{
"pp": "V : Type u_1\nG F : SimpleGraph V\nhle : F ≤ G\nhF : F.IsAcyclic\nh : F.Reachable = G.Reachable\nthis : ¬Maximal (fun F ↦ F ≤ G ∧ F.IsAcyclic) F\nH : SimpleGraph V\nhFH : F < H\nhHG : H ≤ G\nhH : H.IsAcyclic\ne : Sym2 V\nheH : e ∈ H.edgeSet\nheF : e ∉ F.edgeSet\nh_bridge : (F ⊔ fromEdgeSet {e}).IsBridg... | [
"V : Type u_1\nG F : SimpleGraph V\nhle : F ≤ G\nhF : F.IsAcyclic\nh : F.Reachable = G.Reachable\nthis : ¬Maximal (fun F ↦ F ≤ G ∧ F.IsAcyclic) F\nH : SimpleGraph V\nhFH : F < H\nhHG : H ≤ G\nhH : H.IsAcyclic\ne : Sym2 V\nheH : e ∈ H.edgeSet\nheF : e ∉ F.edgeSet\nh_bridge : (F ⊔ fromEdgeSet {e}).IsBridge e\n⊢ e ∉ F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 484,
"column": 35
} | {
"line": 484,
"column": 59
} | {
"line": 484,
"column": 60
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nthis : Fintype V\nh : G.IsTree\n⊢ Nat.card ↑G.edgeSet + 1 = Nat.card V",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fintype.card_ofFinset",
"SimpleGraph.decidableMemEdgeSet",
"Finset.univ",
... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nthis : Fintype V\nh : G.IsTree\n⊢ (Finset.filter (Membership.mem G.edgeSet) Finset.univ).card + 1 = Fintype.card V"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Acyclic | {
"line": 486,
"column": 2
} | {
"line": 486,
"column": 45
} | {
"line": 487,
"column": 2
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nthis : Fintype V\nx✝ : G.Connected ∧ Nat.card ↑G.edgeSet + 1 = Nat.card V\nh₁ : G.Connected\nh₂ : Nat.card ↑G.edgeSet + 1 = Nat.card V\n⊢ G.IsAcyclic",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Sym2.mk",... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nthis : Fintype V\nx✝ : G.Connected ∧ Nat.card ↑G.edgeSet + 1 = Nat.card V\nh₁ : G.Connected\nh₂ : Nat.card ↑G.edgeSet + 1 = Nat.card V\n⊢ ∀ ⦃v w : V⦄, G.Adj v w → G.IsBridge s(v, w)"
] | simp_rw [isAcyclic_iff_forall_adj_isBridge] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite | {
"line": 78,
"column": 28
} | {
"line": 78,
"column": 39
} | {
"line": 78,
"column": 40
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ninst✝⁴ : DecidableEq V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\nG' : SimpleGraph V\nh : G ≤ G'\nc' : G'.ConnectedComponent\ninst✝¹ : Fintype ↑c'.supp\ninst✝ : DecidablePred fun c ↦ c.supp ⊆ c'.supp\nx : G.ConnectedComponent\nx✝¹ : x ∈ ↑{c | c.supp ⊆ c'.supp}\ny :... | [
"V : Type u\nG : SimpleGraph V\ninst✝⁴ : DecidableEq V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\nG' : SimpleGraph V\nh : G ≤ G'\nc' : G'.ConnectedComponent\ninst✝¹ : Fintype ↑c'.supp\ninst✝ : DecidablePred fun c ↦ c.supp ⊆ c'.supp\nx : G.ConnectedComponent\nx✝¹ : x ∈ ↑{c | c.supp ⊆ c'.supp}\ny : G.Connected... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite | {
"line": 80,
"column": 29
} | {
"line": 80,
"column": 40
} | {
"line": 80,
"column": 41
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ninst✝⁴ : DecidableEq V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\nG' : SimpleGraph V\nh : G ≤ G'\nc' : G'.ConnectedComponent\ninst✝¹ : Fintype ↑c'.supp\ninst✝ : DecidablePred fun c ↦ c.supp ⊆ c'.supp\n⊢ ↑({c | c.supp ⊆ c'.supp}.disjiUnion (fun c ↦ c.supp.toFinset) ... | [
"V : Type u\nG : SimpleGraph V\ninst✝⁴ : DecidableEq V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\nG' : SimpleGraph V\nh : G ≤ G'\nc' : G'.ConnectedComponent\ninst✝¹ : Fintype ↑c'.supp\ninst✝ : DecidablePred fun c ↦ c.supp ⊆ c'.supp\n⊢ ⋃ x, ⋃ (_ : x.supp ⊆ c'.supp), x.supp = c'.supp"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 278,
"column": 2
} | {
"line": 279,
"column": 60
} | {
"line": 281,
"column": 0
} | [
{
"pp": "V : Type u_1\ninst✝¹ : Fintype V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nn r : ℕ\nf : G ≃g turanGraph n r\nhr : 0 < r\nJ : SimpleGraph V\nw✝ : DecidableRel J.Adj\nj : J.IsTuranMaximal r\ng : J ≃g turanGraph n r\n⊢ G.IsTuranMaximal r",
"ppTerm": "?m.62",
"assigned": true,
"usedConsta... | [] | use (turanGraph_cliqueFree (n := n) hr).comap f.isContained,
fun H _ cf ↦ (f.symm.comp g).card_edgeFinset_eq ▸ j.2 cf | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 329,
"column": 4
} | {
"line": 329,
"column": 33
} | {
"line": 329,
"column": 34
} | [
{
"pp": "α : Type u\nG : SimpleGraph α\ninst✝ : Fintype α\nn : ℕ\nC : G.Coloring (Fin n)\nt : ℕ\nh : ∀ (c : Fin n), Fintype.card ↑(C.colorClass c) ≤ t\nthis : ∀ (c : Fin n), Nonempty (↑(C.colorClass c) ↪ Fin t)\nF : (c : Fin n) → ↑(C.colorClass c) ↪ Fin t\nc₁ c₂ : Fin n\nv₁ : ↑(C.colorClass c₁)\nv₂ : ↑(C.colorC... | [
"α : Type u\nG : SimpleGraph α\ninst✝ : Fintype α\nn : ℕ\nC : G.Coloring (Fin n)\nt : ℕ\nh : ∀ (c : Fin n), Fintype.card ↑(C.colorClass c) ≤ t\nthis : ∀ (c : Fin n), Nonempty (↑(C.colorClass c) ↪ Fin t)\nF : (c : Fin n) → ↑(C.colorClass c) ↪ Fin t\nc₁ c₂ : Fin n\nv₁ : ↑(C.colorClass c₁)\nv₂ : ↑(C.colorClass c₂)\nhc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents | {
"line": 42,
"column": 4
} | {
"line": 44,
"column": 9
} | {
"line": 44,
"column": 9
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nC : Set G.ConnectedComponent\n⊢ Set.InjOn G.connectedComponentMk (Quot.out '' C)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SimpleGraph.connectedComponentMk",
"Quot.out",
"congrArg",
"Quot.out_eq",
"Membership.mem"... | [] | rintro x ⟨c, ⟨hc, rfl⟩⟩ y ⟨d, ⟨hd, rfl⟩⟩ hxy
simp only [connectedComponentMk] at hxy
aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents | {
"line": 42,
"column": 4
} | {
"line": 44,
"column": 9
} | {
"line": 44,
"column": 9
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nC : Set G.ConnectedComponent\n⊢ Set.InjOn G.connectedComponentMk (Quot.out '' C)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SimpleGraph.connectedComponentMk",
"Quot.out",
"congrArg",
"Quot.out_eq",
"Membership.mem"... | [] | rintro x ⟨c, ⟨hc, rfl⟩⟩ y ⟨d, ⟨hd, rfl⟩⟩ hxy
simp only [connectedComponentMk] at hxy
aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents | {
"line": 87,
"column": 10
} | {
"line": 87,
"column": 76
} | {
"line": 87,
"column": 77
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ns : Set V\nK : G.ConnectedComponent\nhrep : Represents s G.oddComponents\nh : Even K.supp.ncard\n⊢ ?m.31 ∉ G.oddComponents",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"SimpleGraph.oddComponents",
"Membership.mem",
"id",
"S... | [
"V : Type u\nG : SimpleGraph V\ns : Set V\nK : G.ConnectedComponent\nhrep : Represents s G.oddComponents\nh : Even K.supp.ncard\n⊢ ¬Odd (supp ?m.31).ncard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents | {
"line": 86,
"column": 4
} | {
"line": 87,
"column": 86
} | {
"line": 87,
"column": 87
} | [
{
"pp": "case pos\nV : Type u\nG : SimpleGraph V\ns : Set V\nK : G.ConnectedComponent\nhrep : Represents s G.oddComponents\nh : Even K.supp.ncard\n⊢ Even (K.supp \\ s).ncard",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Combinator... | [
"case pos\nV : Type u\nG : SimpleGraph V\ns : Set V\nK : G.ConnectedComponent\nhrep : Represents s G.oddComponents\nh : Even K.supp.ncard\n⊢ Even K.supp.ncard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 381,
"column": 18
} | {
"line": 381,
"column": 34
} | {
"line": 381,
"column": 35
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nr t : ℕ\nK : G.CompleteEquipartiteSubgraph r t\n⊢ #(K.parts.disjiUnion id ⋯) = r * t",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"SimpleGraph.CompleteEquipartiteSubgraph.disjoint",
... | [
"V : Type u_1\nG : SimpleGraph V\nr t : ℕ\nK : G.CompleteEquipartiteSubgraph r t\n⊢ ∑ a ∈ K.parts, #(id a) = r * t"
] | card_disjiUnion, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Represents | {
"line": 90,
"column": 4
} | {
"line": 90,
"column": 30
} | {
"line": 90,
"column": 31
} | [
{
"pp": "case neg\nV : Type u\nG : SimpleGraph V\ns : Set V\nK : G.ConnectedComponent\nhrep : Represents s G.oddComponents\nh : ¬Even K.supp.ncard\nthis : K.supp.ncard ≠ 0\n⊢ Even K.supp.ncard ↔ Even 1",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Nat.not_even_iff_odd._simp_1",
... | [
"case neg\nV : Type u\nG : SimpleGraph V\ns : Set V\nK : G.ConnectedComponent\nhrep : Represents s G.oddComponents\nh : ¬Even K.supp.ncard\nthis : K.supp.ncard ≠ 0\n⊢ Odd K.supp.ncard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 41
} | {
"line": 63,
"column": 42
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\ninst✝ : Subsingleton α\nu : α\n⊢ G.eccent u = 0",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"SimpleGraph.edist_eq_zero_iff._simp_1",
"Eq.mpr",
"instCompleteLinearOrderENat",
"CommSemiring.toSemiring",
"iSup",
... | [
"α : Type u_1\nG : SimpleGraph α\ninst✝ : Subsingleton α\nu : α\n⊢ ∀ (i : α), u = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.