module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 371
values | kind stringclasses 375
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.GroupTheory.Finiteness | {
"line": 493,
"column": 4
} | {
"line": 493,
"column": 35
} | {
"line": 495,
"column": 0
} | [
{
"pp": "case mpr\nG : Type u_3\ninst✝ : Group G\nα : Type\nw✝ : Finite α\nφ : FreeGroup α →* G\nhφ : Function.Surjective ⇑φ\n⊢ FG G",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Group.fg_of_surjective",
"instFGFreeGroupOfFinite",
"FreeGroup",
"FreeGroup.instGroup... | [] | exact Group.fg_of_surjective hφ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.BigOperators.Group.Finset.Basic | {
"line": 1032,
"column": 4
} | {
"line": 1036,
"column": 14
} | {
"line": 1038,
"column": 0
} | [
{
"pp": "M : Type u_4\nι : Type u_7\ninst✝² : Fintype ι\ninst✝¹ : CommMonoid M\np : ι → Prop\nf : ι → M\ninst✝ : DecidablePred p\n⊢ (∏ i, f ↑i) * ∏ i, f ↑i = ∏ i, f i",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableNot",
"Finset.mem_filter._simp_1"... | [] | let s := { x | p x }.toFinset
rw [← Finset.prod_subtype s, ← Finset.prod_subtype sᶜ]
· exact Finset.prod_mul_prod_compl _ _
· simp [s]
· simp [s] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.Finset.Basic | {
"line": 1032,
"column": 4
} | {
"line": 1036,
"column": 14
} | {
"line": 1038,
"column": 0
} | [
{
"pp": "M : Type u_4\nι : Type u_7\ninst✝² : Fintype ι\ninst✝¹ : CommMonoid M\np : ι → Prop\nf : ι → M\ninst✝ : DecidablePred p\n⊢ (∏ i, f ↑i) * ∏ i, f ↑i = ∏ i, f i",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableNot",
"Finset.mem_filter._simp_1"... | [] | let s := { x | p x }.toFinset
rw [← Finset.prod_subtype s, ← Finset.prod_subtype sᶜ]
· exact Finset.prod_mul_prod_compl _ _
· simp [s]
· simp [s] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Group.Finset.Basic | {
"line": 1084,
"column": 6
} | {
"line": 1084,
"column": 30
} | {
"line": 1084,
"column": 31
} | [
{
"pp": "ι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nm : Multiset ι\nhms : ∀ a ∈ m, a ∈ s\n⊢ ∑ a ∈ s, count a m = m.card",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"Multiset.toFinset_sum_count_eq",
"congrArg",
"Multis... | [
"ι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nm : Multiset ι\nhms : ∀ a ∈ m, a ∈ s\n⊢ ∑ a ∈ s, count a m = ∑ a ∈ m.toFinset, count a m"
] | ← toFinset_sum_count_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Commutator.Basic | {
"line": 265,
"column": 2
} | {
"line": 266,
"column": 37
} | {
"line": 268,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH₁ H₂ : Subgroup G\n⊢ H₂ ≤ normalizer ↑⁅H₁, H₂⁆",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Bracket.bracket",
"Preorder.toLE",
"id",
"Subgroup",
"Su... | [] | rw [commutator_comm]
apply normalizer_commutator_ge_left | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Commutator.Basic | {
"line": 265,
"column": 2
} | {
"line": 266,
"column": 37
} | {
"line": 268,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH₁ H₂ : Subgroup G\n⊢ H₂ ≤ normalizer ↑⁅H₁, H₂⁆",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Bracket.bracket",
"Preorder.toLE",
"id",
"Subgroup",
"Su... | [] | rw [commutator_comm]
apply normalizer_commutator_ge_left | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 444,
"column": 42
} | {
"line": 444,
"column": 50
} | {
"line": 444,
"column": 51
} | [
{
"pp": "case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx : FreeAbelianGroup α\nL3 : α\ny₁ y₂ : FreeAbelianGroup α\nih₁ : x * y₁ * of L3 = x * (y₁ * of L3)\nih₂ : x * y₂ * of L3 = x * (y₂ * of L3)\n⊢ x * (y₁ + y₂) * of L3 = x * (y₁ * of L3 + y₂ * of L3)",
"ppTerm": "?of.... | [
"case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx : FreeAbelianGroup α\nL3 : α\ny₁ y₂ : FreeAbelianGroup α\nih₁ : x * y₁ * of L3 = x * (y₁ * of L3)\nih₂ : x * y₂ * of L3 = x * (y₂ * of L3)\n⊢ (x * y₁ + x * y₂) * of L3 = x * (y₁ * of L3 + y₂ * of L3)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 444,
"column": 51
} | {
"line": 444,
"column": 59
} | {
"line": 444,
"column": 60
} | [
{
"pp": "case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx : FreeAbelianGroup α\nL3 : α\ny₁ y₂ : FreeAbelianGroup α\nih₁ : x * y₁ * of L3 = x * (y₁ * of L3)\nih₂ : x * y₂ * of L3 = x * (y₂ * of L3)\n⊢ (x * y₁ + x * y₂) * of L3 = x * (y₁ * of L3 + y₂ * of L3)",
"ppTerm": "... | [
"case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx : FreeAbelianGroup α\nL3 : α\ny₁ y₂ : FreeAbelianGroup α\nih₁ : x * y₁ * of L3 = x * (y₁ * of L3)\nih₂ : x * y₂ * of L3 = x * (y₂ * of L3)\n⊢ (x * y₁ + x * y₂) * of L3 = x * (y₁ * of L3) + x * (y₂ * of L3)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 446,
"column": 31
} | {
"line": 446,
"column": 39
} | {
"line": 446,
"column": 40
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx y z₁ z₂ : FreeAbelianGroup α\nih₁ : x * y * z₁ = x * (y * z₁)\nih₂ : x * y * z₂ = x * (y * z₂)\n⊢ x * y * (z₁ + z₂) = x * (y * (z₁ + z₂))",
"ppTerm": "?add",
"assigned": true,
"usedConstants": [
"Distri... | [
"case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx y z₁ z₂ : FreeAbelianGroup α\nih₁ : x * y * z₁ = x * (y * z₁)\nih₂ : x * y * z₂ = x * (y * z₂)\n⊢ x * y * z₁ + x * y * z₂ = x * (y * (z₁ + z₂))"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 446,
"column": 40
} | {
"line": 446,
"column": 48
} | {
"line": 446,
"column": 49
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx y z₁ z₂ : FreeAbelianGroup α\nih₁ : x * y * z₁ = x * (y * z₁)\nih₂ : x * y * z₂ = x * (y * z₂)\n⊢ x * y * z₁ + x * y * z₂ = x * (y * (z₁ + z₂))",
"ppTerm": "?add",
"assigned": true,
"usedConstants": [
"... | [
"case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx y z₁ z₂ : FreeAbelianGroup α\nih₁ : x * y * z₁ = x * (y * z₁)\nih₂ : x * y * z₂ = x * (y * z₂)\n⊢ x * y * z₁ + x * y * z₂ = x * (y * z₁ + y * z₂)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 446,
"column": 49
} | {
"line": 446,
"column": 57
} | {
"line": 446,
"column": 58
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx y z₁ z₂ : FreeAbelianGroup α\nih₁ : x * y * z₁ = x * (y * z₁)\nih₂ : x * y * z₂ = x * (y * z₂)\n⊢ x * y * z₁ + x * y * z₂ = x * (y * z₁ + y * z₂)",
"ppTerm": "?add",
"assigned": true,
"usedConstants": [
... | [
"case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : Semigroup α\nx y z₁ z₂ : FreeAbelianGroup α\nih₁ : x * y * z₁ = x * (y * z₁)\nih₂ : x * y * z₂ = x * (y * z₂)\n⊢ x * y * z₁ + x * y * z₂ = x * (y * z₁) + x * (y * z₂)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 499,
"column": 33
} | {
"line": 499,
"column": 41
} | {
"line": 499,
"column": 42
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\nR : Type u_2\ninst✝¹ : Monoid α\ninst✝ : Ring R\nf : α →* R\nx y1 y2 : FreeAbelianGroup α\nih1 : (lift ⇑f) (x * y1) = (lift ⇑f) x * (lift ⇑f) y1\nih2 : (lift ⇑f) (x * y2) = (lift ⇑f) x * (lift ⇑f) y2\n⊢ (lift ⇑f) (x * (y1 + y2)) = (lift ⇑f) x ... | [
"case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\nR : Type u_2\ninst✝¹ : Monoid α\ninst✝ : Ring R\nf : α →* R\nx y1 y2 : FreeAbelianGroup α\nih1 : (lift ⇑f) (x * y1) = (lift ⇑f) x * (lift ⇑f) y1\nih2 : (lift ⇑f) (x * y2) = (lift ⇑f) x * (lift ⇑f) y2\n⊢ (lift ⇑f) (x * y1 + x * y2) = (lift ⇑f) x * (lift ⇑f... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 499,
"column": 60
} | {
"line": 499,
"column": 68
} | {
"line": 499,
"column": 69
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\nR : Type u_2\ninst✝¹ : Monoid α\ninst✝ : Ring R\nf : α →* R\nx y1 y2 : FreeAbelianGroup α\nih1 : (lift ⇑f) (x * y1) = (lift ⇑f) x * (lift ⇑f) y1\nih2 : (lift ⇑f) (x * y2) = (lift ⇑f) x * (lift ⇑f) y2\n⊢ (lift ⇑f) (x * y1) + (lift ⇑f) (x * y2) ... | [
"case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\nR : Type u_2\ninst✝¹ : Monoid α\ninst✝ : Ring R\nf : α →* R\nx y1 y2 : FreeAbelianGroup α\nih1 : (lift ⇑f) (x * y1) = (lift ⇑f) x * (lift ⇑f) y1\nih2 : (lift ⇑f) (x * y2) = (lift ⇑f) x * (lift ⇑f) y2\n⊢ (lift ⇑f) (x * y1) + (lift ⇑f) (x * y2) = (lift ⇑f) ... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 537,
"column": 33
} | {
"line": 537,
"column": 41
} | {
"line": 537,
"column": 42
} | [
{
"pp": "case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : CommMonoid α\ns : α\ny1 y2 : FreeAbelianGroup α\nih1 : of s * y1 = y1 * of s\nih2 : of s * y2 = y2 * of s\n⊢ of s * (y1 + y2) = (y1 + y2) * of s",
"ppTerm": "?of.add",
"assigned": true,
"usedConstants": [
"Distrib.... | [
"case of.add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : CommMonoid α\ns : α\ny1 y2 : FreeAbelianGroup α\nih1 : of s * y1 = y1 * of s\nih2 : of s * y2 = y2 * of s\n⊢ of s * y1 + of s * y2 = (y1 + y2) * of s"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeAbelianGroup | {
"line": 539,
"column": 40
} | {
"line": 539,
"column": 48
} | {
"line": 539,
"column": 49
} | [
{
"pp": "case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : CommMonoid α\ny x1 x2 : FreeAbelianGroup α\nih1 : x1 * y = y * x1\nih2 : x2 * y = y * x2\n⊢ x1 * y + x2 * y = y * (x1 + x2)",
"ppTerm": "?add",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"E... | [
"case add\nα : Type u\nG : Type u_1\nβ : Type v\nγ : Type w\ninst✝ : CommMonoid α\ny x1 x2 : FreeAbelianGroup α\nih1 : x1 * y = y * x1\nih2 : x2 * y = y * x2\n⊢ x1 * y + x2 * y = y * x1 + y * x2"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 182,
"column": 28
} | {
"line": 182,
"column": 44
} | {
"line": 182,
"column": 44
} | [
{
"pp": "M : Type u_1\ninst✝ : CommMonoid M\nS : Submonoid M\nb : Con (M × ↥S)\nH : b ∈ {c | ∀ (y : ↥S), c 1 (↑y, y)}\nx✝² x✝¹ : M × ↥S\np : M\nq : ↥S\nx : M\ny : ↥S\nx✝ : (r' S) (p, q) (x, y)\nt : ↥S\nht : ↑t * (↑(x, y).2 * (p, q).1) = ↑t * (↑(p, q).2 * (x, y).1)\n⊢ b (1 * (p, q)) (x, y)",
"ppTerm": "?m.85... | [
"M : Type u_1\ninst✝ : CommMonoid M\nS : Submonoid M\nb : Con (M × ↥S)\nH : b ∈ {c | ∀ (y : ↥S), c 1 (↑y, y)}\nx✝² x✝¹ : M × ↥S\np : M\nq : ↥S\nx : M\ny : ↥S\nx✝ : (r' S) (p, q) (x, y)\nt : ↥S\nht : ↑t * (↑(x, y).2 * (p, q).1) = ↑t * (↑(p, q).2 * (x, y).1)\n⊢ b (1 * (p, q)) (1 * (x, y))"
] | ← one_mul (x, y) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.OreLocalization.Basic | {
"line": 597,
"column": 52
} | {
"line": 597,
"column": 63
} | {
"line": 597,
"column": 64
} | [
{
"pp": "R : Type u_1\nR' : Type u_2\nM : Type u_3\nX : Type u_4\ninst✝¹³ : Monoid M\nS : Submonoid M\ninst✝¹² : OreSet S\ninst✝¹¹ : MulAction M X\ninst✝¹⁰ : SMul R X\ninst✝⁹ : SMul R M\ninst✝⁸ : IsScalarTower R M M\ninst✝⁷ : IsScalarTower R M X\ninst✝⁶ : SMul R' X\ninst✝⁵ : SMul R' M\ninst✝⁴ : IsScalarTower R'... | [
"R : Type u_1\nR' : Type u_2\nM : Type u_3\nX : Type u_4\ninst✝¹³ : Monoid M\nS : Submonoid M\ninst✝¹² : OreSet S\ninst✝¹¹ : MulAction M X\ninst✝¹⁰ : SMul R X\ninst✝⁹ : SMul R M\ninst✝⁸ : IsScalarTower R M M\ninst✝⁷ : IsScalarTower R M X\ninst✝⁶ : SMul R' X\ninst✝⁵ : SMul R' M\ninst✝⁴ : IsScalarTower R' M M\ninst✝³... | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Maps | {
"line": 184,
"column": 2
} | {
"line": 187,
"column": 18
} | {
"line": 189,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type u_3\ninst✝ : CommMonoid P\nf : S.LocalizationMap N\ng : M →* P\nhg : ∀ (y : ↥S), IsUnit (g ↑y)\nj : N →* P\nhj : ∀ (x : M), j (f x) = g x\n⊢ f.lift hg = j",
"ppTerm": "?m.27",
"assigned": true,
... | [] | ext
rw [lift_spec, ← hj, ← hj, ← j.map_mul]
apply congr_arg
rw [← sec_spec'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.MonoidLocalization.Maps | {
"line": 184,
"column": 2
} | {
"line": 187,
"column": 18
} | {
"line": 189,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type u_3\ninst✝ : CommMonoid P\nf : S.LocalizationMap N\ng : M →* P\nhg : ∀ (y : ↥S), IsUnit (g ↑y)\nj : N →* P\nhj : ∀ (x : M), j (f x) = g x\n⊢ f.lift hg = j",
"ppTerm": "?m.27",
"assigned": true,
... | [] | ext
rw [lift_spec, ← hj, ← hj, ← j.map_mul]
apply congr_arg
rw [← sec_spec'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 357,
"column": 6
} | {
"line": 357,
"column": 17
} | {
"line": 357,
"column": 18
} | [
{
"pp": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nR : Type u_4\ninst✝¹ : SMul R M\ninst✝ : IsScalarTower R M M\nc : R\na : M\nb : ↥S\n⊢ (c • 1) • a /ₒ (b * 1) = c • a /ₒ b",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
... | [
"M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nR : Type u_4\ninst✝¹ : SMul R M\ninst✝ : IsScalarTower R M M\nc : R\na : M\nb : ↥S\n⊢ c • 1 • a /ₒ (b * 1) = c • a /ₒ b"
] | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.MonoidLocalization.Basic | {
"line": 487,
"column": 69
} | {
"line": 489,
"column": 73
} | {
"line": 491,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝¹ : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝ : CommMonoid N\nf : M →* N\nh : ∀ (y : ↥S), IsUnit (f ↑y)\ny : ↥S\nw z : N\n⊢ w * ↑((IsUnit.liftRight (f.restrict S) h) y)⁻¹ = z ↔ w = f ↑y * z",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"IsUnit.l... | [] | by
rw [mul_comm]
exact Units.inv_mul_eq_iff_eq_mul (IsUnit.liftRight (f.restrict S) h y) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.OreLocalization.Basic | {
"line": 628,
"column": 48
} | {
"line": 628,
"column": 59
} | {
"line": 628,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_3\nX : Type u_4\ninst✝⁶ : Monoid M\nS : Submonoid M\ninst✝⁵ : OreSet S\ninst✝⁴ : MulAction M X\ninst✝³ : SMul R X\ninst✝² : SMul R M\ninst✝¹ : IsScalarTower R M M\ninst✝ : IsScalarTower R M X\nr : R\nx : X\n⊢ (r • 1) • x /ₒ 1 = r • x /ₒ 1",
"ppTerm": "?m.71",
"assigned"... | [
"R : Type u_1\nM : Type u_3\nX : Type u_4\ninst✝⁶ : Monoid M\nS : Submonoid M\ninst✝⁵ : OreSet S\ninst✝⁴ : MulAction M X\ninst✝³ : SMul R X\ninst✝² : SMul R M\ninst✝¹ : IsScalarTower R M M\ninst✝ : IsScalarTower R M X\nr : R\nx : X\n⊢ r • 1 • x /ₒ 1 = r • x /ₒ 1"
] | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.WithTop | {
"line": 75,
"column": 33
} | {
"line": 75,
"column": 42
} | {
"line": 75,
"column": 43
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : WithTop α\nha : ¬a = 0\nhb : b = 0\n⊢ untopD 0 (a * 0) = untopD 0 a * untopD 0 0",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"cong... | [
"case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : WithTop α\nha : ¬a = 0\nhb : b = 0\n⊢ untopD 0 0 = untopD 0 a * untopD 0 0"
] | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Sub.WithTop | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 56
} | {
"line": 67,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Sub α\ninst✝² : Bot α\ninst✝¹ : Sub β\ninst✝ : Bot β\nf : α → β\nh : ∀ (x y : α), f (x - y) = f x - f y\nh₀ : f ⊥ = ⊥\nx✝ : WithTop α\n⊢ map f (x✝ - ⊤) = map f x✝ - map f ⊤",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"congrArg",
... | [] | simp only [sub_top, map_coe, h₀, map_top] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Sub.WithTop | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 56
} | {
"line": 67,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Sub α\ninst✝² : Bot α\ninst✝¹ : Sub β\ninst✝ : Bot β\nf : α → β\nh : ∀ (x y : α), f (x - y) = f x - f y\nh₀ : f ⊥ = ⊥\nx✝ : WithTop α\n⊢ map f (x✝ - ⊤) = map f x✝ - map f ⊤",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"congrArg",
... | [] | simp only [sub_top, map_coe, h₀, map_top] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Sub.WithTop | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 56
} | {
"line": 67,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝³ : Sub α\ninst✝² : Bot α\ninst✝¹ : Sub β\ninst✝ : Bot β\nf : α → β\nh : ∀ (x y : α), f (x - y) = f x - f y\nh₀ : f ⊥ = ⊥\nx✝ : WithTop α\n⊢ map f (x✝ - ⊤) = map f x✝ - map f ⊤",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"congrArg",
... | [] | simp only [sub_top, map_coe, h₀, map_top] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.WithTop | {
"line": 335,
"column": 33
} | {
"line": 335,
"column": 42
} | {
"line": 335,
"column": 43
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : WithBot α\nha : ¬a = 0\nhb : b = 0\n⊢ unbotD 0 (a * 0) = unbotD 0 a * unbotD 0 0",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithBot",
"HMul.hMul",
"MulZeroClass.to... | [
"case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : WithBot α\nha : ¬a = 0\nhb : b = 0\n⊢ unbotD 0 0 = unbotD 0 a * unbotD 0 0"
] | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 369,
"column": 4
} | {
"line": 369,
"column": 37
} | {
"line": 370,
"column": 4
} | [
{
"pp": "case succ\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMax a → a ∈ s → succ a ∈ s → f a ≤ f (succ a)\na : α\nha : a ∈ s\nn : ℕ\nhn : succ^[n] a ∈ s → f a ≤ f (s... | [
"case pos\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMax a → a ∈ s → succ a ∈ s → f a ≤ f (succ a)\na : α\nha : a ∈ s\nn : ℕ\nhn : succ^[n] a ∈ s → f a ≤ f (succ^[n] a)\nh... | by_cases hb' : IsMax (succ^[n] a) | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Order.SuccPred.Archimedean | {
"line": 400,
"column": 62
} | {
"line": 400,
"column": 76
} | {
"line": 400,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 400,
"column": 62
} | {
"line": 400,
"column": 76
} | {
"line": 400,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 400,
"column": 62
} | {
"line": 400,
"column": 76
} | {
"line": 400,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 403,
"column": 62
} | {
"line": 403,
"column": 76
} | {
"line": 403,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 403,
"column": 62
} | {
"line": 403,
"column": 76
} | {
"line": 403,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 403,
"column": 62
} | {
"line": 403,
"column": 76
} | {
"line": 403,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 406,
"column": 64
} | {
"line": 406,
"column": 78
} | {
"line": 406,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 406,
"column": 64
} | {
"line": 406,
"column": 78
} | {
"line": 406,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 406,
"column": 64
} | {
"line": 406,
"column": 78
} | {
"line": 406,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 409,
"column": 64
} | {
"line": 409,
"column": 78
} | {
"line": 409,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 409,
"column": 64
} | {
"line": 409,
"column": 78
} | {
"line": 409,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 409,
"column": 64
} | {
"line": 409,
"column": 78
} | {
"line": 409,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 457,
"column": 62
} | {
"line": 457,
"column": 76
} | {
"line": 457,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 457,
"column": 62
} | {
"line": 457,
"column": 76
} | {
"line": 457,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 457,
"column": 62
} | {
"line": 457,
"column": 76
} | {
"line": 457,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 460,
"column": 62
} | {
"line": 460,
"column": 76
} | {
"line": 460,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 460,
"column": 62
} | {
"line": 460,
"column": 76
} | {
"line": 460,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 460,
"column": 62
} | {
"line": 460,
"column": 76
} | {
"line": 460,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 463,
"column": 64
} | {
"line": 463,
"column": 78
} | {
"line": 463,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 463,
"column": 64
} | {
"line": 463,
"column": 78
} | {
"line": 463,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 463,
"column": 64
} | {
"line": 463,
"column": 78
} | {
"line": 463,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SuccPred.Archimedean | {
"line": 466,
"column": 64
} | {
"line": 466,
"column": 78
} | {
"line": 466,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.SuccPred.Archimedean | {
"line": 466,
"column": 64
} | {
"line": 466,
"column": 78
} | {
"line": 466,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SuccPred.Archimedean | {
"line": 466,
"column": 64
} | {
"line": 466,
"column": 78
} | {
"line": 466,
"column": 78
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Sym.Basic | {
"line": 311,
"column": 4
} | {
"line": 313,
"column": 78
} | {
"line": 313,
"column": 78
} | [
{
"pp": "case succ\nα : Type u_1\nβ : Type u_2\nn n' m : ℕ\ns : Sym α n\na b : α\ninst✝ : Subsingleton α\nn✝ : ℕ\n⊢ ∀ (a b : Sym α (n✝ + 1)), a = b",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Sym.replicate",
"Membership.mem",
"Exists... | [] | · intro s s'
obtain ⟨b, -⟩ := exists_mem s
rw [eq_replicate_of_subsingleton b s', eq_replicate_of_subsingleton b s] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Vector.Basic | {
"line": 69,
"column": 25
} | {
"line": 69,
"column": 40
} | {
"line": 69,
"column": 41
} | [
{
"pp": "α : Type u_1\nf : Fin 0 → α\n⊢ nil.toList = List.ofFn f",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.ofFn",
"id",
"instOfNatNat",
"List",
"List.ofFn_zero",
"Nat",
"List.Vector.nil",
"OfNat.o... | [
"α : Type u_1\nf : Fin 0 → α\n⊢ nil.toList = []"
] | List.ofFn_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Vector.Basic | {
"line": 292,
"column": 28
} | {
"line": 292,
"column": 46
} | {
"line": 292,
"column": 47
} | [
{
"pp": "α : Type u_1\nn : ℕ\nv : Vector α (n + 1)\n⊢ v.reverse.get 0 = v.get (Fin.last n)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"List.Vector.get",
"Eq.mpr",
"congrArg",
"List.get",
"List.Vector.get_eq_get_toList",
"id",
"Fin.instOfNat",
... | [
"α : Type u_1\nn : ℕ\nv : Vector α (n + 1)\n⊢ v.reverse.toList.get (Fin.cast ⋯ 0) = v.get (Fin.last n)"
] | get_eq_get_toList, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Small.Set | {
"line": 45,
"column": 6
} | {
"line": 45,
"column": 30
} | {
"line": 45,
"column": 30
} | [
{
"pp": "α : Type u1\nβ : Type u2\nγ : Type u3\nι : Type u4\nf : α → β → γ\ns : Set α\nt : Set β\ninst✝¹ : Small.{u, u1} ↑s\ninst✝ : Small.{u, u2} ↑t\n⊢ Small.{u, u3} ↑(Set.image2 f s t)",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"SProd.spro... | [
"α : Type u1\nβ : Type u2\nγ : Type u3\nι : Type u4\nf : α → β → γ\ns : Set α\nt : Set β\ninst✝¹ : Small.{u, u1} ↑s\ninst✝ : Small.{u, u2} ↑t\n⊢ Small.{u, u3} ↑(Function.uncurry f '' s ×ˢ t)"
] | ← Set.image_uncurry_prod | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Hom.Lex | {
"line": 135,
"column": 56
} | {
"line": 136,
"column": 44
} | {
"line": 138,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\nx y : α\nh : x < y\n⊢ (sumLexIicIoi x).symm y = toLex (Sum.inr ⟨y, h⟩)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Sum.Lex.LE",
"Set.Ioi",
"Equiv.instEquivLike",
"congrArg",
"Lex",
"Parti... | [] | by
rw [symm_apply_eq, sumLexIicIoi_apply_inr] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Part | {
"line": 459,
"column": 23
} | {
"line": 459,
"column": 32
} | {
"line": 459,
"column": 32
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\no : Part α\na : α\nh : a ∈ o\nf : α → Part β\n⊢ (some a).bind f = f a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part.some",
"Part.bind_some",
"id",
"Eq"
... | [
"α : Type u_1\nβ : Type u_2\no : Part α\na : α\nh : a ∈ o\nf : α → Part β\n⊢ f a = f a"
] | bind_some | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Part | {
"line": 701,
"column": 28
} | {
"line": 701,
"column": 45
} | {
"line": 701,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ma ++ mb ∈ a ++ b",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part.mem_bind_iff._simp_1",
"Part.instAppend",
... | [
"α : Type u_1\ninst✝ : Append α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ∃ a_1, a_1 ∈ a ∧ ∃ a, a ∈ b ∧ a_1 ++ a = ma ++ mb"
] | simp [append_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Part | {
"line": 710,
"column": 2
} | {
"line": 710,
"column": 19
} | {
"line": 710,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : Part α\nhab : (a ++ b).Dom\n⊢ (a ++ b).get hab = a.get ⋯ ++ b.get ⋯",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Part",
"Part.right_dom_of_append_dom",
"Part.left_dom_of_append_dom",
"Part.instAppend",
"id",
... | [
"α : Type u_1\ninst✝ : Append α\na b : Part α\nhab : (a ++ b).Dom\n⊢ (a.bind fun y ↦ map (fun x ↦ y ++ x) b).get ⋯ = a.get ⋯ ++ b.get ⋯"
] | simp [append_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Part | {
"line": 713,
"column": 2
} | {
"line": 713,
"column": 19
} | {
"line": 715,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"Part.instAppend",
"funext",
"instHAppendOfAppend",
"Part.... | [] | simp [append_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Part | {
"line": 713,
"column": 2
} | {
"line": 713,
"column": 19
} | {
"line": 715,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"Part.instAppend",
"funext",
"instHAppendOfAppend",
"Part.... | [] | simp [append_def] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Part | {
"line": 713,
"column": 2
} | {
"line": 713,
"column": 19
} | {
"line": 715,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Append α\na b : α\n⊢ some a ++ some b = some (a ++ b)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"Part.instAppend",
"funext",
"instHAppendOfAppend",
"Part.... | [] | simp [append_def] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.CompleteLattice.Chain | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 12
} | {
"line": 72,
"column": 13
} | [
{
"pp": "case union\nα : Type u_1\nr : α → α → Prop\nc₂ : Set α\ns✝ : Set (Set α)\na✝ : ∀ a ∈ s✝, ChainClosure r a\nih : ∀ a ∈ s✝, ∀ {c₁ : Set α}, ChainClosure r c₁ → c₁ ⊆ a → a = c₁ ∨ SuccChain r c₁ ⊆ a\nc₁ : Set α\nhc₁ : ChainClosure r c₁\nh : c₁ ⊆ ⋃₀ s✝\n⊢ ∀ x ∈ s✝, ¬x ⊆ c₁ → ¬SuccChain r c₁ ⊆ ⋃₀ s✝ → False"... | [
"case union\nα : Type u_1\nr : α → α → Prop\nc₂ : Set α\ns✝ : Set (Set α)\na✝ : ∀ a ∈ s✝, ChainClosure r a\nih : ∀ a ∈ s✝, ∀ {c₁ : Set α}, ChainClosure r c₁ → c₁ ⊆ a → a = c₁ ∨ SuccChain r c₁ ⊆ a\nc₁ : Set α\nhc₁ : ChainClosure r c₁\nh : c₁ ⊆ ⋃₀ s✝\nc₃ : Set α\n⊢ c₃ ∈ s✝ → ¬c₃ ⊆ c₁ → ¬SuccChain r c₁ ⊆ ⋃₀ s✝ → False... | intro c₃ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.SetTheory.Cardinal.ENat | {
"line": 320,
"column": 75
} | {
"line": 320,
"column": 92
} | {
"line": 320,
"column": 92
} | [
{
"pp": "m : ℕ∞\n⊢ ℵ₀ + ↑m = ℵ₀",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"id",
"Cardinal.aleph0",
"Cardinal.instAdd",
"instHAdd",
"HAdd.h... | [
"m : ℕ∞\n⊢ ℵ₀ = ℵ₀"
] | aleph0_add_ofENat | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.ToNat | {
"line": 68,
"column": 2
} | {
"line": 69,
"column": 20
} | {
"line": 71,
"column": 0
} | [
{
"pp": "⊢ StrictMonoOn (⇑toNat) (Iio ℵ₀)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroOneClass",
"Preorder.toLT",
"_private.Mathlib.SetTheory.Cardinal.ToNat.0.Cardinal.toNat_strictMonoOn._... | [] | simp only [← range_natCast, StrictMonoOn, forall_mem_range, toNat_natCast, Nat.cast_lt]
exact fun _ _ ↦ id | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.ToNat | {
"line": 68,
"column": 2
} | {
"line": 69,
"column": 20
} | {
"line": 71,
"column": 0
} | [
{
"pp": "⊢ StrictMonoOn (⇑toNat) (Iio ℵ₀)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroOneClass",
"Preorder.toLT",
"_private.Mathlib.SetTheory.Cardinal.ToNat.0.Cardinal.toNat_strictMonoOn._... | [] | simp only [← range_natCast, StrictMonoOn, forall_mem_range, toNat_natCast, Nat.cast_lt]
exact fun _ _ ↦ id | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Order | {
"line": 339,
"column": 6
} | {
"line": 339,
"column": 14
} | {
"line": 339,
"column": 14
} | [
{
"pp": "case mk\nα : Type u\n⊢ #α < 2 ^ #α",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"Cardinal.mk",
... | [
"case mk\nα : Type u\n⊢ #α < #(Set α)"
] | ← mk_set | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Order | {
"line": 402,
"column": 6
} | {
"line": 402,
"column": 17
} | {
"line": 402,
"column": 18
} | [
{
"pp": "case mk\nα β : Type u_1\nh : #α < #β\nf : α ↪ β\nhf : ¬Surjective ⇑f\n⊢ #α + 1 ≤ #β",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Function.Surjective.eq_1",
"congrArg",
"Exists",
"Eq.mp",
"Function.Embedding",
"Function.instFunLikeEmbedding",
... | [
"case mk\nα β : Type u_1\nh : #α < #β\nf : α ↪ β\nhf : ¬∀ (b : β), ∃ a, f a = b\n⊢ #α + 1 ≤ #β"
] | Surjective, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Basic | {
"line": 391,
"column": 8
} | {
"line": 391,
"column": 22
} | {
"line": 391,
"column": 23
} | [
{
"pp": "n : ℕ\nh : IsSuccLimit ↑n.succ\n⊢ False",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.cast_succ",
"AddMonoid.toAddSemigroup",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.co... | [
"n : ℕ\nh : IsSuccLimit (↑n + 1)\n⊢ False"
] | Nat.cast_succ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Basic | {
"line": 943,
"column": 2
} | {
"line": 944,
"column": 43
} | {
"line": 946,
"column": 0
} | [
{
"pp": "α β : Type u\nf : α → β\ns : Set β\nh : Injective f\n⊢ #↑(f ⁻¹' s) ≤ #↑s",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"Cardinal.lift",
"Cardinal.mk",
"Set.Elem",
"id",
"LE.le",
"Cardinal.inst... | [] | rw [← lift_id #(↑(f ⁻¹' s)), ← lift_id #(↑s)]
exact mk_preimage_of_injective_lift f s h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Basic | {
"line": 943,
"column": 2
} | {
"line": 944,
"column": 43
} | {
"line": 946,
"column": 0
} | [
{
"pp": "α β : Type u\nf : α → β\ns : Set β\nh : Injective f\n⊢ #↑(f ⁻¹' s) ≤ #↑s",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"Cardinal.lift",
"Cardinal.mk",
"Set.Elem",
"id",
"LE.le",
"Cardinal.inst... | [] | rw [← lift_id #(↑(f ⁻¹' s)), ← lift_id #(↑s)]
exact mk_preimage_of_injective_lift f s h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Algebra.Defs | {
"line": 238,
"column": 59
} | {
"line": 238,
"column": 75
} | {
"line": 240,
"column": 0
} | [
{
"pp": "R : Type u\nS : Type v\nA : Type w\nB : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Module R A\nh₁ : ∀ (r : R) (x y : A), r • x * y = r • (x * y)\nh₂ : ∀ (r : R) (x y : A), x * r • y = r • (x * y)\nr : R\nx : A\n⊢ x * r • 1 = r • x",
"ppTerm": "?m.61",
"assigned": true,
... | [] | rw [h₂, mul_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Algebra.Defs | {
"line": 238,
"column": 59
} | {
"line": 238,
"column": 75
} | {
"line": 240,
"column": 0
} | [
{
"pp": "R : Type u\nS : Type v\nA : Type w\nB : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Module R A\nh₁ : ∀ (r : R) (x y : A), r • x * y = r • (x * y)\nh₂ : ∀ (r : R) (x y : A), x * r • y = r • (x * y)\nr : R\nx : A\n⊢ x * r • 1 = r • x",
"ppTerm": "?m.61",
"assigned": true,
... | [] | rw [h₂, mul_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Algebra.Defs | {
"line": 238,
"column": 59
} | {
"line": 238,
"column": 75
} | {
"line": 240,
"column": 0
} | [
{
"pp": "R : Type u\nS : Type v\nA : Type w\nB : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Module R A\nh₁ : ∀ (r : R) (x y : A), r • x * y = r • (x * y)\nh₂ : ∀ (r : R) (x y : A), x * r • y = r • (x * y)\nr : R\nx : A\n⊢ x * r • 1 = r • x",
"ppTerm": "?m.61",
"assigned": true,
... | [] | rw [h₂, mul_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Algebra.Defs | {
"line": 321,
"column": 79
} | {
"line": 322,
"column": 36
} | {
"line": 324,
"column": 0
} | [
{
"pp": "R : Type u\nA : Type w\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\ns : R\nx y : A\n⊢ x * s • y = s • (x * y)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"HMul.hMul",
"Algebra.algebraMap",
"congrArg",
... | [] | by
rw [smul_def, smul_def, left_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.GroupAction.DomAct.Basic | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 44
} | {
"line": 185,
"column": 4
} | [
{
"pp": "M : Type u_1\nβ : Type u_2\nα : Type u_3\nN : Type u_4\ninst✝² : SMul M α\ninst✝¹ : FaithfulSMul M α\ninst✝ : Nontrivial β\nc₁ c₂ : Mᵈᵐᵃ\nh : ∀ (a : α → β), c₁ • a = c₂ • a\na : α\n⊢ mk.symm c₁ • a = mk.symm c₂ • a",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"DomMulAct",... | [
"M : Type u_1\nβ : Type u_2\nα : Type u_3\nN : Type u_4\ninst✝² : SMul M α\ninst✝¹ : FaithfulSMul M α\ninst✝ : Nontrivial β\nc₁ c₂ : Mᵈᵐᵃ\nh : ∀ (a : α → β), c₁ • a = c₂ • a\na : α\nx y : β\nhne : x ≠ y\n⊢ mk.symm c₁ • a = mk.symm c₂ • a"
] | rcases exists_pair_ne β with ⟨x, y, hne⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.GroupTheory.GroupAction.Hom | {
"line": 190,
"column": 52
} | {
"line": 190,
"column": 63
} | {
"line": 190,
"column": 64
} | [
{
"pp": "M' : Type u_1\nX : Type u_5\ninst✝⁶ : SMul M' X\nY : Type u_6\ninst✝⁵ : SMul M' Y\nF : Type u_8\ninst✝⁴ : FunLike F X Y\ninst✝³ : MulOneClass X\ninst✝² : SMul X Y\ninst✝¹ : IsScalarTower M' X Y\ninst✝ : MulActionHomClass F X X Y\nf : F\nm : M'\nx : X\n⊢ (m • x) • f 1 = id m • f x",
"ppTerm": "?m.47... | [
"M' : Type u_1\nX : Type u_5\ninst✝⁶ : SMul M' X\nY : Type u_6\ninst✝⁵ : SMul M' Y\nF : Type u_8\ninst✝⁴ : FunLike F X Y\ninst✝³ : MulOneClass X\ninst✝² : SMul X Y\ninst✝¹ : IsScalarTower M' X Y\ninst✝ : MulActionHomClass F X X Y\nf : F\nm : M'\nx : X\n⊢ m • x • f 1 = id m • f x"
] | smul_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.LinearMap.End | {
"line": 141,
"column": 12
} | {
"line": 141,
"column": 28
} | {
"line": 142,
"column": 2
} | [
{
"pp": "case zero\nR : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_6\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂ M₂\nσ₁₂ : R →+* R₂\nf : M →ₛₗ[σ₁₂] M₂\ng : End R M\ng₂ : End R₂ M₂\nh : g₂ ∘ₛₗ f = f ∘ₛₗ g\n⊢ (g₂ ^... | [] | simp [one_eq_id] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Module.LinearMap.End | {
"line": 141,
"column": 12
} | {
"line": 141,
"column": 28
} | {
"line": 142,
"column": 2
} | [
{
"pp": "case zero\nR : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_6\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂ M₂\nσ₁₂ : R →+* R₂\nf : M →ₛₗ[σ₁₂] M₂\ng : End R M\ng₂ : End R₂ M₂\nh : g₂ ∘ₛₗ f = f ∘ₛₗ g\n⊢ (g₂ ^... | [] | simp [one_eq_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.LinearMap.End | {
"line": 141,
"column": 12
} | {
"line": 141,
"column": 28
} | {
"line": 142,
"column": 2
} | [
{
"pp": "case zero\nR : Type u_1\nR₂ : Type u_2\nM : Type u_4\nM₂ : Type u_6\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Semiring R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂ M₂\nσ₁₂ : R →+* R₂\nf : M →ₛₗ[σ₁₂] M₂\ng : End R M\ng₂ : End R₂ M₂\nh : g₂ ∘ₛₗ f = f ∘ₛₗ g\n⊢ (g₂ ^... | [] | simp [one_eq_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Module.Submodule.Defs | {
"line": 378,
"column": 28
} | {
"line": 378,
"column": 43
} | {
"line": 379,
"column": 2
} | [
{
"pp": "G : Type u''\nS : Type u'\nR : Type u\nM : Type v\nι : Type w\nT : Type u_1\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Semiring S\ninst✝⁶ : Module R M\ninst✝⁵ : SMul S R\ninst✝⁴ : Module S M\ninst✝³ : IsScalarTower S R M\ninst✝² : SetLike T M\ninst✝¹ : AddSubmonoidClass T M\ninst✝ : SMulM... | [] | simp [mul_smul] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.GroupTheory.GroupAction.SubMulAction | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 30
} | {
"line": 135,
"column": 30
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass S R M\nN : S\nx : M\nh : ∀ (a : R), a • x ∈ N\n⊢ x ∈ N",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"instHSMul",
"Mo... | [] | simpa using h 1 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.GroupTheory.GroupAction.SubMulAction | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 30
} | {
"line": 135,
"column": 30
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass S R M\nN : S\nx : M\nh : ∀ (a : R), a • x ∈ N\n⊢ x ∈ N",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"instHSMul",
"Mo... | [] | simpa using h 1 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.GroupAction.SubMulAction | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 30
} | {
"line": 135,
"column": 30
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass S R M\nN : S\nx : M\nh : ∀ (a : R), a • x ∈ N\n⊢ x ∈ N",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"instHSMul",
"Mo... | [] | simpa using h 1 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Module.Submodule.Map | {
"line": 459,
"column": 19
} | {
"line": 459,
"column": 60
} | {
"line": 459,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_5\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\np p' : Submodule R M\nx : M\n⊢ x ∈ map p.subtype (comap p.subtype p') → x ∈ p ⊓ p'",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"Submodule",
"RingHomSurjective.ids",
... | [] | rintro ⟨⟨_, h₁⟩, h₂, rfl⟩; exact ⟨h₁, h₂⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.Submodule.Map | {
"line": 459,
"column": 19
} | {
"line": 459,
"column": 60
} | {
"line": 459,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_5\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\np p' : Submodule R M\nx : M\n⊢ x ∈ map p.subtype (comap p.subtype p') → x ∈ p ⊓ p'",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"Submodule",
"RingHomSurjective.ids",
... | [] | rintro ⟨⟨_, h₁⟩, h₂, rfl⟩; exact ⟨h₁, h₂⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.GroupWithZero.Center | {
"line": 28,
"column": 28
} | {
"line": 28,
"column": 37
} | {
"line": 28,
"column": 38
} | [
{
"pp": "M₀ : Type u_1\ninst✝ : MulZeroClass M₀\nx✝¹ x✝ : M₀\n⊢ x✝¹ * x✝ * 0 = x✝¹ * (x✝ * 0)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"id",
"MulZeroClass.mul_zero",
"Zero.toOfNat0",
... | [
"M₀ : Type u_1\ninst✝ : MulZeroClass M₀\nx✝¹ x✝ : M₀\n⊢ 0 = x✝¹ * (x✝ * 0)"
] | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.GroupWithZero.Center | {
"line": 28,
"column": 38
} | {
"line": 28,
"column": 47
} | {
"line": 28,
"column": 48
} | [
{
"pp": "M₀ : Type u_1\ninst✝ : MulZeroClass M₀\nx✝¹ x✝ : M₀\n⊢ 0 = x✝¹ * (x✝ * 0)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"id",
"MulZeroClass.mul_zero",
"Zero.toOfNat0",
"OfNat... | [
"M₀ : Type u_1\ninst✝ : MulZeroClass M₀\nx✝¹ x✝ : M₀\n⊢ 0 = x✝¹ * 0"
] | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Centralizer | {
"line": 27,
"column": 57
} | {
"line": 27,
"column": 65
} | {
"line": 27,
"column": 66
} | [
{
"pp": "M : Type u_1\nS : Set M\na b : M\ninst✝ : Distrib M\nha : a ∈ S.centralizer\nhb : b ∈ S.centralizer\nc : M\nhc : c ∈ S\n⊢ c * (a + b) = a * c + b * c",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrAr... | [
"M : Type u_1\nS : Set M\na b : M\ninst✝ : Distrib M\nha : a ∈ S.centralizer\nhb : b ∈ S.centralizer\nc : M\nhc : c ∈ S\n⊢ c * a + c * b = a * c + b * c"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 32,
"column": 24
} | {
"line": 32,
"column": 38
} | {
"line": 32,
"column": 39
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : ↑n * (x✝¹ * x✝) = ↑n * x✝¹ * x✝\n⊢ ↑(n + 1) * (x✝¹ * x✝) = ↑(n + 1) * x✝¹ * x✝",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.... | [
"case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : ↑n * (x✝¹ * x✝) = ↑n * x✝¹ * x✝\n⊢ (↑n + 1) * (x✝¹ * x✝) = (↑n + 1) * x✝¹ * x✝"
] | Nat.cast_succ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 35,
"column": 33
} | {
"line": 35,
"column": 42
} | {
"line": 35,
"column": 43
} | [
{
"pp": "case zero\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\n⊢ x✝¹ * x✝ * 0 = x✝¹ * (x✝ * 0)",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
... | [
"case zero\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\n⊢ 0 = x✝¹ * (x✝ * 0)"
] | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 35,
"column": 43
} | {
"line": 35,
"column": 52
} | {
"line": 35,
"column": 53
} | [
{
"pp": "case zero\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\n⊢ 0 = x✝¹ * (x✝ * 0)",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"AddMonoid.... | [
"case zero\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\n⊢ 0 = x✝¹ * 0"
] | mul_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 24
} | {
"line": 36,
"column": 38
} | {
"line": 36,
"column": 39
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * x✝ * ↑(n + 1) = x✝¹ * (x✝ * ↑(n + 1))",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.... | [
"case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * x✝ * (↑n + 1) = x✝¹ * (x✝ * (↑n + 1))"
] | Nat.cast_succ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 39
} | {
"line": 36,
"column": 47
} | {
"line": 36,
"column": 48
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * x✝ * (↑n + 1) = x✝¹ * (x✝ * (↑n + 1))",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssocSemiring.to... | [
"case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * x✝ * ↑n + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * (↑n + 1))"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 53
} | {
"line": 36,
"column": 61
} | {
"line": 36,
"column": 62
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * (x✝ * ↑n) + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * (↑n + 1))",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssoc... | [
"case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * (x✝ * ↑n) + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * ↑n + x✝ * 1)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 36,
"column": 62
} | {
"line": 36,
"column": 70
} | {
"line": 36,
"column": 71
} | [
{
"pp": "case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * (x✝ * ↑n) + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * ↑n + x✝ * 1)",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAs... | [
"case succ\nM : Type u_1\ninst✝ : NonAssocSemiring M\nx✝¹ x✝ : M\nn : ℕ\nihn : x✝¹ * x✝ * ↑n = x✝¹ * (x✝ * ↑n)\n⊢ x✝¹ * (x✝ * ↑n) + x✝¹ * x✝ * 1 = x✝¹ * (x✝ * ↑n) + x✝¹ * (x✝ * 1)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 56,
"column": 12
} | {
"line": 56,
"column": 20
} | {
"line": 56,
"column": 21
} | [
{
"pp": "M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * (-1 + -↑n) = x✝¹ * (x✝ * (-1 + -↑n))",
"ppTerm": "?m.192",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClas... | [
"M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * (-1 + -↑n))"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 56,
"column": 21
} | {
"line": 56,
"column": 29
} | {
"line": 56,
"column": 30
} | [
{
"pp": "M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * (-1 + -↑n))",
"ppTerm": "?m.200",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"AddMonoid.toAd... | [
"M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * -1 + x✝ * -↑n)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Center | {
"line": 56,
"column": 30
} | {
"line": 56,
"column": 38
} | {
"line": 56,
"column": 39
} | [
{
"pp": "M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * -1 + x✝ * -↑n)",
"ppTerm": "?m.208",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"AddMonoid.t... | [
"M : Type u_1\ninst✝ : NonAssocRing M\nn✝ : ℤ\nx✝¹ x✝ : M\nn : ℕ\n⊢ x✝¹ * x✝ * -1 + x✝¹ * x✝ * -↑n = x✝¹ * (x✝ * -1) + x✝¹ * (x✝ * -↑n)"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
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