module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Ring.Abs | {
"line": 251,
"column": 2
} | {
"line": 251,
"column": 13
} | {
"line": 251,
"column": 14
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na : R\nn : ℕ\n⊢ a ^ n = -1 ↔ a = -1 ∧ Odd n",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na : R\nn : ℕ\n⊢ a ^ n = -1 ↔ a = -1 ∧ Odd n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Bounds.Image | {
"line": 171,
"column": 50
} | {
"line": 172,
"column": 66
} | {
"line": 174,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : Preorder β\nf : α → β\na : α\ns : Set α\nhf : StrictMono f\n⊢ IsGreatest (f '' s) (f a) ↔ IsGreatest s a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.mem_image._simp_1",
"PartialOrder.toP... | [] | by
simp [IsGreatest, hf.injective.eq_iff, hf.mem_upperBounds_image] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 441,
"column": 13
} | {
"line": 441,
"column": 24
} | {
"line": 441,
"column": 25
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Icc a b = Ioc a b\n⊢ ¬a ≤ b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Icc a b = Ioc a b\n⊢ ¬a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Basic | {
"line": 448,
"column": 13
} | {
"line": 448,
"column": 24
} | {
"line": 448,
"column": 25
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Icc a b = Ioo a b\n⊢ ¬a ≤ b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Icc a b = Ioo a b\n⊢ ¬a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Basic | {
"line": 455,
"column": 13
} | {
"line": 455,
"column": 24
} | {
"line": 455,
"column": 25
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Ioc a b = Ico a b\n⊢ ¬a < b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Ioc a b = Ico a b\n⊢ ¬a < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Basic | {
"line": 459,
"column": 13
} | {
"line": 459,
"column": 24
} | {
"line": 459,
"column": 25
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Ioo a b = Ioc a b\n⊢ ¬a < b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Preorder α\na b : α\nh : Ioo a b = Ioc a b\n⊢ ¬a < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Basic | {
"line": 482,
"column": 30
} | {
"line": 482,
"column": 41
} | {
"line": 482,
"column": 42
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\na b c : α\ny : ↑(Icc a a)\n⊢ ↑y = ↑⟨a, ⋯⟩",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"Membership.mem",
"id",
"Subtype.mk",
"Set.instIccUnique._proof_1",
"Set.Icc",
"Subt... | [
"α : Type u_1\ninst✝ : PartialOrder α\na b c : α\ny : ↑(Icc a a)\n⊢ ↑y = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Bounds.Image | {
"line": 436,
"column": 2
} | {
"line": 436,
"column": 35
} | {
"line": 436,
"column": 36
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type u_1\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → γ\nhf : BddAbove (range f)\nhg : Monotone g\n⊢ BddAbove (range (g ∘ f))",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"congrArg",
... | [
"α : Type u\nβ : Type v\nγ : Type u_1\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → γ\nhf : BddAbove (range f)\nhg : Monotone g\n⊢ BddAbove (g '' range f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WellFounded | {
"line": 45,
"column": 6
} | {
"line": 45,
"column": 22
} | {
"line": 45,
"column": 22
} | [
{
"pp": "α : Sort u_1\nr : α → α → Prop\nx : α\n⊢ ¬Acc r x ↔ Nonempty { f // f 0 = x ∧ ∀ (n : ℕ), r (f (n + 1)) (f n) }",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Exists",
"id",
"Subtype",
"instOfNatNat",
"Acc",
"i... | [
"α : Sort u_1\nr : α → α → Prop\nx : α\n⊢ ¬Acc r x ↔ ∃ a, a 0 = x ∧ ∀ (n : ℕ), r (a (n + 1)) (a n)"
] | nonempty_subtype | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Equiv.Set | {
"line": 140,
"column": 2
} | {
"line": 140,
"column": 49
} | {
"line": 140,
"column": 50
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Set α\nt : Set β\nu : Set γ\n⊢ ⇑(prodAssoc α β γ) '' (s ×ˢ t) ×ˢ u = s ×ˢ t ×ˢ u",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"Equiv.instEquivLike",
"SProd.sprod",
"congrArg",... | [
"α : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Set α\nt : Set β\nu : Set γ\n⊢ ⇑(prodAssoc α β γ).symm ⁻¹' (s ×ˢ t) ×ˢ u = s ×ˢ t ×ˢ u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Equiv.Set | {
"line": 139,
"column": 60
} | {
"line": 140,
"column": 74
} | {
"line": 142,
"column": 0
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Set α\nt : Set β\nu : Set γ\n⊢ ⇑(prodAssoc α β γ) '' (s ×ˢ t) ×ˢ u = s ×ˢ t ×ˢ u",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"Equiv.instEquivLike",
"SProd.sprod",
"congrArg",... | [] | by
simpa only [Equiv.image_eq_preimage_symm] using prod_assoc_symm_preimage | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Logic.Equiv.Set | {
"line": 168,
"column": 6
} | {
"line": 168,
"column": 17
} | {
"line": 168,
"column": 18
} | [
{
"pp": "α✝¹ : Sort u\nβ✝¹ : Sort v\nγ : Sort w\nα✝ : Type u_1\nβ✝ : Type u_2\nα : Type u_3\nβ : Type u_4\ne : α ≃ β\ns : Set α\na : α\nm : a ∈ s\n⊢ e.symm ↑⟨e a, ⋯⟩ ∈ s",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Eq... | [
"α✝¹ : Sort u\nβ✝¹ : Sort v\nγ : Sort w\nα✝ : Type u_1\nβ✝ : Type u_2\nα : Type u_3\nβ : Type u_4\ne : α ≃ β\ns : Set α\na : α\nm : a ∈ s\n⊢ a ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Equiv.Set | {
"line": 464,
"column": 6
} | {
"line": 464,
"column": 42
} | {
"line": 464,
"column": 43
} | [
{
"pp": "α✝¹ : Sort u\nβ✝¹ : Sort v\nγ : Sort w\nα✝ : Type u_1\nβ✝ : Type u_2\nα : Type u_3\nβ : Type u_4\nf : α → β\ns : Set ↑(range f)\ny : ↑(range f)\nm : y ∈ s\n⊢ ⟨f ↑⟨rangeSplitting f y, ⋯⟩, ⋯⟩ ∈ s",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Subtype.mk.congr... | [
"α✝¹ : Sort u\nβ✝¹ : Sort v\nγ : Sort w\nα✝ : Type u_1\nβ✝ : Type u_2\nα : Type u_3\nβ : Type u_4\nf : α → β\ns : Set ↑(range f)\ny : ↑(range f)\nm : y ∈ s\n⊢ y ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Invertible | {
"line": 34,
"column": 60
} | {
"line": 34,
"column": 94
} | {
"line": 36,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\na : R\ninst✝ : Invertible a\n⊢ ⅟a < 0 ↔ a < 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"invOf_nonneg._simp_1",
"Preorder.t... | [] | simp only [← not_le, invOf_nonneg] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Invertible | {
"line": 34,
"column": 60
} | {
"line": 34,
"column": 94
} | {
"line": 36,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\na : R\ninst✝ : Invertible a\n⊢ ⅟a < 0 ↔ a < 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"invOf_nonneg._simp_1",
"Preorder.t... | [] | simp only [← not_le, invOf_nonneg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Invertible | {
"line": 34,
"column": 60
} | {
"line": 34,
"column": 94
} | {
"line": 36,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\na : R\ninst✝ : Invertible a\n⊢ ⅟a < 0 ↔ a < 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"invOf_nonneg._simp_1",
"Preorder.t... | [] | simp only [← not_le, invOf_nonneg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Bounds.Basic | {
"line": 893,
"column": 2
} | {
"line": 893,
"column": 50
} | {
"line": 893,
"column": 51
} | [
{
"pp": "α : Type u_1\ninst✝ : HeytingAlgebra α\na : α\n⊢ IsGreatest {w | Disjoint w a} aᶜ",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Order.Bounds.Basic.0.isGreatest_compl._simp_1_1",
"Eq.mpr",
"congrArg",
"Compl.compl",
"OrderBot.toBot"... | [
"α : Type u_1\ninst✝ : HeytingAlgebra α\na : α\n⊢ IsGreatest {w | w ⊓ a ≤ ⊥} aᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Bounds.Basic | {
"line": 897,
"column": 2
} | {
"line": 897,
"column": 70
} | {
"line": 897,
"column": 71
} | [
{
"pp": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na : α\n⊢ IsLeast {w | Codisjoint a w} (￢a)",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"CoheytingAlgebra.toHNot",
"Eq.mpr",
"Codisjoint",
"Lattice.toSemilatticeSup",
"congrArg",
"PartialOrder.toPreor... | [
"α : Type u_1\ninst✝ : CoheytingAlgebra α\na : α\n⊢ IsLeast {w | ⊤ ≤ a ⊔ w} (￢a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 202,
"column": 43
} | {
"line": 202,
"column": 54
} | {
"line": 202,
"column": 55
} | [
{
"pp": "α : Type u_1\ninst✝ : Semiring α\nna nb nc da db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * db + nb * da = k * nc\nh₂ : da * db = k * dc\n⊢ Invertible ↑(da * db)",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCo... | [
"α : Type u_1\ninst✝ : Semiring α\nna nb nc da db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * db + nb * da = k * nc\nh₂ : da * db = k * dc\n⊢ Invertible (↑da * ↑db)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 224,
"column": 43
} | {
"line": 224,
"column": 54
} | {
"line": 224,
"column": 55
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * ↑db + nb * ↑da = ↑k * nc\nh₂ : da * db = k * dc\n⊢ Invertible ↑(da * db)",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toA... | [
"α : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * ↑db + nb * ↑da = ↑k * nc\nh₂ : da * db = k * dc\n⊢ Invertible (↑da * ↑db)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 450,
"column": 43
} | {
"line": 450,
"column": 54
} | {
"line": 450,
"column": 55
} | [
{
"pp": "α : Type u_1\ninst✝ : Semiring α\nna nb nc da db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * nb = k * nc\nh₂ : da * db = k * dc\n⊢ Invertible ↑(da * db)",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWi... | [
"α : Type u_1\ninst✝ : Semiring α\nna nb nc da db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * nb = k * nc\nh₂ : da * db = k * dc\n⊢ Invertible (↑da * ↑db)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Abel | {
"line": 235,
"column": 2
} | {
"line": 235,
"column": 39
} | {
"line": 235,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝ : AddCommGroup α\nn : ℤ\nx a : α\nn' : ℤ\na' : α\nh₁ : -n = n'\nh₂ : -a = a'\n⊢ -termg n x a = termg n' x a'",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"Eq.mpr",
"NegZeroClass.toNeg",
"instHSMul",
"neg_zsmul",
... | [
"α : Type u_1\ninst✝ : AddCommGroup α\nn : ℤ\nx a : α\nn' : ℤ\na' : α\nh₁ : -n = n'\nh₂ : -a = a'\n⊢ -a + -(n • x) = -(n • x) + -a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 28
} | {
"line": 39,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 ≤ a\nhb₀ : 0 < b\nhb₁ : b ≤ 1\n⊢ a ≤ a / b",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 ≤ a\nhb₀ : 0 < b\nhb₁ : b ≤ 1\n⊢ a ≤ a / b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 13
} | {
"line": 50,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ 1 / a ≤ b ↔ 1 / b ≤ a",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DivInvMonoid.toI... | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ a⁻¹ ≤ b ↔ b⁻¹ ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 13
} | {
"line": 53,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ 1 / a < b ↔ 1 / b < a",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DivInvMonoid.toI... | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ a⁻¹ < b ↔ b⁻¹ < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 13
} | {
"line": 56,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ a ≤ 1 / b ↔ b ≤ 1 / a",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DivInvMonoid.toI... | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ a ≤ b⁻¹ ↔ b ≤ a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 13
} | {
"line": 59,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ a < 1 / b ↔ b < 1 / a",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DivInvMonoid.toI... | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nhb : 0 < b\n⊢ a < b⁻¹ ↔ b < a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 13
} | {
"line": 70,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : a ≤ b\n⊢ 1 / b ≤ 1 / a",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DivInvMonoid.toInv",
... | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : a ≤ b\n⊢ b⁻¹ ≤ a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 13
} | {
"line": 76,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : 1 / a ≤ 1 / b\n⊢ b ≤ a",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : 1 / a ≤ 1 / b\n⊢ b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 13
} | {
"line": 79,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : 1 / a < 1 / b\n⊢ b < a",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : 1 / a < 1 / b\n⊢ b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 28
} | {
"line": 85,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\nha : 0 ≤ a\nhb : 1 ≤ b\n⊢ a / b ≤ a",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\nha : 0 ≤ a\nhb : 1 ≤ b\n⊢ a / b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 28
} | {
"line": 89,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\nha : 0 < a\nhb : 1 < b\n⊢ a / b < a",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\nha : 0 < a\nhb : 1 < b\n⊢ a / b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 470,
"column": 43
} | {
"line": 470,
"column": 54
} | {
"line": 470,
"column": 55
} | [
{
"pp": "α : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * nb = ↑k * nc\nh₂ : da * db = k * dc\n⊢ Invertible ↑(da * db)",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoid... | [
"α : Type u_1\ninst✝ : Ring α\nna nb nc : ℤ\nda db dc k : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh₁ : na * nb = ↑k * nc\nh₂ : da * db = k * dc\n⊢ Invertible (↑da * ↑db)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 143,
"column": 58
} | {
"line": 145,
"column": 41
} | {
"line": 147,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a / 3 + a / 3 + a / 3 = a",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"instHDiv",
... | [] | by
rw [← add_div, ← add_div, ← two_mul, ← add_one_mul 2 a, two_add_one_eq_three,
mul_div_cancel_left₀ a three_ne_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Field.Basic | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 35
} | {
"line": 182,
"column": 36
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : Semifield α\ninst✝³ : PartialOrder α\ninst✝² : PosMulReflectLT α\ninst✝¹ : IsStrictOrderedRing α\nβ : Type u_4\ninst✝ : Preorder β\nf : β → α\nhf : StrictMono f\nc : α\nhc : 0 < c\n⊢ StrictMono fun x ↦ f x / c",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_2\ninst✝⁴ : Semifield α\ninst✝³ : PartialOrder α\ninst✝² : PosMulReflectLT α\ninst✝¹ : IsStrictOrderedRing α\nβ : Type u_4\ninst✝ : Preorder β\nf : β → α\nhf : StrictMono f\nc : α\nhc : 0 < c\n⊢ StrictMono fun x ↦ f x * c⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 556,
"column": 24
} | {
"line": 556,
"column": 52
} | {
"line": 556,
"column": 53
} | [
{
"pp": "α : Type u\ninst✝ : DivisionSemiring α\nx✝³ x✝² : α\nx✝¹ x✝ : ℕ\nh : IsNNRat (x✝³ * x✝²⁻¹) x✝¹ x✝\n⊢ IsNNRat (x✝³ / x✝²) x✝¹ x✝",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"GroupWithZero.toD... | [
"α : Type u\ninst✝ : DivisionSemiring α\nx✝³ x✝² : α\nx✝¹ x✝ : ℕ\nh : IsNNRat (x✝³ * x✝²⁻¹) x✝¹ x✝\n⊢ IsNNRat (x✝³ * x✝²⁻¹) x✝¹ x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Basic | {
"line": 560,
"column": 24
} | {
"line": 560,
"column": 52
} | {
"line": 560,
"column": 53
} | [
{
"pp": "α : Type u\ninst✝ : DivisionRing α\nx✝³ x✝² : α\nx✝¹ : ℤ\nx✝ : ℕ\nh : IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝\n⊢ IsRat (x✝³ / x✝²) x✝¹ x✝",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass... | [
"α : Type u\ninst✝ : DivisionRing α\nx✝³ x✝² : α\nx✝¹ : ℤ\nx✝ : ℕ\nh : IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝\n⊢ IsRat (x✝³ * x✝²⁻¹) x✝¹ x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 261,
"column": 48
} | {
"line": 261,
"column": 70
} | {
"line": 261,
"column": 71
} | [
{
"pp": "α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\ns : Set α\nha : 0 ≤ a\nhs : IsGLB s b\n⊢ IsGLB ((fun b ↦ b * a) '' s) (b * a)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMu... | [
"α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\ns : Set α\nha : 0 ≤ a\nhs : IsGLB s b\n⊢ IsGLB ((fun a_1 ↦ a * a_1) '' s) (a * b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 280,
"column": 48
} | {
"line": 280,
"column": 70
} | {
"line": 280,
"column": 71
} | [
{
"pp": "α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\ns : Set α\nha : 0 ≤ a\nhs : IsLUB s b\n⊢ IsLUB ((fun b ↦ b * a) '' s) (b * a)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMu... | [
"α : Type u_2\ninst✝³ : Semifield α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\na b : α\ninst✝ : IsStrictOrderedRing α\ns : Set α\nha : 0 ≤ a\nhs : IsLUB s b\n⊢ IsLUB ((fun a_1 ↦ a * a_1) '' s) (a * b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 376,
"column": 2
} | {
"line": 376,
"column": 35
} | {
"line": 376,
"column": 36
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nh : b ≤ a\nhb : b ≤ 0\n⊢ a / b ≤ 1",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nh : b ≤ a\nhb : b ≤ 0\n⊢ a / b ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 381,
"column": 6
} | {
"line": 381,
"column": 16
} | {
"line": 381,
"column": 17
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ ≤ b⁻¹ ↔ b ≤ a",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv"... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ 1 / a ≤ b⁻¹ ↔ b ≤ a"
] | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 394,
"column": 2
} | {
"line": 394,
"column": 13
} | {
"line": 394,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ < b ↔ b⁻¹ < a",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ < b ↔ b⁻¹ < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 13
} | {
"line": 397,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a < b⁻¹ ↔ b < a⁻¹",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a < b⁻¹ ↔ b < a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 475,
"column": 2
} | {
"line": 475,
"column": 13
} | {
"line": 475,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ 1 / a ≤ b ↔ 1 / b ≤ a",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv"... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ ≤ b ↔ b⁻¹ ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 478,
"column": 2
} | {
"line": 478,
"column": 13
} | {
"line": 478,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ 1 / a < b ↔ 1 / b < a",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"Preorder.... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ < b ↔ b⁻¹ < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 481,
"column": 2
} | {
"line": 481,
"column": 13
} | {
"line": 481,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a ≤ 1 / b ↔ b ≤ 1 / a",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv"... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a ≤ b⁻¹ ↔ b ≤ a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 484,
"column": 2
} | {
"line": 484,
"column": 13
} | {
"line": 484,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a < 1 / b ↔ b < 1 / a",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"Preorder.... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a < b⁻¹ ↔ b < a⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 496,
"column": 2
} | {
"line": 496,
"column": 13
} | {
"line": 496,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\nh : 1 / a ≤ 1 / b\n⊢ b ≤ a",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\nh : 1 / a ≤ 1 / b\n⊢ b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 499,
"column": 2
} | {
"line": 499,
"column": 13
} | {
"line": 499,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\nh : 1 / a < 1 / b\n⊢ b < a",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nhb : b < 0\nh : 1 / a < 1 / b\n⊢ b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 504,
"column": 2
} | {
"line": 504,
"column": 23
} | {
"line": 504,
"column": 24
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ 1 / a ≤ 1 / b ↔ b ≤ a",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv"... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ ≤ b⁻¹ ↔ b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 509,
"column": 2
} | {
"line": 509,
"column": 23
} | {
"line": 509,
"column": 24
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ 1 / a < 1 / b ↔ b < a",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"Preorder.... | [
"α : Type u_2\ninst✝³ : Field α\ninst✝² : PartialOrder α\ninst✝¹ : PosMulReflectLT α\ninst✝ : IsStrictOrderedRing α\na b : α\nha : a < 0\nhb : b < 0\n⊢ a⁻¹ < b⁻¹ ↔ b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.Basic | {
"line": 612,
"column": 2
} | {
"line": 612,
"column": 74
} | {
"line": 613,
"column": 4
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\nh : a < b\n⊢ ∃ ε > 0, a < b - ε",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Eq.mpr",
"Preorder.toLT",
... | [
"α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\nh : a < b\n⊢ ∃ ε, a + ε < b ∧ 0 < ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Forall2 | {
"line": 54,
"column": 68
} | {
"line": 62,
"column": 24
} | {
"line": 64,
"column": 0
} | [
{
"pp": "α : Type u_1\n⊢ (Forall₂ fun x1 x2 ↦ x1 = x2) = Eq",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"congrArg",
"List.Forall₂.rec",
"eq_isEquiv",
"List.cons",
"funext",
"List",
"List.forall₂_refl",
"congr",
"True",
"IsEquiv... | [] | by
funext a b; apply propext
constructor
· intro h
induction h
· rfl
simp only [*]
· rintro rfl
exact forall₂_refl _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Field.Basic | {
"line": 687,
"column": 4
} | {
"line": 687,
"column": 36
} | {
"line": 687,
"column": 37
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nε : α\nhε : 0 < ε\nn : ℕ\nB : α\nB_pos : 0 < B\npos : 0 < 1 + ↑n * (B + 1) ^ (n - 1)\nq r : α\nhr : |r| ≤ B\nhqr : |q - r| ≤ 1 ∧ |q - r| + |q - r| * ↑n * (B + 1) ^ (n - 1) ≤ ε\nh : 0 = |q - r|\n⊢ |q - r| * ... | [
"case inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nε : α\nhε : 0 < ε\nn : ℕ\nB : α\nB_pos : 0 < B\npos : 0 < 1 + ↑n * (B + 1) ^ (n - 1)\nq r : α\nhr : |r| ≤ B\nhqr : |q - r| ≤ 1 ∧ |q - r| + |q - r| * ↑n * (B + 1) ^ (n - 1) ≤ ε\nh : 0 = |q - r|\n⊢ 0 < ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.InsertIdx | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 44
} | {
"line": 38,
"column": 45
} | [
{
"pp": "α : Type u\nl : List α\nn : ℕ\na : α\n⊢ l <+ l.insertIdx n a",
"ppTerm": "?m.3",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nl : List α\nn : ℕ\na : α\n⊢ l <+ l.insertIdx n a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.InsertIdx | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 13
} | {
"line": 68,
"column": 14
} | [
{
"pp": "α : Type u\nn : ℕ\na : α\nl : List α\nb : α\nhb : b ∈ l.insertIdx n a\n⊢ b ∈ a :: l",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Membership.mem",
"id",
"List.cons",
"List",
"List.instMembership",
"List.mem_cons._simp_1",
... | [
"α : Type u\nn : ℕ\na : α\nl : List α\nb : α\nhb : b ∈ l.insertIdx n a\n⊢ b = a ∨ b ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.InsertIdx | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 32
} | {
"line": 80,
"column": 33
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\nl : List α\nn : ℕ\na : α\n⊢ map f (l.insertIdx n a) = (map f l).insertIdx n (f a)",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nf : α → β\nl : List α\nn : ℕ\na : α\n⊢ map f (l.insertIdx n a) = (map f l).insertIdx n (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.InsertIdx | {
"line": 87,
"column": 32
} | {
"line": 87,
"column": 47
} | {
"line": 87,
"column": 47
} | [
{
"pp": "α : Type u\nβ : Type v\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nhl : ∀ (a : α), a ∈ l → p a\nn✝ : ℕ\na : α\nas : List α\nh : ∀ (a_1 : α), a_1 ∈ a :: as → p a_1\nn : ℕ\n⊢ (pmap f (a :: as) h).eraseIdx (n + 1) = pmap f ((a :: as).eraseIdx (n + 1)) ⋯",
"ppTerm": "?m.45",
"assigned": true,... | [
"α : Type u\nβ : Type v\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nhl : ∀ (a : α), a ∈ l → p a\nn✝ : ℕ\na : α\nas : List α\nh✝ : ∀ (a_1 : α), a_1 ∈ a :: as → p a_1\nh : p a ∧ ∀ (x : α), x ∈ as → p x\nn : ℕ\n⊢ (pmap f (a :: as) h✝).eraseIdx (n + 1) = pmap f ((a :: as).eraseIdx (n + 1)) ⋯"
] | forall_mem_cons | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Forall2 | {
"line": 178,
"column": 12
} | {
"line": 178,
"column": 29
} | {
"line": 178,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nR : α → β → Prop\na : α\nl₁ : List α\nIH : ∀ {l₂ : List β}, l₁.length = l₂.length → (∀ {a : α} {b : β}, (a, b) ∈ l₁.zip l₂ → R a b) → Forall₂ R l₁ l₂\nb : β\nl₂ : List β\nh₂ : ∀ {a_1 : α} {b_1 : β}, (a_1, b_1) ∈ (a :: l₁).zip (b :: l₂) → R a_1 b_1\nh₁ : l₁.length = l₂.length... | [
"α : Type u_1\nβ : Type u_2\nR : α → β → Prop\na : α\nl₁ : List α\nIH : ∀ {l₂ : List β}, l₁.length = l₂.length → (∀ {a : α} {b : β}, (a, b) ∈ l₁.zip l₂ → R a b) → Forall₂ R l₁ l₂\nb : β\nl₂ : List β\nh₂ : ∀ {a_1 : α} {b_1 : β}, (a_1, b_1) ∈ (a :: l₁).zip (b :: l₂) → R a_1 b_1\nh₁ : l₁.length = l₂.length\na✝ : α\nb✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.InsertIdx | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 32
} | {
"line": 92,
"column": 33
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\nl : List α\nn : ℕ\n⊢ (map f l).eraseIdx n = map f (l.eraseIdx n)",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nf : α → β\nl : List α\nn : ℕ\n⊢ (map f l).eraseIdx n = map f (l.eraseIdx n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.InsertIdx | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 13
} | {
"line": 120,
"column": 14
} | [
{
"pp": "α : Type u\nn : ℕ\nx : α\nl₁ l₂ : List α\nhl : (fun l ↦ l.insertIdx n x) l₁ = (fun l ↦ l.insertIdx n x) l₂\n⊢ l₁ = l₂",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nn : ℕ\nx : α\nl₁ l₂ : List α\nhl : (fun l ↦ l.insertIdx n x) l₁ = (fun l ↦ l.insertIdx n x) l₂\n⊢ l₁ = l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Perm.Basic | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 17
} | {
"line": 57,
"column": 18
} | [
{
"pp": "α : Type u_1\nl : List α\nn : ℕ\nh : n < l.length\n⊢ l[n] :: l.eraseIdx n ~ l",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nl : List α\nn : ℕ\nh : n < l.length\n⊢ l[n] :: l.eraseIdx n ~ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Forall2 | {
"line": 341,
"column": 4
} | {
"line": 341,
"column": 21
} | {
"line": 341,
"column": 22
} | [
{
"pp": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nR : α → β → Prop\nf : γ → β\nl₁ : List α\nl₂ l' : List γ\nhl1 : l' <+ l₂\nh1 : Forall₂ R l₁ (map f l')\nh2 : map f l' <+ map f l₂\n⊢ Forall₂ (fun a c ↦ R a (f c)) l₁ l' ∧ l' <+ l₂",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
... | [
"case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nR : α → β → Prop\nf : γ → β\nl₁ : List α\nl₂ l' : List γ\nhl1 : l' <+ l₂\nh1 : Forall₂ R l₁ (map f l')\nh2 : map f l' <+ map f l₂\n⊢ Forall₂ (fun a c ↦ R a (f c)) l₁ l'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 33
} | {
"line": 98,
"column": 34
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : GroupWithZero α\na : α\nm n : ℤ\nha : ¬a = 0\nhn : ¬n = 0\nhm : ¬m = 0\n⊢ zpow' a (m * n) = zpow' (zpow' a m) n",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"IsDomain.to... | [
"case neg\nα : Type u_1\ninst✝ : GroupWithZero α\na : α\nm n : ℤ\nha : ¬a = 0\nhn : ¬n = 0\nhm : ¬m = 0\n⊢ a ^ (m * n) = (a ^ m) ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 29
} | {
"line": 113,
"column": 30
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : CommGroupWithZero α\nn : ℤ\na b : α\nha : ¬a = 0\nhb : ¬b = 0\n⊢ zpow' (a * b) n = zpow' a n * zpow' b n",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"HMul.hMul",
... | [
"case neg\nα : Type u_1\ninst✝ : CommGroupWithZero α\nn : ℤ\na b : α\nha : ¬a = 0\nhb : ¬b = 0\n⊢ (a * b) ^ n = a ^ n * b ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Perm.Basic | {
"line": 242,
"column": 2
} | {
"line": 242,
"column": 32
} | {
"line": 242,
"column": 33
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : List α\nf : α → β\ng : α → List β\n⊢ map f l ++ flatMap g l ~ flatMap (fun x ↦ f x :: g x) l",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nl : List α\nf : α → β\ng : α → List β\n⊢ map f l ++ flatMap g l ~ flatMap (fun x ↦ f x :: g x) l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 104,
"column": 60
} | {
"line": 104,
"column": 71
} | {
"line": 104,
"column": 72
} | [
{
"pp": "α : Type u\nh : Injective length\nx y : α\nthis : [x] = [y]\n⊢ x = y",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nh : Injective length\nx y : α\nthis : [x] = [y]\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 113,
"column": 18
} | {
"line": 113,
"column": 29
} | {
"line": 113,
"column": 30
} | [
{
"pp": "case e_tail\nα : Type u\nhα : Subsingleton α\nhead✝¹ : α\ntail✝¹ : List α\nih : ∀ ⦃l2 : List α⦄, tail✝¹.length = l2.length → tail✝¹ = l2\nhead✝ : α\ntail✝ : List α\nhl : (head✝¹ :: tail✝¹).length = (head✝ :: tail✝).length\n⊢ tail✝¹.length = tail✝.length",
"ppTerm": "?e_tail",
"assigned": false,... | [
"case e_tail\nα : Type u\nhα : Subsingleton α\nhead✝¹ : α\ntail✝¹ : List α\nih : ∀ ⦃l2 : List α⦄, tail✝¹.length = l2.length → tail✝¹ = l2\nhead✝ : α\ntail✝ : List α\nhl : (head✝¹ :: tail✝¹).length = (head✝ :: tail✝).length\n⊢ tail✝¹.length = tail✝.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 169,
"column": 31
} | {
"line": 169,
"column": 73
} | {
"line": 169,
"column": 74
} | [
{
"pp": "M : Type u_4\ninst✝ : Monoid M\nl : List M\nh : l.prod ≠ 1\n⊢ ∃ x, x ∈ l ∧ x ≠ 1",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_4\ninst✝ : Monoid M\nl : List M\nh : l.prod ≠ 1\n⊢ ∃ x, x ∈ l ∧ x ≠ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 355,
"column": 13
} | {
"line": 355,
"column": 28
} | {
"line": 356,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝ : Inhabited α\n⊢ [].getLastI = [].getLast?.getD default",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"eq_self",
"of_eq_true",
"Eq"
],
"usedFVars": [
"α",
"inst✝"
],
"usedGoals": []
}
] | [] | simp [getLastI] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Basic | {
"line": 355,
"column": 13
} | {
"line": 355,
"column": 28
} | {
"line": 356,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝ : Inhabited α\n⊢ [].getLastI = [].getLast?.getD default",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"eq_self",
"of_eq_true",
"Eq"
],
"usedFVars": [
"α",
"inst✝"
],
"usedGoals": []
}
] | [] | simp [getLastI] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Basic | {
"line": 355,
"column": 13
} | {
"line": 355,
"column": 28
} | {
"line": 356,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝ : Inhabited α\n⊢ [].getLastI = [].getLast?.getD default",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"eq_self",
"of_eq_true",
"Eq"
],
"usedFVars": [
"α",
"inst✝"
],
"usedGoals": []
}
] | [] | simp [getLastI] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 446,
"column": 23
} | {
"line": 446,
"column": 34
} | {
"line": 446,
"column": 35
} | [
{
"pp": "α : Type u\nb : α\nl : List α\na : α\nh : a ∈ (b :: l).head?\n⊢ b = a",
"ppTerm": "?m.39",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nb : α\nl : List α\na : α\nh : a ∈ (b :: l).head?\n⊢ b = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 644,
"column": 34
} | {
"line": 644,
"column": 67
} | {
"line": 644,
"column": 68
} | [
{
"pp": "α : Type u\nl₁ l₂ : List α\ninst✝ : Inhabited α\nhl : l₁.length = l₂.length\nh : ∀ (n : ℕ), l₁[n]! = l₂[n]!\nn : ℕ\nh₁ : n < l₁.length\nh₂ : n < l₂.length\n⊢ l₁[n] = l₂[n]",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.instGetElem?Nat... | [
"α : Type u\nl₁ l₂ : List α\ninst✝ : Inhabited α\nhl : l₁.length = l₂.length\nh : ∀ (n : ℕ), l₁[n]! = l₂[n]!\nn : ℕ\nh₁ : n < l₁.length\nh₂ : n < l₂.length\n⊢ l₁[n]! = l₂[n]!"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 673,
"column": 30
} | {
"line": 673,
"column": 41
} | {
"line": 673,
"column": 42
} | [
{
"pp": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nl✝ l₁ l₂ l : List α\ni j : ℕ\nh : i ≠ j\na : α\nhj : j < (l.set i a).length\n⊢ j < l.length",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nl✝ l₁ l₂ l : List α\ni j : ℕ\nh : i ≠ j\na : α\nhj : j < (l.set i a).length\n⊢ j < l.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 750,
"column": 24
} | {
"line": 750,
"column": 35
} | {
"line": 750,
"column": 36
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\nh : Injective (map f)\nx y : α\nhxy : f x = f y\nthis : [x] = [y]\n⊢ x = y",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nf : α → β\nh : Injective (map f)\nx y : α\nhxy : f x = f y\nthis : [x] = [y]\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 778,
"column": 2
} | {
"line": 778,
"column": 13
} | {
"line": 778,
"column": 14
} | [
{
"pp": "α : Type u\nl : List α\n⊢ l = [] ∨ ∃ L b, l = L ++ [b]",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nl : List α\n⊢ l = [] ∨ ∃ L b, l = L ++ [b]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Defs | {
"line": 114,
"column": 72
} | {
"line": 115,
"column": 45
} | {
"line": 117,
"column": 0
} | [
{
"pp": "q : ℚ\nn : ℕ\n⊢ q ^ n = q.num ^ n /. ↑q.den ^ n",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"Rat.num",
"congrArg",
"Rat.mk_eq_divInt",
"Rat",
"Rat.divInt",
"Int.natCast_pow",
"Rat.instPowNat",
... | [] | by
rw [pow_def, mk_eq_divInt, Int.natCast_pow] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Rat.Defs | {
"line": 213,
"column": 62
} | {
"line": 213,
"column": 78
} | {
"line": 213,
"column": 79
} | [
{
"pp": "q : ℚ\nhq : q.num = 0\n⊢ q = 0",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"q : ℚ\nhq : q.num = 0\n⊢ q = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Defs | {
"line": 227,
"column": 23
} | {
"line": 227,
"column": 41
} | {
"line": 227,
"column": 42
} | [
{
"pp": "q : ℚ\nn d : ℤ\nhq : q ≠ 0\nhqnd : q = n /. d\nthis : n = 0\n⊢ q = 0",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"q : ℚ\nn d : ℤ\nhq : q ≠ 0\nhqnd : q = n /. d\nthis : n = 0\n⊢ q = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Defs | {
"line": 230,
"column": 23
} | {
"line": 230,
"column": 41
} | {
"line": 230,
"column": 42
} | [
{
"pp": "q : ℚ\nn d : ℤ\nhq : q ≠ 0\nhqnd : q = n /. d\nthis : d = 0\n⊢ q = 0",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"q : ℚ\nn d : ℤ\nhq : q ≠ 0\nhqnd : q = n /. d\nthis : d = 0\n⊢ q = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 440,
"column": 36
} | {
"line": 440,
"column": 62
} | {
"line": 440,
"column": 63
} | [
{
"pp": "G : Type u_7\ninst✝ : CommGroup G\na b : G\nl : List G\n⊢ a * b⁻¹ * l.alternatingProd = a * (b :: l).alternatingProd⁻¹",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InvOneClass.toOne",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"... | [
"G : Type u_7\ninst✝ : CommGroup G\na b : G\nl : List G\n⊢ a * b⁻¹ * l.alternatingProd = a * (b * l.alternatingProd⁻¹)⁻¹"
] | alternatingProd_cons' b l, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 453,
"column": 4
} | {
"line": 453,
"column": 75
} | {
"line": 453,
"column": 76
} | [
{
"pp": "case cons\nn a : ℕ\nl : List ℕ\nih : l.sum % n = (map (fun x ↦ x % n) l).sum % n\n⊢ (a :: l).sum % n = (map (fun x ↦ x % n) (a :: l)).sum % n",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.map",
"AddMonoid.toAddZeroClass",
... | [
"case cons\nn a : ℕ\nl : List ℕ\nih : l.sum % n = (map (fun x ↦ x % n) l).sum % n\n⊢ (a + l.sum) % n = (a + (map (fun x ↦ x % n) l).sum) % n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.List.Basic | {
"line": 459,
"column": 4
} | {
"line": 459,
"column": 76
} | {
"line": 459,
"column": 77
} | [
{
"pp": "case cons\nn a : ℕ\nl : List ℕ\nih : l.prod % n = (map (fun x ↦ x % n) l).prod % n\n⊢ (a :: l).prod % n = (map (fun x ↦ x % n) (a :: l)).prod % n",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.mod_mul_mod",
"HMul.hMul",
"Nat.instOne",
... | [
"case cons\nn a : ℕ\nl : List ℕ\nih : l.prod % n = (map (fun x ↦ x % n) l).prod % n\n⊢ a * l.prod % n = a * (map (fun x ↦ x % n) l).prod % n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Basic | {
"line": 1015,
"column": 41
} | {
"line": 1015,
"column": 82
} | {
"line": 1015,
"column": 82
} | [
{
"pp": "case cons\nα : Type u\nβ : Type v\ninst✝³ : BEq α\ninst✝² : LawfulBEq α\ninst✝¹ : BEq β\ninst✝ : LawfulBEq β\nf : α → β\nfinj : Injective f\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : ∀ {l₁ : List α}, map f (foldl List.erase l₁ tail✝) = foldl (fun l a ↦ l.erase (f a)) (map f l₁) tail✝\nl₁ : List α\n⊢ map f ... | [] | simp only [foldl_cons, map_erase finj, *] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Ring.Rat | {
"line": 57,
"column": 70
} | {
"line": 57,
"column": 81
} | {
"line": 57,
"column": 82
} | [
{
"pp": "a b : ℕ\nhab : ↑a = ↑b\n⊢ a = b",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℕ\nhab : ↑a = ↑b\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.NNRat.Defs | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 37
} | {
"line": 59,
"column": 38
} | [
{
"pp": "r : ℚ\nhr : 0 ≤ r\np q : ℚ\nhpq : p ≤ q\n⊢ r * p ≤ r * q",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"r : ℚ\nhr : 0 ≤ r\np q : ℚ\nhpq : p ≤ q\n⊢ r * p ≤ r * q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.NNRat.Defs | {
"line": 261,
"column": 2
} | {
"line": 261,
"column": 28
} | {
"line": 261,
"column": 29
} | [
{
"pp": "q : ℚ\n⊢ q.toNNRat = 0 ↔ q ≤ 0",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"q : ℚ\n⊢ q.toNNRat = 0 ↔ q ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 36,
"column": 2
} | {
"line": 36,
"column": 13
} | {
"line": 36,
"column": 14
} | [
{
"pp": "a : ℤ\nha : 0 ≤ a\nb : ℕ\n⊢ 0 ≤ mkRat a b",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a : ℤ\nha : 0 ≤ a\nb : ℕ\n⊢ 0 ≤ mkRat a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 79,
"column": 54
} | {
"line": 79,
"column": 65
} | {
"line": 79,
"column": 66
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : b ≠ 0\n⊢ 0 < ↑b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"Int.instLTInt",
"instOfNat",
"Nat",
"LT.lt",
"instNatCastInt",
"instLTNat",
... | [
"a : ℤ\nb : ℕ\nhb : b ≠ 0\n⊢ 0 < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.NNRat.Defs | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 40
} | {
"line": 334,
"column": 41
} | [
{
"pp": "q : ℚ≥0\n⊢ 0 < q.num ↔ 0 < q",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"NNRat.coe_eq_zero._simp_1",
"Rat.instOfNat",
"Eq.mpr",
"Rat.num",
"Preorder.toLT",
"ne_iff_gt_iff_ge._simp_1",
"Rat.num_eq_zero._simp_1",
"congrArg",
... | [
"q : ℚ≥0\n⊢ 0 ≤ q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.NNRat.Defs | {
"line": 338,
"column": 60
} | {
"line": 338,
"column": 82
} | {
"line": 338,
"column": 83
} | [
{
"pp": "q : ℚ≥0\n⊢ q.num.Coprime q.den",
"ppTerm": "?m.1",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"id",
"NNRat.num",
"NNRat.den"
],
"usedFVars": [
"q"
],
"usedGoals": [
{
"new": true,
"index": 0,
"kind": "synth... | [
"q : ℚ≥0\n⊢ (↑q).num.natAbs.Coprime (↑q).den"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Rat | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 13
} | {
"line": 81,
"column": 14
} | [
{
"pp": "q : ℚ≥0\nhq : q ≠ 0\n⊢ (↑q.den).natAbs.Coprime q.num",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"id",
"Int",
"NNRat.num",
"Nat.cast",
"NNRat.den",
"Int.natAbs",
"instNatCastInt"
],
"usedFVars": [
"q"... | [
"q : ℚ≥0\nhq : q ≠ 0\n⊢ q.den.Coprime q.num"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Rat | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 13
} | {
"line": 85,
"column": 14
} | [
{
"pp": "q : ℚ≥0\nhq : q ≠ 0\n⊢ (↑q.den).natAbs.Coprime q.num",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"id",
"Int",
"NNRat.num",
"Nat.cast",
"NNRat.den",
"Int.natAbs",
"instNatCastInt"
],
"usedFVars": [
"q"... | [
"q : ℚ≥0\nhq : q ≠ 0\n⊢ q.den.Coprime q.num"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Divisibility.Units | {
"line": 78,
"column": 2
} | {
"line": 79,
"column": 21
} | {
"line": 81,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Monoid α\na u : α\nhu : IsUnit u\n⊢ u ∣ a",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Units.val",
"Dvd.dvd",
"semigroupDvd",
"Units.coe_dvd",
"IsUnit",
"Units",
"Exists.casesOn",
"Monoid.toSemigroup",
... | [] | rcases hu with ⟨u, rfl⟩
apply Units.coe_dvd | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Divisibility.Units | {
"line": 78,
"column": 2
} | {
"line": 79,
"column": 21
} | {
"line": 81,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Monoid α\na u : α\nhu : IsUnit u\n⊢ u ∣ a",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Units.val",
"Dvd.dvd",
"semigroupDvd",
"Units.coe_dvd",
"IsUnit",
"Units",
"Exists.casesOn",
"Monoid.toSemigroup",
... | [] | rcases hu with ⟨u, rfl⟩
apply Units.coe_dvd | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rat.Cast.Defs | {
"line": 47,
"column": 2
} | {
"line": 47,
"column": 29
} | {
"line": 47,
"column": 30
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionSemiring α\nq : ℚ≥0\na : α\n⊢ Commute (↑q) a",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"NNRat.cast_def",
"congrAr... | [
"α : Type u_3\ninst✝ : DivisionSemiring α\nq : ℚ≥0\na : α\n⊢ Commute (↑q.num / ↑q.den) a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Lemmas | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 44
} | {
"line": 78,
"column": 45
} | [
{
"pp": "q₁ q₂ : ℚ\n⊢ (q₁ - q₂).den ∣ q₁.den.lcm q₂.den",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Nat.lcm",
"Rat.instSub",
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"AddMonoid.toAddZeroClass",
"Rat",
"sub_eq_add_neg",
"HSub.hSub",
"R... | [
"q₁ q₂ : ℚ\n⊢ (q₁ + -q₂).den ∣ q₁.den.lcm q₂.den"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Cast.Defs | {
"line": 61,
"column": 34
} | {
"line": 61,
"column": 77
} | {
"line": 61,
"column": 78
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionSemiring α\na b : ℕ\nhb : ↑b ≠ 0\nd : ℕ\nh : d ≠ 0\nn : ℕ\nc : (↑n).natAbs.Coprime d\nhn : 0 ≤ { num := ↑n, den := d, den_nz := h, reduced := c }\ne : divNat a b = ⟨{ num := ↑n, den := d, den_nz := h, reduced := c }, hn⟩\nhd : ↑d = 0\nthis : Rat.divInt ↑a ↑b = ↑⟨{ num := ↑... | [
"α : Type u_3\ninst✝ : DivisionSemiring α\na b : ℕ\nhb : ↑b ≠ 0\nd : ℕ\nh : d ≠ 0\nn : ℕ\nc : (↑n).natAbs.Coprime d\nhn : 0 ≤ { num := ↑n, den := d, den_nz := h, reduced := c }\ne : divNat a b = ⟨{ num := ↑n, den := d, den_nz := h, reduced := c }, hn⟩\nhd : ↑d = 0\nthis : Rat.divInt ↑a ↑b = ↑⟨{ num := ↑n, den := d,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Lemmas | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 15
} | {
"line": 103,
"column": 16
} | [
{
"pp": "case a\nq : ℚ\nn : ℤ\n⊢ (q + ↑n).den ∣ q.den",
"ppTerm": "?a✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case a\nq : ℚ\nn : ℤ\n⊢ (q + ↑n).den ∣ q.den"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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