module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 573,
"column": 31
} | {
"line": 573,
"column": 50
} | {
"line": 573,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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 h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Sum | {
"line": 236,
"column": 23
} | {
"line": 236,
"column": 61
} | {
"line": 236,
"column": 61
} | [
{
"pp": "V : Type u_3\nW : Type u_5\nG : SimpleGraph V\nH : SimpleGraph W\nn : ℕ\nx✝ : G.Colorable n ∧ H.Colorable n\ncG : G.Colorable n\ncH : H.Colorable n\n⊢ (G ⊕g H).Colorable n",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Nat.max_self",
"Eq.mpr",
"congrArg",
... | [] | rw [← n.max_self]; exact cG.sum_max cH | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Sum | {
"line": 236,
"column": 23
} | {
"line": 236,
"column": 61
} | {
"line": 236,
"column": 61
} | [
{
"pp": "V : Type u_3\nW : Type u_5\nG : SimpleGraph V\nH : SimpleGraph W\nn : ℕ\nx✝ : G.Colorable n ∧ H.Colorable n\ncG : G.Colorable n\ncH : H.Colorable n\n⊢ (G ⊕g H).Colorable n",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Nat.max_self",
"Eq.mpr",
"congrArg",
... | [] | rw [← n.max_self]; exact cG.sum_max cH | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 577,
"column": 31
} | {
"line": 577,
"column": 50
} | {
"line": 577,
"column": 51
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 579,
"column": 6
} | {
"line": 579,
"column": 25
} | {
"line": 580,
"column": 4
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 579,
"column": 6
} | {
"line": 579,
"column": 25
} | {
"line": 580,
"column": 4
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 579,
"column": 6
} | {
"line": 579,
"column": 25
} | {
"line": 580,
"column": 4
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | {
"line": 592,
"column": 2
} | {
"line": 592,
"column": 59
} | {
"line": 594,
"column": 0
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ns t : Set V\nsconn : (⊤.induce s).Preconnected\ntconn : (⊤.induce t).Preconnected\nsintert : (s ∩ t).Nonempty\n⊢ (⊤.induce (s ∪ t)).Connected",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph",
"SimpleGraph.Subgraph.in... | [] | exact Subgraph.induce_union_connected sconn tconn sintert | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 596,
"column": 6
} | {
"line": 596,
"column": 25
} | {
"line": 597,
"column": 2
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 596,
"column": 6
} | {
"line": 596,
"column": 25
} | {
"line": 597,
"column": 2
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Bipartite | {
"line": 596,
"column": 6
} | {
"line": 596,
"column": 25
} | {
"line": 597,
"column": 2
} | [
{
"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... | [] | simpa using h hl hr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.AdjMatrix | {
"line": 83,
"column": 2
} | {
"line": 84,
"column": 21
} | {
"line": 86,
"column": 0
} | [
{
"pp": "α : Type u_1\nV : Type u_2\nA : Matrix V V α\ninst✝¹ : Zero α\ninst✝ : One α\nh : A.IsAdjMatrix\n⊢ A.diag = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Matrix.diag",
"congrArg",
"Pi.instZero",
"Matrix.IsAdjMatrix.apply_diag",
"funext",
"T... | [] | ext
simp [h.apply_diag] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.AdjMatrix | {
"line": 83,
"column": 2
} | {
"line": 84,
"column": 21
} | {
"line": 86,
"column": 0
} | [
{
"pp": "α : Type u_1\nV : Type u_2\nA : Matrix V V α\ninst✝¹ : Zero α\ninst✝ : One α\nh : A.IsAdjMatrix\n⊢ A.diag = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Matrix.diag",
"congrArg",
"Pi.instZero",
"Matrix.IsAdjMatrix.apply_diag",
"funext",
"T... | [] | ext
simp [h.apply_diag] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 64
} | {
"line": 222,
"column": 4
} | [
{
"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\nl : r < #h.finpartition.parts\nz : Finset V\nhz : Set.BijOn h.finpartition.part ↑z ↑h.finpartition.parts\n⊢ ¬G.CliqueFree #z",
"ppTerm": "?m.62",
"assigned": t... | [
"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\nl : r < #h.finpartition.parts\nz : Finset V\nhz : Set.BijOn h.finpartition.part ↑z ↑h.finpartition.parts\nv : V\nhv : v ∈ ↑z\nw : V\nhw : w ∈ ↑z\nhn : v ≠ w\n⊢ G.Adj v w"
] | refine IsNClique.not_cliqueFree ⟨fun v hv w hw hn ↦ ?_, rfl⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 47
} | {
"line": 128,
"column": 4
} | [
{
"pp": "V : Type u_1\nV' : Type u_2\nG : SimpleGraph V\nG' : SimpleGraph V'\nK : Type u_3\nK' : Type u_4\nC : G.EdgeLabeling K\nf : (x y : V) → G.Adj x y → K\nf_symm : ∀ (x y : V) (H : G.Adj x y), f y x ⋯ = f x y H\ne : Sym2 V\na b : V\n⊢ f a b ≍ f b a",
"ppTerm": "?m.33",
"assigned": true,
"usedCo... | [
"V : Type u_1\nV' : Type u_2\nG : SimpleGraph V\nG' : SimpleGraph V'\nK : Type u_3\nK' : Type u_4\nC : G.EdgeLabeling K\nf : (x y : V) → G.Adj x y → K\nf_symm : ∀ (x y : V) (H : G.Adj x y), f y x ⋯ = f x y H\ne : Sym2 V\na b : V\n⊢ ∀ (a_1 : G.Adj a b) (a' : G.Adj b a), a_1 ≍ a' → f a b a_1 ≍ f b a a'"
] | apply Function.hfunext (by simp [adj_comm]) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 243,
"column": 4
} | {
"line": 244,
"column": 32
} | {
"line": 245,
"column": 2
} | [
{
"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\nl : #fp.parts < #univ ∧ #fp.parts < r\nx y : V\nhn : x ≠ y\nhe : fp.part x = fp.part y\nz : Finset V\nzc : #z = r\n⊢ ∃ x ∈ ↑z... | [] | exact exists_ne_map_eq_of_card_lt_of_maps_to (zc.symm ▸ l.2) fun a _ ↦
fp.part_mem.2 (mem_univ a) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 236,
"column": 4
} | {
"line": 239,
"column": 95
} | {
"line": 240,
"column": 2
} | [
{
"pp": "α : Type u\nG : SimpleGraph α\ns : Set α\nr t : ℕ\n⊢ Fin r × Fin t → Fin (r * t)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"add_lt_add_of_le_of_lt",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
... | [] | refine fun v ↦ ⟨v.2 * r + v.1, ?_⟩
conv_rhs =>
rw [← Nat.sub_one_add_one_eq_of_pos v.2.pos, Nat.mul_add_one, mul_comm r (t - 1)]
exact add_lt_add_of_le_of_lt (Nat.mul_le_mul_right r (Nat.le_pred_of_lt v.2.prop)) v.1.prop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 236,
"column": 4
} | {
"line": 239,
"column": 95
} | {
"line": 240,
"column": 2
} | [
{
"pp": "α : Type u\nG : SimpleGraph α\ns : Set α\nr t : ℕ\n⊢ Fin r × Fin t → Fin (r * t)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"add_lt_add_of_le_of_lt",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
... | [] | refine fun v ↦ ⟨v.2 * r + v.1, ?_⟩
conv_rhs =>
rw [← Nat.sub_one_add_one_eq_of_pos v.2.pos, Nat.mul_add_one, mul_comm r (t - 1)]
exact add_lt_add_of_le_of_lt (Nat.mul_le_mul_right r (Nat.le_pred_of_lt v.2.prop)) v.1.prop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 362,
"column": 36
} | {
"line": 362,
"column": 50
} | {
"line": 362,
"column": 51
} | [
{
"pp": "n r : ℕ\n| #(range n) * (r - 1)",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"instSubNat",
"instMulNat",
"instOfNatNat",
"Finset.range",
"instHSub",
... | [
"n r : ℕ\n| #(range n) • (r - 1)"
] | ← smul_eq_mul, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | {
"line": 366,
"column": 8
} | {
"line": 366,
"column": 22
} | {
"line": 366,
"column": 23
} | [
{
"pp": "case e_a.e_a\nn r : ℕ\n⊢ (∑ x ∈ range r, ∑ w ∈ range r, if (n + x) % r ≠ (n + w) % r then 1 else 0) = #(range r) * (r - 1)",
"ppTerm": "?e_a.e_a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableNot",
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
... | [
"case e_a.e_a\nn r : ℕ\n⊢ (∑ x ∈ range r, ∑ w ∈ range r, if (n + x) % r ≠ (n + w) % r then 1 else 0) = #(range r) • (r - 1)"
] | ← smul_eq_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 70
} | {
"line": 325,
"column": 0
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\ninst✝ : Nontrivial α\n⊢ G.diam = 1 ↔ G = ⊤",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"instAddMonoidWithOneENat",
"Nat.instOne",
"ENat.instNatCast",
"congrArg",
"Iff.rf... | [] | rw [diam, ENat.toNat_eq_iff one_ne_zero, Nat.cast_one, ediam_eq_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 70
} | {
"line": 325,
"column": 0
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\ninst✝ : Nontrivial α\n⊢ G.diam = 1 ↔ G = ⊤",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"instAddMonoidWithOneENat",
"Nat.instOne",
"ENat.instNatCast",
"congrArg",
"Iff.rf... | [] | rw [diam, ENat.toNat_eq_iff one_ne_zero, Nat.cast_one, ediam_eq_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 70
} | {
"line": 325,
"column": 0
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\ninst✝ : Nontrivial α\n⊢ G.diam = 1 ↔ G = ⊤",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"instAddMonoidWithOneENat",
"Nat.instOne",
"ENat.instNatCast",
"congrArg",
"Iff.rf... | [] | rw [diam, ENat.toNat_eq_iff one_ne_zero, Nat.cast_one, ediam_eq_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 450,
"column": 24
} | {
"line": 450,
"column": 27
} | {
"line": 450,
"column": 27
} | [
{
"pp": "case refine_2\nα : Type u_1\nG : SimpleGraph α\ninst✝ : Nonempty α\ne : ℕ∞\nh : ∀ (u : α), G.eccent u = e\nu : α\nhu : u ∈ Set.univ\n⊢ G.eccent u = G.radius",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"SimpleGraph.radius"... | [
"case refine_2\nα : Type u_1\nG : SimpleGraph α\ninst✝ : Nonempty α\ne : ℕ∞\nh : ∀ (u : α), G.eccent u = e\nu : α\nhu : u ∈ Set.univ\n⊢ e = G.radius"
] | h u | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 464,
"column": 4
} | {
"line": 465,
"column": 79
} | {
"line": 466,
"column": 4
} | [
{
"pp": "case pos\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nht : t = 0\nthis : ∀ (r' : ℕ), IsEmpty (Fin r' × Fin t)\nh_bot : ∀ (r' : ℕ), completeEquipartiteGraph r' t = ⊥\n⊢ completeEquipartiteGraph (r + 1) t ⊑ G ↔ ∃ K s, #s = t ∧ ∀ p ∈ K.parts, G.IsCompleteBetween ↑p ↑s",
"ppTerm": "?pos✝",
"assigned"... | [
"case pos\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nht : t = 0\nthis : ∀ (r' : ℕ), IsEmpty (Fin r' × Fin t)\nh_bot : ∀ (r' : ℕ), completeEquipartiteGraph r' t = ⊥\n⊢ ⊥ ⊑ G ↔ Nonempty (G.CompleteEquipartiteSubgraph r t)"
] | simp_rw [h_bot (r + 1), ht, Finset.card_eq_zero, exists_eq_left, IsCompleteBetween, mem_coe,
notMem_empty, IsEmpty.forall_iff, implies_true, exists_true_iff_nonempty] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 479,
"column": 6
} | {
"line": 479,
"column": 50
} | {
"line": 480,
"column": 6
} | [
{
"pp": "case neg.refine_1\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nht : ¬t = 0\nx✝ : Nonempty (G.CompleteEquipartiteSubgraph (r + 1) t)\nK' : G.CompleteEquipartiteSubgraph (r + 1) t\nparts : Finset (Finset V)\nhparts_sub : parts ⊆ K'.parts\nhparts_card : #parts = (#K'.parts).pred\nK : G.CompleteEquipartiteSu... | [
"case neg.refine_1\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nht : ¬t = 0\nx✝ : Nonempty (G.CompleteEquipartiteSubgraph (r + 1) t)\nK' : G.CompleteEquipartiteSubgraph (r + 1) t\nparts : Finset (Finset V)\nhparts_sub : parts ⊆ K'.parts\nhparts_card : #parts = (#K'.parts).pred\nK : G.CompleteEquipartiteSubgraph r t :... | have hs_mem : s ∈ K'.parts := by simp [← hs] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity | {
"line": 68,
"column": 13
} | {
"line": 68,
"column": 33
} | {
"line": 68,
"column": 34
} | [
{
"pp": "case hn\nW : Type u_1\nH : SimpleGraph W\nn : ℕ\nhn : n ≥ 2\nG : SimpleGraph (Fin (n + 1))\ninst✝ : DecidableRel G.Adj\nh : H.Free G\ne : Sym2 (Fin (n + 1))\nhe : e ∈ G.edgeFinset\n⊢ n - 1 ≤ ↑(#(bipartiteBelow (fun v e ↦ v ∉ e) univ e))",
"ppTerm": "?hn",
"assigned": true,
"usedConstants": ... | [
"case hn\nW : Type u_1\nH : SimpleGraph W\nn : ℕ\nhn : n ≥ 2\nG : SimpleGraph (Fin (n + 1))\ninst✝ : DecidableRel G.Adj\nh : H.Free G\ne : Sym2 (Fin (n + 1))\nhe : e ∈ G.edgeFinset\n⊢ n - 1 ≤ ↑(#(bipartiteBelow (fun v e ↦ v ∉ e.toFinset) univ e))"
] | ← Sym2.mem_toFinset, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 82,
"column": 8
} | {
"line": 82,
"column": 22
} | {
"line": 82,
"column": 23
} | [
{
"pp": "n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nv : Fin n\nht'_pos : 0 < t'\nhv : v ∈ K.vertsᶜ\np : Finset (Fin n)\nhp : p ∈ K.parts\nhs : ∀ (x : Finset (Fin n)), x ∉ powersetCard t p ∨ ∃ x_1 ∈ x, ¬G.Adj v x_1\n| #(K.parts \\ {p}) * t'",
... | [
"n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nv : Fin n\nht'_pos : 0 < t'\nhv : v ∈ K.vertsᶜ\np : Finset (Fin n)\nhp : p ∈ K.parts\nhs : ∀ (x : Finset (Fin n)), x ∉ powersetCard t p ∨ ∃ x_1 ∈ x, ¬G.Adj v x_1\n| #(K.parts \\ {p}) • t'"
] | ← smul_eq_mul, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.Combinatorics.SimpleGraph.IncMatrix | {
"line": 77,
"column": 59
} | {
"line": 78,
"column": 67
} | {
"line": 80,
"column": 0
} | [
{
"pp": "R : Type u_1\nα : Type u_2\nG : SimpleGraph α\ninst✝² : MulZeroOneClass R\ninst✝¹ : DecidableEq α\ninst✝ : DecidableRel G.Adj\na b : α\ne : Sym2 α\n⊢ incMatrix R G a e * incMatrix R G b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e",
"ppTerm": "?m.28",
"assigned": true,
"usedConst... | [] | by
simp [incMatrix_apply', Set.indicator_apply, ← ite_and, and_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 251,
"column": 16
} | {
"line": 251,
"column": 30
} | {
"line": 251,
"column": 31
} | [
{
"pp": "ε : ℝ\nhε : 0 < ε\nr t : ℕ\nhr_pos : 0 < r\nht_pos : 0 < t\nε' : ℝ := 1 / (↑(r - 1) * ↑r) + ε\nhε' : 0 < ε'\nt' : ℕ := ⌊↑t / (↑r * ε)⌋₊ + 1\nht_lt_rt'ε : ↑t < ↑r * ↑t' * ε\nht'_pos : 0 < t'\nN' : ℕ\nih :\n ∀ (b : ℕ),\n N' ≤ b →\n ∀ {G : SimpleGraph (Fin b)} [inst : DecidableRel G.Adj],\n ... | [
"ε : ℝ\nhε : 0 < ε\nr t : ℕ\nhr_pos : 0 < r\nht_pos : 0 < t\nε' : ℝ := 1 / (↑(r - 1) * ↑r) + ε\nhε' : 0 < ε'\nt' : ℕ := ⌊↑t / (↑r * ε)⌋₊ + 1\nht_lt_rt'ε : ↑t < ↑r * ↑t' * ε\nht'_pos : 0 < t'\nN' : ℕ\nih :\n ∀ (b : ℕ),\n N' ≤ b →\n ∀ {G : SimpleGraph (Fin b)} [inst : DecidableRel G.Adj],\n ↑G.minDegr... | mul_div_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 355,
"column": 2
} | {
"line": 355,
"column": 68
} | {
"line": 356,
"column": 2
} | [
{
"pp": "V : Type u_1\nG G' : SimpleGraph V\nh : G ≤ G'\nhmf : G'.IsMatchingFree\nx : G.Subgraph\nhc : x.IsPerfectMatching\nv : V\n⊢ v ∈ (Subgraph.map (Hom.ofLE h) x).verts",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"RelHom.instFunLike",
"congrArg",
"... | [
"V : Type u_1\nG G' : SimpleGraph V\nh : G ≤ G'\nhmf : G'.IsMatchingFree\nx : G.Subgraph\nhc : x.IsPerfectMatching\nv : V\n⊢ v ∈ x.verts"
] | simp only [Subgraph.map_verts, Hom.coe_ofLE, id_eq, Set.image_id'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.LapMatrix | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 57
} | {
"line": 226,
"column": 0
} | [
{
"pp": "V : Type u_1\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\n⊢ Fintype.card G.ConnectedComponent = finrank ℝ ↥(toLin' (lapMatrix ℝ G)).ker",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
... | [] | rw [Module.finrank_eq_card_basis G.lapMatrix_ker_basis] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.LapMatrix | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 57
} | {
"line": 226,
"column": 0
} | [
{
"pp": "V : Type u_1\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\n⊢ Fintype.card G.ConnectedComponent = finrank ℝ ↥(toLin' (lapMatrix ℝ G)).ker",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
... | [] | rw [Module.finrank_eq_card_basis G.lapMatrix_ker_basis] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.LapMatrix | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 57
} | {
"line": 226,
"column": 0
} | [
{
"pp": "V : Type u_1\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\n⊢ Fintype.card G.ConnectedComponent = finrank ℝ ↥(toLin' (lapMatrix ℝ G)).ker",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
... | [] | rw [Module.finrank_eq_card_basis G.lapMatrix_ker_basis] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Partition | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 10
} | {
"line": 97,
"column": 2
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nP : G.Partition\nv w : V\nh : G.Adj v w\n⊢ P.partOfVertex v ≠ P.partOfVertex w",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"SimpleGraph.Partition.partOfVertex",
"Eq",
"Set"
],
"usedFVars": [
"V",
"G",
"P... | [
"V : Type u\nG : SimpleGraph V\nP : G.Partition\nv w : V\nh : G.Adj v w\nhn : P.partOfVertex v = P.partOfVertex w\n⊢ False"
] | intro hn | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Combinatorics.SimpleGraph.Partition | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 10
} | {
"line": 97,
"column": 2
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nP : G.Partition\nv w : V\nh : G.Adj v w\n⊢ P.partOfVertex v ≠ P.partOfVertex w",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"SimpleGraph.Partition.partOfVertex",
"Eq",
"Set"
],
"usedFVars": [
"V",
"G",
"P... | [
"V : Type u\nG : SimpleGraph V\nP : G.Partition\nv w : V\nh : G.Adj v w\nhn : P.partOfVertex v = P.partOfVertex w\n⊢ False"
] | intro hn | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Combinatorics.SimpleGraph.Partition | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 17
} | {
"line": 99,
"column": 2
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nP : G.Partition\nv w : V\nh : G.Adj v w\nhn : P.partOfVertex v = P.partOfVertex w\nhw : w ∈ P.partOfVertex w\n⊢ False",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"congrArg",
"Membership.mem",
"Eq.mp",
"SimpleGraph.Partitio... | [
"V : Type u\nG : SimpleGraph V\nP : G.Partition\nv w : V\nh : G.Adj v w\nhn : P.partOfVertex v = P.partOfVertex w\nhw : w ∈ P.partOfVertex v\n⊢ False"
] | rw [← hn] at hw | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 517,
"column": 69
} | {
"line": 524,
"column": 35
} | {
"line": 526,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nv w : V\ninst✝ : Finite V\nhadj : G.Adj v w\nhcyc : G.IsCycles\n⊢ (G.deleteEdges {s(v, w)}).Reachable v w",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"SimpleGraph.Reachable.symm",
"SimpleGraph.Adj.toWalk",
"SimpleGraph.deleteE... | [] | by
have : fromEdgeSet {s(v, w)} = hadj.toWalk.toSubgraph.spanningCoe := by
simp only [Walk.toSubgraph, singletonSubgraph_le_iff, subgraphOfAdj_verts, Set.mem_insert_iff,
Set.mem_singleton_iff, or_true, sup_of_le_left]
exact (Subgraph.spanningCoe_subgraphOfAdj hadj).symm
rw [show G.deleteEdges {s(v, w)... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 550,
"column": 6
} | {
"line": 550,
"column": 15
} | {
"line": 551,
"column": 4
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nv : V\ninst✝ : Finite V\nc : G.ConnectedComponent\nh : G.IsCycles\nhv : v ∈ c.supp\nw : V\nhw : w ∈ G.neighborSet v\nu : V\np : G.Walk u u\nhp : p.IsCycle ∧ s(v, w) ∈ p.edges\nhvp : v ∈ p.support\nc' : G.ConnectedComponent\nhc' : p.toSubgraph.verts = c'.supp\n⊢ v ∈ p.su... | [] | exact hvp | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 280,
"column": 50
} | {
"line": 311,
"column": 27
} | {
"line": 314,
"column": 4
} | [
{
"pp": "ε : ℝ\nhε : 0 < ε\nr t : ℕ\nhr_pos : 0 < r\nht_pos : 0 < t\nε' : ℝ := 1 / (↑(r - 1) * ↑r) + ε\nhε' : 0 < ε'\nt' : ℕ := ⌊↑t / (↑r * ε)⌋₊ + 1\nht_lt_rt'ε : ↑t < ↑r * ↑t' * ε\nht'_pos : 0 < t'\nN' : ℕ\nN : ℕ := max (max 1 N') ⌈(↑(t'.choose t) ^ r * ↑t + ↑r * ↑t') * (↑t' - ↑t) / (↑r * ↑t' * ε - ↑t)⌉₊\nn : ... | [] | by
refine ⟨univ.map ⟨fun p : K.parts ↦ y p.val p.prop, fun p₁ p₂ (heq : y p₁ _ = y p₂ _) ↦ ?_⟩,
?_, fun {p} hp ↦ ?_, fun p₁ hp₁ p₂ hp₂ hne v₁ hv₁ v₂ hv₂ ↦ ?_⟩
· have hy₁' := mem_powersetCard.mp (hy p₁.val p₁.prop)
have hy₂' := mem_powersetCard.mp (hy p₂.val p₂.prop)
rw [← heq] at hy₂... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 179,
"column": 23
} | {
"line": 179,
"column": 33
} | {
"line": 179,
"column": 33
} | [
{
"pp": "V : Type u_1\na✝ : Nontrivial V\nn : ℕ\nhn : ↑n ≤ ENat.card V - 1\nhh : (completeGraph V).vertexCoverNum < ↑n\nthis✝ : ↑n - 1 ≤ ENat.card V\nt : Set V\nht₁ : t.encard = ↑(n - 1)\nht₂ : (completeGraph V).IsVertexCover t\nthis : 1 < (Set.univ \\ t).encard\na b : V\nleft✝¹ : a ∈ Set.univ \\ t\nleft✝ : b ∈... | [] | simp [hne] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 179,
"column": 23
} | {
"line": 179,
"column": 33
} | {
"line": 179,
"column": 33
} | [
{
"pp": "V : Type u_1\na✝ : Nontrivial V\nn : ℕ\nhn : ↑n ≤ ENat.card V - 1\nhh : (completeGraph V).vertexCoverNum < ↑n\nthis✝ : ↑n - 1 ≤ ENat.card V\nt : Set V\nht₁ : t.encard = ↑(n - 1)\nht₂ : (completeGraph V).IsVertexCover t\nthis : 1 < (Set.univ \\ t).encard\na b : V\nleft✝¹ : a ∈ Set.univ \\ t\nleft✝ : b ∈... | [] | simp [hne] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 179,
"column": 23
} | {
"line": 179,
"column": 33
} | {
"line": 179,
"column": 33
} | [
{
"pp": "V : Type u_1\na✝ : Nontrivial V\nn : ℕ\nhn : ↑n ≤ ENat.card V - 1\nhh : (completeGraph V).vertexCoverNum < ↑n\nthis✝ : ↑n - 1 ≤ ENat.card V\nt : Set V\nht₁ : t.encard = ↑(n - 1)\nht₂ : (completeGraph V).IsVertexCover t\nthis : 1 < (Set.univ \\ t).encard\na b : V\nleft✝¹ : a ∈ Set.univ \\ t\nleft✝ : b ∈... | [] | simp [hne] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 98
} | {
"line": 151,
"column": 4
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nu : Set V\nf : ↑(⊤.deleteVerts u).coe.oddComponents → V\nhf : ∀ (c : ↑(⊤.deleteVerts u).coe.oddComponents), f c ∈ u\ng : ↑(⊤.deleteVerts u).coe.oddComponents → ↑(⊤.deleteVerts u).verts\nhgf : ∀ (c : ↑(⊤.deleteV... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nu : Set V\nf : ↑(⊤.deleteVerts u).coe.oddComponents → V\nhf : ∀ (c : ↑(⊤.deleteVerts u).coe.oddComponents), f c ∈ u\ng : ↑(⊤.deleteVerts u).coe.oddComponents → ↑(⊤.deleteVerts u).verts\nhgf : ∀ (c : ↑(⊤.deleteVerts u).coe.... | replace hcd : g c = g d := Subtype.val_injective <| hM.1.eq_of_adj_right (hgf c) (hcd ▸ hgf d) | Lean.Elab.Tactic.evalReplace | Lean.Parser.Tactic.replace |
Mathlib.Data.Nat.PSub | {
"line": 102,
"column": 54
} | {
"line": 106,
"column": 44
} | {
"line": 108,
"column": 0
} | [
{
"pp": "m n : ℕ\n⊢ m.psub' n = m.psub n",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"not_le",
"Iff.mpr",
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Option.some",
"id",
... | [] | by
rw [psub']
split_ifs with h
· exact (psub_eq_sub h).symm
· exact (psub_eq_none.2 (not_le.1 h)).symm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.Partrec | {
"line": 80,
"column": 6
} | {
"line": 85,
"column": 22
} | {
"line": 86,
"column": 6
} | [
{
"pp": "case false\np : ℕ →. Bool\nH : ∃ n, true ∈ p n ∧ ∀ k < n, (p k).Dom\nm : ℕ\nIH : (y : ℕ) → lbp p y m → (∀ n < y, false ∈ p n) → { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }\nal : ∀ n < m, false ∈ p n\npm : (p m).Dom\ne : (p m).get pm = false\n⊢ { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }",
"ppTerm": "... | [
"case true\np : ℕ →. Bool\nH : ∃ n, true ∈ p n ∧ ∀ k < n, (p k).Dom\nm : ℕ\nIH : (y : ℕ) → lbp p y m → (∀ n < y, false ∈ p n) → { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }\nal : ∀ n < m, false ∈ p n\npm : (p m).Dom\ne : (p m).get pm = true\n⊢ { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }"
] | · suffices ∀ᵉ k ≤ m, false ∈ p k from IH _ ⟨rfl, this⟩ fun n h => this _ (le_of_lt_succ h)
intro n h
rcases h.lt_or_eq_dec with h | h
· exact al _ h
· rw [h]
exact ⟨_, e⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.Ackermann | {
"line": 92,
"column": 57
} | {
"line": 100,
"column": 46
} | {
"line": 102,
"column": 0
} | [
{
"pp": "n : ℕ\n⊢ ack 3 n = 2 ^ (n + 3) - 3",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"ack",
"Nat.mul_sub_left_distrib",
"NonAssocSemiring.toAddCommMonoidWithOne",
"_private.Mathlib.Computability.Ackermann.0.ack_three._proof... | [] | by
induction n with
| zero => simp
| succ n IH =>
rw [ack_succ_succ, IH, ack_two, Nat.succ_add, Nat.pow_succ 2 (n + 3), mul_comm _ 2,
Nat.mul_sub_left_distrib, ← Nat.sub_add_comm, two_mul 3, Nat.add_sub_add_right]
calc 2 * 3
_ ≤ 2 * 2 ^ 3 := by simp
_ ≤ 2 * 2 ^ (n + 3) := by gcongr <;>... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.PartrecCode | {
"line": 179,
"column": 8
} | {
"line": 179,
"column": 69
} | {
"line": 179,
"column": 69
} | [
{
"pp": "c : Code\n⊢ ofNatCode c.encodeCode = c",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"cond",
"False",
"Nat.Partrec.Code.ofNatCode.eq_4",
"Bool.not_false",
"Nat.Partrec.Code.rfind'",
"HMul.hMul",
"Bool.not",
"Nat.bodd_mul",
"Na... | [] | induction c <;> simp [encodeCode, ofNatCode, Nat.div2_val, *] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Computability.PartrecCode | {
"line": 179,
"column": 8
} | {
"line": 179,
"column": 69
} | {
"line": 179,
"column": 69
} | [
{
"pp": "c : Code\n⊢ ofNatCode c.encodeCode = c",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"cond",
"False",
"Nat.Partrec.Code.ofNatCode.eq_4",
"Bool.not_false",
"Nat.Partrec.Code.rfind'",
"HMul.hMul",
"Bool.not",
"Nat.bodd_mul",
"Na... | [] | induction c <;> simp [encodeCode, ofNatCode, Nat.div2_val, *] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.PartrecCode | {
"line": 179,
"column": 8
} | {
"line": 179,
"column": 69
} | {
"line": 179,
"column": 69
} | [
{
"pp": "c : Code\n⊢ ofNatCode c.encodeCode = c",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"cond",
"False",
"Nat.Partrec.Code.ofNatCode.eq_4",
"Bool.not_false",
"Nat.Partrec.Code.rfind'",
"HMul.hMul",
"Bool.not",
"Nat.bodd_mul",
"Na... | [] | induction c <;> simp [encodeCode, ofNatCode, Nat.div2_val, *] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.Ackermann | {
"line": 336,
"column": 60
} | {
"line": 338,
"column": 32
} | {
"line": 340,
"column": 0
} | [
{
"pp": "⊢ ¬Primrec fun n ↦ ack n n",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"Nat.Primrec",
"not_nat_primrec_ack_self",
"congrArg",
"Primcodable.ofDenumerable",
"id",
"Primrec",
"Primrec.nat_iff",
"Nat",
... | [] | by
rw [Primrec.nat_iff]
exact not_nat_primrec_ack_self | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 265,
"column": 4
} | {
"line": 266,
"column": 51
} | {
"line": 268,
"column": 0
} | [
{
"pp": "case neg.inr\nV : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a c : V\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhnGac : ¬G.Adj a c\nhnxc : x ≠ c\nhnac : a ≠ c\nhM2 : M2.IsPerfectMatching\nhM2ac : M2.Adj a c\nhM2sub : M2.spanningCoe ≤ G ⊔ edge a c\nthis : (G : SimpleGraph V) → G.LocallyFinite... | [] | exact tutte_exists_isAlternating_isCycles p hp hcalt (hnM2 _ hnbc) hpac hnpxb hM2ac
hab.symm hnbc hxa.ne.symm hle (aux (by simp)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 308,
"column": 11
} | {
"line": 308,
"column": 45
} | {
"line": 308,
"column": 46
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\nhc✝ : ¬Fintype.card ↑Gmax.uni... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\nhc✝ : ¬Fintype.card ↑Gmax.universalVerts ... | edge_le_iff (v := a.1.1) (w := c), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 32
} | {
"line": 167,
"column": 4
} | [
{
"pp": "f : ℝ → ℝ\nhf : GrowsPolynomially f\nc₁ : ℝ\nleft✝¹ : c₁ > 0\nc₂ : ℝ\nleft✝ : c₂ > 0\nh : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhlt : c₁ < c₂\nx : ℝ\nhx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhx_nonneg : 0 ≤ x\nh' : 3 / 4 * x... | [
"f : ℝ → ℝ\nhf : GrowsPolynomially f\nc₁ : ℝ\nleft✝¹ : c₁ > 0\nc₂ : ℝ\nleft✝ : c₂ > 0\nh : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhlt : c₁ < c₂\nx : ℝ\nhx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhx_nonneg : 0 ≤ x\nh' : 3 / 4 * x ∈ Set.Icc (... | have hu := hx (3 / 4 * x) h' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 32
} | {
"line": 178,
"column": 4
} | [
{
"pp": "f : ℝ → ℝ\nhf : GrowsPolynomially f\nc₁ : ℝ\nleft✝¹ : c₁ > 0\nc₂ : ℝ\nleft✝ : c₂ > 0\nh : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhgt : c₂ < c₁\nx : ℝ\nhx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhx_nonneg : 0 ≤ x\nh' : 3 / 4 * x... | [
"f : ℝ → ℝ\nhf : GrowsPolynomially f\nc₁ : ℝ\nleft✝¹ : c₁ > 0\nc₂ : ℝ\nleft✝ : c₂ > 0\nh : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhgt : c₂ < c₁\nx : ℝ\nhx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhx_nonneg : 0 ≤ x\nh' : 3 / 4 * x ∈ Set.Icc (... | have hu := hx (3 / 4 * x) h' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 270,
"column": 6
} | {
"line": 270,
"column": 36
} | {
"line": 271,
"column": 6
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 - ε x)\nh_diff_q : DifferentiableOn ℝ q (Set.Ioi 1)\n⊢ (fun x ↦ deriv (fun z ↦ z ^ p a b) x * (1 - ε x) + x ^ p a b * der... | [
"case left\nα : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 - ε x)\nh_diff_q : DifferentiableOn ℝ q (Set.Ioi 1)\n⊢ (fun x ↦ deriv (fun z ↦ z ^ p a b) x * (1 - ε x)) =O[atTop] fun x ↦... | refine IsBigO.add ?left ?right | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 282,
"column": 8
} | {
"line": 282,
"column": 36
} | {
"line": 283,
"column": 6
} | [
{
"pp": "case inl.inl\nf g : ℝ → ℝ\nhf : GrowsPolynomially f\nhg : GrowsPolynomially g\nthis : GrowsPolynomially fun x ↦ |f x| * |g x|\nhf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x\nhg' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ g x\nhmain : (fun x ↦ f x * g x) =ᶠ[atTop] fun x ↦ |f x| * |g x|\n⊢ GrowsPolynomially fun x ↦ f x * g x",
... | [] | rwa [iff_eventuallyEq hmain] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 275,
"column": 4
} | {
"line": 302,
"column": 18
} | {
"line": 303,
"column": 2
} | [
{
"pp": "f g : ℝ → ℝ\nhf : GrowsPolynomially f\nhg : GrowsPolynomially g\nthis : GrowsPolynomially fun x ↦ |f x| * |g x|\n⊢ GrowsPolynomially fun x ↦ f x * g x",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | [] | cases eventually_atTop_nonneg_or_nonpos hf with
| inl hf' =>
cases eventually_atTop_nonneg_or_nonpos hg with
| inl hg' =>
have hmain : (fun x => f x * g x) =ᶠ[atTop] fun x => |f x| * |g x| := by
filter_upwards [hf', hg'] with x hx₁ hx₂
rw [abs_of_nonneg hx₁, abs_of_nonneg hx₂... | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 275,
"column": 4
} | {
"line": 302,
"column": 18
} | {
"line": 303,
"column": 2
} | [
{
"pp": "f g : ℝ → ℝ\nhf : GrowsPolynomially f\nhg : GrowsPolynomially g\nthis : GrowsPolynomially fun x ↦ |f x| * |g x|\n⊢ GrowsPolynomially fun x ↦ f x * g x",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | [] | cases eventually_atTop_nonneg_or_nonpos hf with
| inl hf' =>
cases eventually_atTop_nonneg_or_nonpos hg with
| inl hg' =>
have hmain : (fun x => f x * g x) =ᶠ[atTop] fun x => |f x| * |g x| := by
filter_upwards [hf', hg'] with x hx₁ hx₂
rw [abs_of_nonneg hx₁, abs_of_nonneg hx₂... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 275,
"column": 4
} | {
"line": 302,
"column": 18
} | {
"line": 303,
"column": 2
} | [
{
"pp": "f g : ℝ → ℝ\nhf : GrowsPolynomially f\nhg : GrowsPolynomially g\nthis : GrowsPolynomially fun x ↦ |f x| * |g x|\n⊢ GrowsPolynomially fun x ↦ f x * g x",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | [] | cases eventually_atTop_nonneg_or_nonpos hf with
| inl hf' =>
cases eventually_atTop_nonneg_or_nonpos hg with
| inl hg' =>
have hmain : (fun x => f x * g x) =ᶠ[atTop] fun x => |f x| * |g x| := by
filter_upwards [hf', hg'] with x hx₁ hx₂
rw [abs_of_nonneg hx₁, abs_of_nonneg hx₂... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 361,
"column": 8
} | {
"line": 361,
"column": 38
} | {
"line": 362,
"column": 8
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 + ε x)\nh_diff_q : DifferentiableOn ℝ q (Set.Ioi 1)\n⊢ (fun x ↦ deriv (fun z ↦ z ^ p a b) x * (1 + ε x) + x ^ p a b * der... | [
"case left\nα : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 + ε x)\nh_diff_q : DifferentiableOn ℝ q (Set.Ioi 1)\n⊢ (fun x ↦ deriv (fun z ↦ z ^ p a b) x * (1 + ε x)) =O[atTop] fun x ↦... | refine IsBigO.add ?left ?right | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 20
} | {
"line": 335,
"column": 2
} | [
{
"pp": "f g : ℝ → ℝ\nhf : GrowsPolynomially f\nhg : GrowsPolynomially g\nhf' : 0 ≤ᶠ[atTop] f\nhg' : 0 ≤ᶠ[atTop] g\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\n⊢ ∃ c₁ > 0,\n ∃ c₂ > 0,\n ∀ᶠ (x : ℝ) in atTop,\n ∀ u ∈ Set.Icc (b * x) x,\n (fun x ↦ f x + g x) u ∈ Set.Icc (c₁ * (fun x ↦ f x + g x) x) (c₂ * ... | [
"f g : ℝ → ℝ\nhf✝ : GrowsPolynomially f\nhg : GrowsPolynomially g\nhf' : 0 ≤ᶠ[atTop] f\nhg' : 0 ≤ᶠ[atTop] g\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhf : ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\n⊢ ∃ c₁ > 0,\n ∃ c₂ > 0,\n ∀ᶠ (x : ℝ) in atTop,\n ∀ u ∈ ... | have hf := hf b hb | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 22
} | {
"line": 378,
"column": 4
} | [
{
"pp": "case inl\nf g : ℝ → ℝ\nhf : GrowsPolynomially f\nhfg : ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : ℝ) in atTop, ‖g x‖ ≤ c * ‖f x‖\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb_ub : b < 1\nhf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x\n⊢ ∃ c₁ > 0,\n ∃ c₂ > 0,\n ∀ᶠ (x : ℝ) in atTop,\n ∀ u ∈ Set.Icc (b * x) x,\n (fun x ↦ ... | [
"case inl\nf g : ℝ → ℝ\nhf✝ : GrowsPolynomially f\nhfg : ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : ℝ) in atTop, ‖g x‖ ≤ c * ‖f x‖\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb_ub : b < 1\nhf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x\nhf : ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\n⊢ ∃ c₁ > 0,\... | have hf := hf b hb | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 420,
"column": 4
} | {
"line": 420,
"column": 22
} | {
"line": 421,
"column": 4
} | [
{
"pp": "case inr\nf g : ℝ → ℝ\nhf : GrowsPolynomially f\nhfg : ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : ℝ) in atTop, ‖g x‖ ≤ c * ‖f x‖\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb_ub : b < 1\nhf' : ∀ᶠ (x : ℝ) in atTop, f x ≤ 0\n⊢ ∃ c₁ > 0,\n ∃ c₂ > 0,\n ∀ᶠ (x : ℝ) in atTop,\n ∀ u ∈ Set.Icc (b * x) x,\n (fun x ↦ ... | [
"case inr\nf g : ℝ → ℝ\nhf✝ : GrowsPolynomially f\nhfg : ∀ ⦃c : ℝ⦄, 0 < c → ∀ᶠ (x : ℝ) in atTop, ‖g x‖ ≤ c * ‖f x‖\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb_ub : b < 1\nhf' : ∀ᶠ (x : ℝ) in atTop, f x ≤ 0\nhf : ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\n⊢ ∃ c₁ > 0,\... | have hf := hf b hb | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 747,
"column": 80
} | {
"line": 748,
"column": 29
} | {
"line": 749,
"column": 6
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nc₁ : ℝ\nhc₁_mem : c₁ ∈ Set.Ioo 0 1\nhc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁... | [] | by
gcongr; exact hn₃ i | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 493,
"column": 8
} | {
"line": 493,
"column": 36
} | {
"line": 494,
"column": 6
} | [
{
"pp": "case inl\nf : ℝ → ℝ\nhf : GrowsPolynomially f\nthis : GrowsPolynomially fun x ↦ |(f x)⁻¹|\nhf' : ∀ᶠ (x : ℝ) in atTop, 0 < f x\nhmain : (fun x ↦ (f x)⁻¹) =ᶠ[atTop] fun x ↦ |(f x)⁻¹|\n⊢ GrowsPolynomially fun x ↦ (f x)⁻¹",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | rwa [iff_eventuallyEq hmain] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Data.Nat.Bitwise | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 64
} | {
"line": 62,
"column": 2
} | [
{
"pp": "f : Bool → Bool → Bool\nn : ℕ\n⊢ (if n = 0 then if f false true = true then 0 else 0\n else\n if 0 = 0 then if f true false = true then n else 0\n else\n have n' := n / 2;\n have m' := 0 / 2;\n let b₁ := n % 2 = 1;\n let b₂ := 0 % 2 = 1;\n have r := bitwi... | [
"f : Bool → Bool → Bool\nn : ℕ\n⊢ n = 0 → 0 = if f true false = true then n else 0"
] | simp only [ite_self, Nat.zero_div, ite_true, ite_eq_right_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Nat.Bitwise | {
"line": 78,
"column": 6
} | {
"line": 78,
"column": 16
} | {
"line": 78,
"column": 17
} | [
{
"pp": "C : ℕ → Sort u_1\nz : C 0\nf : (b : Bool) → (n : ℕ) → C n → C (bit b n)\nn : ℕ\nh : n ≠ 0\n⊢ binaryRec z f n = ⋯ ▸ f n.bodd n.div2 (binaryRec z f n.div2)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Nat.bit",
"Eq.mpr",
"bne",
"Nat.instAndOp",
"con... | [
"C : ℕ → Sort u_1\nz : C 0\nf : (b : Bool) → (n : ℕ) → C n → C (bit b n)\nn : ℕ\nh : n ≠ 0\n⊢ (if n0 : n = 0 then ⋯ ▸ z\n else\n have x := f (1 &&& n != 0) (n >>> 1) (binaryRec z f (n >>> 1));\n ⋯ ▸ x) =\n ⋯ ▸ f n.bodd n.div2 (binaryRec z f n.div2)"
] | binaryRec, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.ReduceOption | {
"line": 85,
"column": 87
} | {
"line": 97,
"column": 68
} | {
"line": 99,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List (Option α)\nl' : List α\na : α\n⊢ l.reduceOption = l'.concat a ↔ ∃ l₁ l₂, l = l₁ ++ some a :: l₂ ∧ l₁.reduceOption = l' ∧ l₂.reduceOption = []",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"List.reduceOption_re... | [] | by
rw [concat_eq_append]
constructor
· intro h
rw [reduceOption_eq_append_iff] at h
obtain ⟨l₁, _, h, hl₁, hl₂⟩ := h
rw [reduceOption_eq_singleton_iff] at hl₂
obtain ⟨m, n, hl₂⟩ := hl₂
use l₁ ++ replicate m none, replicate n none
simp_rw [h, reduceOption_append, reduceOption_replicate_none... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Num.Lemmas | {
"line": 364,
"column": 18
} | {
"line": 364,
"column": 66
} | {
"line": 365,
"column": 2
} | [
{
"pp": "x✝ : Num\n⊢ x✝ * 1 = x✝",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"Nat.instMulOneClass",
"id",
"MulOne.toMul",
"instMulNat",
... | [] | rw [← to_nat_inj, mul_to_nat, cast_one, mul_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Num.Lemmas | {
"line": 364,
"column": 18
} | {
"line": 364,
"column": 66
} | {
"line": 365,
"column": 2
} | [
{
"pp": "x✝ : Num\n⊢ x✝ * 1 = x✝",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"Nat.instMulOneClass",
"id",
"MulOne.toMul",
"instMulNat",
... | [] | rw [← to_nat_inj, mul_to_nat, cast_one, mul_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.Lemmas | {
"line": 364,
"column": 18
} | {
"line": 364,
"column": 66
} | {
"line": 365,
"column": 2
} | [
{
"pp": "x✝ : Num\n⊢ x✝ * 1 = x✝",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"Nat.instMulOneClass",
"id",
"MulOne.toMul",
"instMulNat",
... | [] | rw [← to_nat_inj, mul_to_nat, cast_one, mul_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.Tape | {
"line": 299,
"column": 50
} | {
"line": 300,
"column": 53
} | {
"line": 302,
"column": 0
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nl : List Γ\n⊢ (List.map f.f l).headI = f.f l.headI",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"List.map",
"List.cons",
"List",
"Lis... | [] | by
cases l <;> [exact (PointedMap.map_pt f).symm; rfl] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.TuringMachine.Tape | {
"line": 417,
"column": 22
} | {
"line": 417,
"column": 35
} | {
"line": 417,
"column": 35
} | [
{
"pp": "case head\nΓ : Type ?u.6\ninst✝ : Inhabited Γ\n⊢ Γ",
"ppTerm": "?head",
"assigned": true,
"usedConstants": [
"Inhabited.default"
],
"usedFVars": [
"Γ",
"inst✝"
],
"usedGoals": []
}
] | [] | apply default | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Computability.TuringMachine.Tape | {
"line": 417,
"column": 22
} | {
"line": 417,
"column": 35
} | {
"line": 417,
"column": 35
} | [
{
"pp": "case left\nΓ : Type ?u.6\ninst✝ : Inhabited Γ\n⊢ ListBlank Γ",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"Turing.ListBlank.inhabited",
"Turing.ListBlank"
],
"usedFVars": [
"Γ",
"inst✝"
],
"usedGoals": []
}
] | [] | apply default | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Computability.TuringMachine.Tape | {
"line": 417,
"column": 22
} | {
"line": 417,
"column": 35
} | {
"line": 417,
"column": 35
} | [
{
"pp": "case right\nΓ : Type ?u.6\ninst✝ : Inhabited Γ\n⊢ ListBlank Γ",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"Turing.ListBlank.inhabited",
"Turing.ListBlank"
],
"usedFVars": [
"Γ",
"inst✝"
],
"usedGoals": []
}
... | [] | apply default | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 442,
"column": 14
} | {
"line": 442,
"column": 57
} | {
"line": 443,
"column": 4
} | [
{
"pp": "case goto\nΓ : Type u_1\nΛ : Type u_2\nσ : Type u_3\ninst✝¹ : Inhabited Λ\ninst✝ : Inhabited Γ\nM : Λ → Stmt Γ Λ σ\nS : Finset Λ\nss : Supports M S\nl₁ : Λ\na✝ : Γ → σ → Λ\nv : σ\nT : Tape Γ\nhs : SupportsStmt S (goto a✝)\n⊢ (stepAux (goto a✝) v T).l ∈ Finset.insertNone S",
"ppTerm": "?goto",
"... | [] | exact Finset.some_mem_insertNone.2 (hs _ _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 442,
"column": 14
} | {
"line": 442,
"column": 57
} | {
"line": 443,
"column": 4
} | [
{
"pp": "case goto\nΓ : Type u_1\nΛ : Type u_2\nσ : Type u_3\ninst✝¹ : Inhabited Λ\ninst✝ : Inhabited Γ\nM : Λ → Stmt Γ Λ σ\nS : Finset Λ\nss : Supports M S\nl₁ : Λ\na✝ : Γ → σ → Λ\nv : σ\nT : Tape Γ\nhs : SupportsStmt S (goto a✝)\n⊢ (stepAux (goto a✝) v T).l ∈ Finset.insertNone S",
"ppTerm": "?goto",
"... | [] | exact Finset.some_mem_insertNone.2 (hs _ _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 442,
"column": 14
} | {
"line": 442,
"column": 57
} | {
"line": 443,
"column": 4
} | [
{
"pp": "case goto\nΓ : Type u_1\nΛ : Type u_2\nσ : Type u_3\ninst✝¹ : Inhabited Λ\ninst✝ : Inhabited Γ\nM : Λ → Stmt Γ Λ σ\nS : Finset Λ\nss : Supports M S\nl₁ : Λ\na✝ : Γ → σ → Λ\nv : σ\nT : Tape Γ\nhs : SupportsStmt S (goto a✝)\n⊢ (stepAux (goto a✝) v T).l ∈ Finset.insertNone S",
"ppTerm": "?goto",
"... | [] | exact Finset.some_mem_insertNone.2 (hs _ _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.RegularExpressions | {
"line": 193,
"column": 2
} | {
"line": 199,
"column": 66
} | {
"line": 201,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝ : DecidableEq α\na head✝ : α\nx : List α\n⊢ (char a).rmatch (head✝ :: x) = true ↔ head✝ :: x = [a]",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.singleton_inj",
"False",
"Decidable.casesOn",
"RegularExp... | [] | · rcases x with - | ⟨head, tail⟩
· rw [rmatch, deriv, List.singleton_inj]
split <;> tauto
· rw [rmatch, rmatch, deriv, cons.injEq]
split
· simp_rw [deriv_one, zero_rmatch, reduceCtorEq, and_false]
· simp_rw [deriv_zero, zero_rmatch, reduceCtorEq, and_false] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.RegularExpressions | {
"line": 203,
"column": 2
} | {
"line": 207,
"column": 16
} | {
"line": 209,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nP Q : RegularExpression α\nx : List α\n⊢ (P + Q).rmatch x = true ↔ P.rmatch x = true ∨ Q.rmatch x = true",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"RegularExpression.deriv_add",
"Eq.mpr",
"RegularExpression.rmatch",
... | [] | induction x generalizing P Q with
| nil => simp only [rmatch, matchEpsilon, Bool.or_eq_true_iff]
| cons _ _ ih =>
rw [rmatch, deriv_add]
exact ih _ _ | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
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