file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Finset/Preimage.lean | Finset.preimage_union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\ns t : Finset β\nhst : InjOn f (f ⁻¹' ↑(s ∪ t))\n⊢ ↑(preimage (s ∪ t) f hst) =\n ↑(preimage s f (_ : ∀ (x₁ : α), x₁ ∈ f ⁻¹' ↑s → ∀ (x₂ : α), x₂ ∈ f ⁻¹' ↑s... | [
72,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.succ_ok | [
{
"state_after": "q : Λ'\ns : Option Γ'\nn : ℕ\nc d : List Γ'\n⊢ Reaches₁\n (fun x =>\n match x with\n | { l := none, var := var, stk := stk } => none\n | { l := some l, var := v, stk := S } => some (TM2.stepAux (tr l) v S))\n { l := some (Λ'.succ q), var := s, stk := elim (trNum ↑n ++ [Γ'.... | [
1556,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/GroupTheory/Abelianization.lean | Abelianization.lift.unique | [] | [
154,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/SubsetProperties.lean | finite_cover_nhds | [] | [
812,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.strongTopology.continuousSMul | [
{
"state_after": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹⁶ : NormedField 𝕜₁\ninst✝¹⁵ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_4\nE' : Type ?u.55678\nF : Type u_3\nF' : Type ?u.55684\ninst✝¹⁴ : AddCommGroup E\ninst✝¹³ : Module 𝕜₁ E\ninst✝¹² : AddCommGroup E'\ninst✝¹¹ : Module ℝ E'\ninst✝¹⁰ : AddCommGroup ... | [
152,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Part.lean | Part.map_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\ng : β → γ\nf : α → β\no : Part α\n⊢ map g (map f o) = map (g ∘ f) o",
"tactic": "erw [← bind_some_eq_map, bind_map, bind_some_eq_map]"
}
] | [
563,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.succ_mul_choose_eq | [
{
"state_after": "no goals",
"state_before": "⊢ succ 0 * choose 0 0 = choose (succ 0) (succ 0) * succ 0",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "k : ℕ\n⊢ succ 0 * choose 0 (k + 1) = choose (succ 0) (succ (k + 1)) * succ (k + 1)",
"tactic": "simp [choose]"
}... | [
126,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/List/Basic.lean | List.get?_drop | [
{
"state_after": "case a\nι : Type ?u.214450\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ L : List α\ni j : ℕ\na✝ : α\n⊢ a✝ ∈ get? (drop i L) j ↔ a✝ ∈ get? L (i + j)",
"state_before": "ι : Type ?u.214450\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ L : List α\ni j : ℕ\n⊢ get? (drop i L) ... | [
2243,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2240,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.bound_of_ball_bound | [
{
"state_after": "case intro\n𝕜 : Type u_1\n𝕜₂ : Type ?u.2556341\n𝕜₃ : Type ?u.2556344\nE : Type u_2\nEₗ : Type ?u.2556350\nF : Type ?u.2556353\nFₗ : Type u_3\nG : Type ?u.2556359\nGₗ : Type ?u.2556362\n𝓕 : Type ?u.2556365\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedAddCom... | [
1429,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.coe_top | [] | [
282,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_add_two_sub_fib_add_one | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ fib (n + 2) - fib (n + 1) = fib n",
"tactic": "rw [fib_add_two, add_tsub_cancel_right]"
}
] | [
112,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | cauchy_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nf : Filter α\n⊢ (NeBot f ∧ ∀ (s : Set (α × α)), s ∈ 𝓤 α → ∃ t, t ∈ f ∧ ∀ (x : α), x ∈ t → ∀ (y : α), y ∈ t → (x, y) ∈ s) ↔\n NeBot f ∧ ∀ (s : Set (α × α)), s ∈ 𝓤 α → ∃ t, t ∈ f ∧ t ×ˢ t ⊆ s",
"tactic": "si... | [
57,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.toFun_eq_coe | [] | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mem_mul | [] | [
325,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mul_mem_sup | [] | [
1039,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_apply_apply | [] | [
2042,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2041,
1
] |
Mathlib/Order/Lattice.lean | le_sup_of_le_right | [] | [
157,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Real/Basic.lean | Real.le_mk_of_forall_le | [
{
"state_after": "x y : ℝ\nf : CauSeq ℚ abs\nh : ∃ i, ∀ (j : ℕ), j ≥ i → x ≤ ↑(↑f j)\n⊢ x ≤ mk f",
"state_before": "x y : ℝ\nf : CauSeq ℚ abs\n⊢ (∃ i, ∀ (j : ℕ), j ≥ i → x ≤ ↑(↑f j)) → x ≤ mk f",
"tactic": "intro h"
},
{
"state_after": "case h\nx✝ y : ℝ\nf : CauSeq ℚ abs\nh✝ : ∃ i, ∀ (j : ℕ), j ... | [
626,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.union_distrib_iInter_right | [] | [
1408,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.inter_right | [] | [
1009,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_sum_disjoint | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.254025\nδ : Type ?u.254028\ninst✝² : AddCommMonoid α\ninst✝¹ : TopologicalSpace α\nf g : β → α\na✝ b : α\ns✝ : Finset β\ninst✝ : ContinuousAdd α\nι : Type u_1\ns : Finset ι\nt : ι → Set β\na : ι → α\nhs : Set.Pairwise (↑s) (Disjoint on t)\nhf : ∀ (i : ι)... | [
347,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.neighborSet_snd_subgraphOfAdj | [
{
"state_after": "ι : Sort ?u.223778\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nv w : V\nhvw : Adj G v w\n⊢ Subgraph.neighborSet (subgraphOfAdj G (_ : Adj G w v)) w = {v}",
"state_before": "ι : Sort ?u.223778\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nv w : V\nhvw :... | [
953,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Algebra/Module/Equiv.lean | AddEquiv.coe_toLinearEquiv_symm | [] | [
793,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.le_toNNRat_iff_coe_le | [
{
"state_after": "no goals",
"state_before": "p q✝ : ℚ\nq : ℚ≥0\nhp : 0 ≤ p\n⊢ q ≤ toNNRat p ↔ ↑q ≤ p",
"tactic": "rw [← coe_le_coe, Rat.coe_toNNRat p hp]"
}
] | [
391,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.comap_exp_nhdsWithin_zero | [
{
"state_after": "this : (exp ⁻¹' {0})ᶜ = Set.univ\n⊢ comap exp (𝓝[{0}ᶜ] 0) = comap re atBot",
"state_before": "⊢ comap exp (𝓝[{0}ᶜ] 0) = comap re atBot",
"tactic": "have : (exp ⁻¹' {0})ᶜ = Set.univ := eq_univ_of_forall exp_ne_zero"
},
{
"state_after": "no goals",
"state_before": "this : (... | [
444,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/Algebra/MulAction.lean | continuousSMul_sInf | [
{
"state_after": "ι : Sort ?u.29067\nM : Type u_2\nX : Type u_1\ninst✝¹ : TopologicalSpace M\ninst✝ : SMul M X\nts : Set (TopologicalSpace X)\nh : ∀ (t : TopologicalSpace X), t ∈ ts → ContinuousSMul M X\n⊢ Continuous fun p => p.fst • p.snd",
"state_before": "ι : Sort ?u.29067\nM : Type u_2\nX : Type u_1\nin... | [
192,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Order/SupIndep.lean | Finset.supIndep_empty | [] | [
78,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.apply_symm_apply | [] | [
174,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.linearIndependent | [] | [
293,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Algebra/Category/GroupCat/Colimits.lean | AddCommGroupCat.Colimits.quot_neg | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_neg_right | [
{
"state_after": "no goals",
"state_before": "x y : ℤ\n⊢ gcd x (-y) = gcd x y",
"tactic": "rw [Int.gcd, Int.gcd, natAbs_neg]"
}
] | [
294,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | left_le_midpoint | [] | [
142,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.bind_ret | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\na : α\ns : Seq α\n⊢ join (ret (f a), Seq.map (ret ∘ f) s) = (f a, Seq.map f s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\na : α\ns : Seq α\n⊢ bind (a, s) (ret ∘ f) = map f (a, s)",
"tactic": "dsimp [bind, map]"
},
... | [
978,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Order/WithBot.lean | WithTop.top_ne_coe | [] | [
606,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le_of_succ_le | [] | [
281,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
280,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_union_add_mk_inter | [] | [
2092,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2090,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_preimage_mul_left | [
{
"state_after": "ι : Type ?u.2206531\ninst✝ : Fintype ι\na : ℝ\nh : a ≠ 0\ns : Set ℝ\n⊢ ↑↑(ofReal (abs a⁻¹) • volume) s = ofReal (abs a⁻¹) * ↑↑volume s",
"state_before": "ι : Type ?u.2206531\ninst✝ : Fintype ι\na : ℝ\nh : a ≠ 0\ns : Set ℝ\n⊢ ↑↑(Measure.map (fun x => a * x) volume) s = ofReal (abs a⁻¹) * ↑↑... | [
324,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.ext_iff | [
{
"state_after": "V : Type ?u.110454\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.110463\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf : NormedAddGroupHom V₁ V₂\nx : V₁\n⊢ ↑f x = ↑f x",
"state_before": "V : Typ... | [
122,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/CompleteLattice.lean | le_sSup | [] | [
140,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.eventually_smallSets_eventually | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4511\nι : Sort ?u.4514\nl l' la : Filter α\nlb : Filter β\np : α → Prop\n⊢ (∃ s, s ∈ l ∧ ∀ᶠ (x : α) in l', x ∈ s → p x) ↔ ∃ s, s ∈ l ∧ ∃ t, t ∈ l' ∧ ∀ (x : α), x ∈ t → x ∈ s → p x",
"tactic": "simp only [eventually_iff_exists_mem]"
... | [
161,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_countable | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1730339\nγ : Type ?u.1730342\nδ : Type ?u.1730345\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : MeasurableSingletonClass α\nf : α → ℝ≥0∞\ns : Set α\nhs : Set.Countable s\n⊢ (∫⁻ (a : α) in s, f a ∂μ) = ∫⁻ (a : α) in ⋃ (x : α) (_ : x ∈... | [
1467,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1461,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioo_of_Icc | [] | [
204,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Init/CcLemmas.lean | imp_eq_of_eq_false_left | [] | [
58,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.invRev | [
{
"state_after": "case not\nα : Type u\nL L₁ L₂ L₃ L₄ a b : List (α × Bool)\nx : α\ny : Bool\n⊢ Step (FreeGroup.invRev (a ++ (x, y) :: (x, !y) :: b)) (FreeGroup.invRev (a ++ b))",
"state_before": "α : Type u\nL L₁✝ L₂✝ L₃ L₄ L₁ L₂ : List (α × Bool)\nh : Step L₁ L₂\n⊢ Step (FreeGroup.invRev L₁) (FreeGroup.in... | [
618,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | Commute.sq_sub_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.117642\nM : Type ?u.117645\ninst✝ : Ring R\na b : R\nh : Commute a b\n⊢ a ^ 2 - b ^ 2 = (a + b) * (a - b)",
"tactic": "rw [sq, sq, h.mul_self_sub_mul_self_eq]"
}
] | [
241,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
11
] |
Mathlib/Analysis/Convex/Combination.lean | AffineBasis.convexHull_eq_nonneg_coord | [
{
"state_after": "R : Type u_2\nE : Type u_3\nF : Type ?u.476113\nι✝ : Type ?u.476116\nι' : Type ?u.476119\nα : Type ?u.476122\ninst✝⁸ : LinearOrderedField R\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : LinearOrderedAddCommGroup α\ninst✝⁴ : Module R E\ninst✝³ : Module R F\ninst✝² : Module R α\nin... | [
502,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WOppSide.nonempty | [] | [
156,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_add_pi_div_two | [
{
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"tactic": "simp [cos_add]"
}
] | [
1288,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_succ | [
{
"state_after": "b : Ordinal\n⊢ 0 ^ succ b = 0 ^ b * 0",
"state_before": "a b : Ordinal\nh : a = 0\n⊢ a ^ succ b = a ^ b * a",
"tactic": "subst a"
},
{
"state_after": "no goals",
"state_before": "b : Ordinal\n⊢ 0 ^ succ b = 0 ^ b * 0",
"tactic": "simp only [zero_opow (succ_ne_zero _), m... | [
62,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Std/Data/List/Lemmas.lean | List.subset_cons | [] | [
238,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
238,
9
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.congr_symm | [
{
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683,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.max_val | [
{
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"tactic": "simp"
}
] | [
333,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/CharP/Basic.lean | NeZero.not_char_dvd | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : AddMonoidWithOne R\nr : R\nn p✝ : ℕ\na : ℕ+\np : ℕ\ninst✝ : CharP R p\nk : ℕ\nh : NeZero ↑k\n⊢ ¬p ∣ k",
"tactic": "rwa [← CharP.cast_eq_zero_iff R p k, ← Ne.def, ← neZero_iff]"
}
] | [
750,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/RingTheory/SimpleModule.lean | IsSimpleModule.isAtom | [] | [
97,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEquiv.map_apply | [] | [
4293,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4292,
11
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | finrank_eq_one_iff_of_nonzero' | [
{
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"state_before": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv : V\nnz : v ≠ 0\n... | [
1264,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | add_le_mul_of_left_le_right | [] | [
860,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Std/Data/List/Lemmas.lean | List.filterMap_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ filterMap some l = l",
"tactic": "erw [filterMap_eq_map, map_id]"
}
] | [
1201,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1200,
9
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.CompleteBipartiteGraph.chromaticNumber | [
{
"state_after": "V✝ : Type u\nG : SimpleGraph V✝\nα : Type v\nC : Coloring G α\nV : Type u_1\nW : Type u_2\ninst✝¹ : Nonempty V\ninst✝ : Nonempty W\n⊢ ∀ (C' : Coloring (completeBipartiteGraph V W) Bool), Function.Surjective ↑C'",
"state_before": "V✝ : Type u\nG : SimpleGraph V✝\nα : Type v\nC : Coloring G ... | [
418,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Order/Lattice.lean | inf_le_right' | [] | [
404,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_u_le_trans | [] | [
167,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_le_iff_comap | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.1095879\nR₂ : Type u_2\nR₃ : Type ?u.1095885\nR₄ : Type ?u.1095888\nS : Type ?u.1095891\nK : Type ?u.1095894\nK₂ : Type ?u.1095897\nM : Type u_4\nM' : Type ?u.1095903\nM₁ : Type ?u.1095906\nM₂ : Type u_3\nM₃ : Type ?u.1095912\nM₄ : Typ... | [
1244,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_neg | [] | [
924,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | NNReal.pi_pos | [
{
"state_after": "no goals",
"state_before": "⊢ 0 < pi",
"tactic": "exact_mod_cast Real.pi_pos"
}
] | [
198,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.eq_of_isMaxOn_of_ball_subset | [
{
"state_after": "no goals",
"state_before": "E : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℂ E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℂ F\ninst✝ : StrictConvexSpace ℝ F\nf : E → F\ns : Set E\nz w : E\nhd : DiffContOnCl ℂ f s\nhz : IsMaxOn (norm ∘ f) s z\nhsub : b... | [
316,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Algebra/Star/Free.lean | FreeAlgebra.star_ι | [
{
"state_after": "no goals",
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"tactic": "simp [star, Star.star]"
}
] | [
70,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/List/Basic.lean | List.drop_eq_nil_iff_le | [
{
"state_after": "ι : Type ?u.198909\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nk : ℕ\nh : drop k l = []\n⊢ length l ≤ k",
"state_before": "ι : Type ?u.198909\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nk : ℕ\n⊢ drop k l = [] ↔ length l ≤ k",
"tactic": "ref... | [
2106,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2098,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_succ_eval | [
{
"state_after": "no goals",
"state_before": "S✝ : Type u\ninst✝¹ : Semiring S✝\nS : Type u_1\ninst✝ : Semiring S\nn : ℕ\nk : S\n⊢ eval k (pochhammer S (n + 1)) = eval k (pochhammer S n) * (k + ↑n)",
"tactic": "rw [pochhammer_succ_right, mul_add, eval_add, eval_mul_X, ← Nat.cast_comm, ← C_eq_nat_cast,\n... | [
115,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prodComparison_natural | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁵ : Category C\nX Y : C\nD : Type u₂\ninst✝⁴ : Category D\nF : C ⥤ D\nA A' B B' : C\ninst✝³ : HasBinaryProduct A B\ninst✝² : HasBinaryProduct A' B'\ninst✝¹ : HasBinaryProduct (F.obj A) (F.obj B)\ninst✝ : HasBinaryProduct (F.obj A') (F.obj B')\nf... | [
1274,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp₂Measurable_eq_mk | [
{
"state_after": "α : Type u_4\nβ : Type u_2\nγ : Type u_1\nδ : Type u_3\ninst✝¹⁵ : MeasurableSpace α\nμ ν : Measure α\ninst✝¹⁴ : TopologicalSpace β\ninst✝¹³ : TopologicalSpace γ\ninst✝¹² : TopologicalSpace δ\ninst✝¹¹ : MeasurableSpace β\ninst✝¹⁰ : PseudoMetrizableSpace β\ninst✝⁹ : BorelSpace β\ninst✝⁸ : Second... | [
361,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.fold_op_eq | [] | [
554,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.coe_top | [] | [
1005,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.trans | [] | [
82,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_sups_subset_left | [] | [
386,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | NormedField.exists_lt_nnnorm_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.377356\nγ : Type ?u.377359\nι : Type ?u.377362\ninst✝ : DenselyNormedField α\nr₁ r₂ : ℝ≥0\nh : r₁ < r₂\n⊢ ∃ x, r₁ < ‖x‖₊ ∧ ‖x‖₊ < r₂",
"tactic": "exact_mod_cast exists_lt_norm_lt α r₁.prop h"
}
] | [
771,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | exists_deriv_eq_zero | [] | [
309,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/List/Join.lean | List.bind_eq_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : List α\nf : α → List β\n⊢ (∀ (l_1 : List β), l_1 ∈ map f l → l_1 = []) ↔ ∀ (x : α), x ∈ l → f x = []",
"tactic": "simp only [mem_map, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]"
}
] | [
85,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.toList_ofList | [
{
"state_after": "case refine'_1\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nl : List X\nhl : l ≠ []\nhc : List.Chain' IsMaximal l\n⊢ List.length (toList (ofList l hl hc)) = List.length l\n\ncase refine'_2\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nl : List X\nhl : l ≠ [... | [
314,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
src/lean/Init/Core.lean | Quot.inductionOn | [] | [
1237,
10
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1233,
11
] |
Mathlib/Data/Bool/Basic.lean | Bool.xor_left_comm | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (a b c : Bool), xor a (xor b c) = xor b (xor a c)",
"tactic": "decide"
}
] | [
270,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.comp_left | [] | [
234,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_eq_zero_of_ae_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.2312986\nF : Type u_2\nG : Type ?u.2312992\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nhq0_lt : 0 < q\nhf_zero : f =... | [
696,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.coe_one | [] | [
351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.coe_comp | [] | [
1090,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ext_inner_map | [
{
"state_after": "𝕜 : Type ?u.2756723\nE : Type ?u.2756726\nF : Type ?u.2756729\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerPr... | [
1262,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_bot | [] | [
151,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Fintype/Card.lean | Function.Embedding.nonempty_iff_card_le | [] | [
803,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_subtypeDomain_index | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝³ : (i : ι) → Zero (β i)\ninst✝² : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝¹ : CommMonoid γ\nv : Π₀ (i : ι), β i\np : ι → Prop\ninst✝ : DecidablePred p\nh... | [
2120,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2116,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.rel_nthLe_of_lt | [] | [
119,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | isLUB_ciSup | [] | [
489,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.coe_copy | [] | [
284,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_id_const | [] | [
1367,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.mul_le | [] | [
1030,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
Mathlib/Data/Int/Order/Units.lean | Int.isUnit_sq | [
{
"state_after": "no goals",
"state_before": "a : ℤ\nha : IsUnit a\n⊢ a ^ 2 = 1",
"tactic": "rw [sq, isUnit_mul_self ha]"
}
] | [
26,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_self' | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.911590\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ny : { x // x ∈ S }\n⊢ ↑(toMap f) ↑y *\n ↑(↑(IsUnit.liftRight (MonoidHom.restrict (toMap f) S) (_ : ... | [
840,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.mk_list_sum | [] | [
947,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.lift_rel_rec | [] | [
1305,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1299,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.commute_nat_add | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ↑f fun x => ↑n + x",
"tactic": "simpa only [nsmul_one, add_left_iterate] using Function.Commute.iterate_right f.map_one_add n"
}
] | [
335,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.LiftRel.equiv | [] | [
603,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.mem_torsionBy_iff | [] | [
259,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
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