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/Order/Lattice.lean | AntitoneOn.inf | [] | [
1223,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
11
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.exists_reduced_factors' | [] | [
928,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Data/Nat/Choose/Factorization.lean | Nat.factorization_centralBinom_of_two_mul_self_lt_three_mul | [
{
"state_after": "case refine'_1\np n k : ℕ\nn_big : 2 < n\np_le_n : p ≤ n\nbig : 2 * n < 3 * p\n⊢ p ≠ 2\n\ncase refine'_2\np n k : ℕ\nn_big : 2 < n\np_le_n : p ≤ n\nbig : 2 * n < 3 * p\n⊢ n ≤ 2 * n - n",
"state_before": "p n k : ℕ\nn_big : 2 < n\np_le_n : p ≤ n\nbig : 2 * n < 3 * p\n⊢ ↑(factorization (cent... | [
103,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/RingTheory/Localization/Ideal.lean | IsLocalization.isPrime_iff_isPrime_disjoint | [
{
"state_after": "case mp\nR : Type u_2\ninst✝³ : CommSemiring R\nM : Submonoid R\nS : Type u_1\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : IsLocalization M S\nJ : Ideal S\n⊢ Ideal.IsPrime J → Ideal.IsPrime (Ideal.comap (algebraMap R S) J) ∧ Disjoint ↑M ↑(Ideal.comap (algebraMap R S) J)\n\ncase mpr\... | [
135,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.exists_irreducible_of_natDegree_pos | [
{
"state_after": "R✝ : Type u\nS : Type ?u.662441\nσ : Type v\nM : Type w\ninst✝⁶ : CommRing R✝\ninst✝⁵ : CommRing S\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R✝ M\nR : Type u\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : WfDvdMonoid R\nf : R[X]\nhf : degree f ≤ 0\n⊢ natDegree f ≤ 0",
"state_before": "... | [
978,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_add_mod | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\n⊢ (a * b + c) % b = c % b",
"tactic": "simp [Nat.add_mod]"
}
] | [
801,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec | [
{
"state_after": "case pos\nn : Type ?u.226982\np : Type ?u.226985\nR : Type u₂\n𝕜 : Type u_1\ninst✝³ : Field 𝕜\ninst✝² : DecidableEq n\ninst✝¹ : DecidableEq p\ninst✝ : CommRing R\nr : ℕ\nM✝ M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜\nH : IsTwoBlockDiagonal M\n⊢ ∃ L L', IsTwoBlockDiagonal (List.prod (List.ma... | [
593,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.apply_eq_iff_eq | [] | [
273,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq_has_pos_limit_a | [
{
"state_after": "case intro.intro\nx : ℝ\nx_pos : 0 < x\nhx : ∀ (n : ℕ), x ≤ stirlingSeq (succ n)\n⊢ ∃ a, 0 < a ∧ Tendsto stirlingSeq atTop (𝓝 a)",
"state_before": "⊢ ∃ a, 0 < a ∧ Tendsto stirlingSeq atTop (𝓝 a)",
"tactic": "obtain ⟨x, x_pos, hx⟩ := stirlingSeq'_bounded_by_pos_constant"
},
{
... | [
210,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | conj_cong_is_cong | [
{
"state_after": "case intro\nN✝ : ℕ\ng : ConjAct SL(2, ℤ)\nΓ : Subgroup SL(2, ℤ)\nN : ℕ+\nHN : Gamma ↑N ≤ Γ\n⊢ IsCongruenceSubgroup (g • Γ)",
"state_before": "N : ℕ\ng : ConjAct SL(2, ℤ)\nΓ : Subgroup SL(2, ℤ)\nh : IsCongruenceSubgroup Γ\n⊢ IsCongruenceSubgroup (g • Γ)",
"tactic": "obtain ⟨N, HN⟩ := h"... | [
250,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioo_mem_nhdsWithin_Ioi | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderClosedTopology α\na✝ b✝ : α\ninst✝ : TopologicalSpace γ\na b c : α\nH : b ∈ Ico a c\n⊢ Ioo b c ⊆ Ioo a c",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α... | [
398,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eq_of_ae_eq | [] | [
110,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_mul_comm | [
{
"state_after": "R : Type u\ninst✝⁶ : CommSemiring R\nM : Type v\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nι : Type w\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\nκ : Type ?u.257671\ninst✝¹ : DecidableEq κ\ninst✝ : Fintype κ\nb✝ : Basis ι R M\nc : Basis κ R M\nf g : M →ₗ[R] M\nH : ∃ s, Nonempty (Basis { ... | [
116,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.le_prod_iff | [
{
"state_after": "case mp\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.375689\nM₆ : Type ?u.375692\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂... | [
702,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.step_wf | [
{
"state_after": "u : XgcdType\nhr : r u ≠ 0\n⊢ r u - 1 < u.bp",
"state_before": "u : XgcdType\nhr : r u ≠ 0\n⊢ sizeOf (step u) < sizeOf u",
"tactic": "change u.r - 1 < u.bp"
},
{
"state_after": "u : XgcdType\nhr : r u ≠ 0\nh₀ : r u - 1 + 1 = r u\n⊢ r u - 1 < u.bp",
"state_before": "u : Xgcd... | [
315,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.prod_left_fst | [] | [
993,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
1
] |
Mathlib/Data/Finset/Slice.lean | Finset.ne_of_mem_slice | [] | [
161,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.le_iff_Icc | [] | [
228,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Iic_disjoint_Ioc | [] | [
43,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.symmetric_isOrtho | [] | [
266,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sinh (-x) = -sinh x",
"tactic": "simp [sinh, exp_neg, (neg_div _ _).symm, add_mul]"
}
] | [
1350,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1350,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_nat_cast | [
{
"state_after": "case none\nn : ℕ\n⊢ none ^ ↑n = none ^ n\n\ncase some\nn : ℕ\nval✝ : ℝ≥0\n⊢ Option.some val✝ ^ ↑n = Option.some val✝ ^ n",
"state_before": "x : ℝ≥0∞\nn : ℕ\n⊢ x ^ ↑n = x ^ n",
"tactic": "cases x"
},
{
"state_after": "no goals",
"state_before": "case none\nn : ℕ\n⊢ none ^ ↑n... | [
474,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.exists_mem_ne_zero_of_ne_bot | [] | [
116,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/WithBot.lean | WithTop.wellFounded_gt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.119578\nγ : Type ?u.119581\nδ : Type ?u.119584\ninst✝ : Preorder α\nh : WellFounded fun x x_1 => x > x_1\na : WithTop α\n⊢ Acc (fun x x_1 => x < x_1) (↑WithTop.toDual a) → Acc (fun x x_1 => x > x_1) a",
"state_before": "α : Type u_1\nβ : Type ?u.119578\nγ : Type ?... | [
1279,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_imp_distrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.167876\nι : Sort x\nf : Filter α\ninst✝ : NeBot f\np : α → Prop\nq : Prop\n⊢ (∃ᶠ (x : α) in f, p x → q) ↔ (∀ᶠ (x : α) in f, p x) → q",
"tactic": "simp"
}
] | [
1364,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.div_one | [] | [
113,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/Connected.lean | totallyDisconnectedSpace_iff_connectedComponent_singleton | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.122829\nπ : ι → Type ?u.122834\ninst✝ : TopologicalSpace α\ns t u v : Set α\n⊢ (∀ (x : α), Set.Subsingleton (connectedComponent x)) ↔ ∀ (x : α), connectedComponent x = {x}",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.122829\nπ : ι → Type ?u.122... | [
1315,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | IsUnit.mul_right_eq_zero | [] | [
60,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Ioc | [] | [
458,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_lf_add_left | [
{
"state_after": "y z : PGame\nh : y ⧏ z\nx : PGame\n⊢ y + x ⧏ z + x",
"state_before": "y z : PGame\nh : y ⧏ z\nx : PGame\n⊢ x + y ⧏ x + z",
"tactic": "rw [lf_congr add_comm_equiv add_comm_equiv]"
},
{
"state_after": "no goals",
"state_before": "y z : PGame\nh : y ⧏ z\nx : PGame\n⊢ y + x ⧏ z... | [
1752,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1750,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.element_of_chain_eq_pow_second_of_chain | [
{
"state_after": "M : Type u_1\ninst✝¹ : CancelCommMonoidWithZero M\ninst✝ : UniqueFactorizationMonoid M\nq r : Associates M\nn : ℕ\nhn : n ≠ 0\nc : Fin (n + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nhr : r ∣ q\nhq : q ≠ 0\ni : (fun x => ℕ) (normalizedFactors r) := ↑... | [
187,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.apply | [] | [
95,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
11
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inf_comm | [] | [
915,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
11
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.orthogonal_eq_top_iff | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.91898\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nK : Submodule 𝕜 E\n⊢ Kᗮ = ⊤ → K = ⊥",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?... | [
214,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.LiftRel.trans | [] | [
1088,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_induction₂ | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\ns : Set R\np : R → R → Prop\na b : R\nha : a ∈ closure s\nhb : b ∈ closure s\nHs : ∀ (x : R), x ∈ s → ∀ (y : R), y ∈ s → p x y\nH0_left : ∀ (x : R), p 0 x\nH0_right : ∀ (x : R), p x 0\nH1_left : ∀ (x : R), p ... | [
952,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.mem_eraseTop | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\nx : X\nh : 0 < s.length\n⊢ x ∈ range (eraseTop s).series ↔ x ≠ top s ∧ x ∈ range s.series",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\nx : X... | [
436,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/List/Rotate.lean | List.reverse_rotate | [
{
"state_after": "α : Type u\nl : List α\nn : ℕ\n⊢ rotate (reverse (rotate l n)) n = reverse l",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ reverse (rotate l n) = rotate (reverse l) (length l - n % length l)",
"tactic": "rw [← length_reverse l, ← rotate_eq_iff]"
},
{
"state_after": "case ... | [
368,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bodd_negOfNat | [
{
"state_after": "case succ\nn✝ : ℕ\n⊢ bodd (negOfNat (Nat.succ n✝)) = !Nat.bodd n✝",
"state_before": "n : ℕ\n⊢ bodd (negOfNat n) = Nat.bodd n",
"tactic": "cases n <;> simp"
},
{
"state_after": "no goals",
"state_before": "case succ\nn✝ : ℕ\n⊢ bodd (negOfNat (Nat.succ n✝)) = !Nat.bodd n✝",
... | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_sup_inf | [
{
"state_after": "ι : Type ?u.32963\nα : Type u_1\nβ : Type ?u.32969\nπ : ι → Type ?u.32974\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a ⊔ b ≤ a ∆ b ⊔ a ⊓ b",
"state_before": "ι : Type ?u.32963\nα : Type u_1\nβ : Type ?u.32969\nπ : ι → Type ?u.32974\ninst✝ : GeneralizedCoheytingAlgebra α\na b c ... | [
200,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsPrenex.castLE | [] | [
785,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_add_mul_monomial | [
{
"state_after": "case hc\nσ : Type u_2\nR : Type u_1\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nφ ψ : MvPowerSeries σ R\na : R\n⊢ n ≤ m + n",
"state_before": "σ : Type u_2\nR : Type u_1\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nφ ψ : MvPowerSeries σ R\na : R\n⊢ ↑(coeff R (m + n)) (φ * ↑(monomial R n) a) = ↑(coeff R m) φ ... | [
256,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.StrongEpi.iff_of_arrow_iso | [
{
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179,
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176,
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.pow_apply | [] | [
156,
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154,
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Mathlib/Data/Sym/Basic.lean | Sym.erase_cons_head | [] | [
231,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.self_le_sinh_iff | [
{
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] | [
763,
50
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760,
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Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.AnalyticSet.measurablySeparable | [
{
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414,
62
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407,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mrange_fst | [] | [
1311,
69
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1310,
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Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.tensor_left_unitality | [
{
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432,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atBot_prod_self | [
{
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1470,
78
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1468,
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Mathlib/Data/Num/Lemmas.lean | Num.lxor'_to_nat | [
{
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] | [
953,
76
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952,
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Mathlib/Algebra/DirectSum/Module.lean | DirectSum.linearEquivFunOnFintype_symm_coe | [
{
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188,
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186,
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | Metric.preimage_smul_ball | [
{
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438,
32
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437,
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.map_finsupp_sum | [] | [
1926,
14
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1924,
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Mathlib/Data/List/NatAntidiagonal.lean | List.Nat.map_swap_antidiagonal | [
{
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102,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Order/UpperLower/Basic.lean | upperClosure_image | [
{
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1330,
76
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1326,
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Mathlib/Data/Sum/Order.lean | Sum.inr_mono | [] | [
191,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | HasDerivAt.arsinh | [] | [
306,
34
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304,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Eq.sameCycle | [
{
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}
] | [
89,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
11
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Mathlib/Data/Set/Prod.lean | Set.insert_prod | [
{
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183,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.subtype_apply | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.add_eq_sup | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.neg_one_pow_div_two_of_three_mod_four | [
{
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"state_before": "n : ℕ\nhn : n % 4 = 3\n⊢ (-1) ^ (n / 2) = -1",
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},
{
"state_after": "no goals",
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131,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.eq_of_mem_of_mem | [] | [
83,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/LinearAlgebra/Basis.lean | Basis.equiv'_symm_apply | [] | [
1059,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_iff_exists_coe | [] | [
719,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isOrtho_zero_right | [] | [
769,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
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Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_torsionBySet_eq_top | [] | [
372,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
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Mathlib/Order/Filter/Basic.lean | Filter.map_inf | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.281757\nι : Sort x\nf g : Filter α\nm : α → β\nh : Injective m\n⊢ map m f ⊓ map m g ≤ map m (f ⊓ g)",
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2516,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2511,
1
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Mathlib/Analysis/NormedSpace/ConformalLinearMap.lean | isConformalMap_const_smul | [] | [
72,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | GeneralizedContinuedFraction.of_correctness_of_terminates | [] | [
262,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
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Mathlib/Data/Finset/Basic.lean | Finset.erase_injOn | [] | [
2016,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2016,
1
] |
Mathlib/LinearAlgebra/FinsuppVectorSpace.lean | Basis.equivFun_symm_stdBasis | [
{
"state_after": "no goals",
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"tac... | [
178,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.injective | [] | [
2022,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2021,
11
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Mathlib/Data/Finset/Prod.lean | Finset.product_inter | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.75579\ns s'... | [
253,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.ext | [] | [
131,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Data/Sum/Interval.lean | Sum.Ioo_inr_inl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : LocallyFiniteOrder β\na₁ a₂ : α\nb₁ b₂ : β\na b : α ⊕ β\n⊢ Ioo (inr b₁) (inl a₂) = ∅",
"tactic": "rfl"
}
] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | ContinuousLinearMap.set_integral_compLp | [] | [
1073,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
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Mathlib/Data/List/Chain.lean | List.Chain.pairwise | [
{
"state_after": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na✝ b✝ : α\ninst✝ : IsTrans α R\na b : α\nl : List α\nh : R a b\nhb : Chain R b l\n⊢ ∀ (a_1 : α), a_1 ∈ l → R a a_1",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na✝ b✝ : α\ninst✝ : IsTrans α R... | [
125,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
11
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Mathlib/Data/Fintype/BigOperators.lean | Fintype.card_pi | [] | [
145,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/Algebra/Associated.lean | dvd_prime_pow | [
{
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1228,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
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Mathlib/NumberTheory/Padics/Hensel.lean | calc_norm_le_one | [
{
"state_after": "no goals",
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162,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
9
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Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.symm | [] | [
275,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.init | [] | [
272,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_div_dvd' | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\np q : K[X]\nhq : q ≠ 0\n⊢ ↑C (leadingCoeff (q / gcd p q))⁻¹ * (p / gcd p q) ∣ p",
"tactic": "simpa using num_div_dvd p hq"
}
] | [
1183,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
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Mathlib/Data/List/Zip.lean | List.zipWith_comm_of_comm | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type ?u.89441\nδ : Type ?u.89444\nε : Type ?u.89447\nf : α → α → β\ncomm : ∀ (x y : α), f x y = f y x\nl l' : List α\n⊢ zipWith (fun b a => f a b) l' l = zipWith f l' l",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.89441\nδ : Type ?u.89444\nε : Type... | [
288,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_le_mul_of_nonneg_right | [
{
"state_after": "no goals",
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"tactic": "if hba : b ≤ a then simp [Nat.le_antisymm hba h₁] else\nif hc0 : c ≤ 0 then simp [Nat.le_antisymm hc0 (zero_le c), Nat.mul_zero] else\nexact Nat.le_of_lt (Nat.mul_lt_mul_of_pos_right (Nat.not_le.1 hba) (N... | [
765,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
762,
11
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Mathlib/CategoryTheory/Types.lean | CategoryTheory.types_hom | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Real/NNReal.lean | Set.OrdConnected.image_real_toNNReal | [
{
"state_after": "s : Set ℝ\nt : Set ℝ≥0\nh : OrdConnected s\nx : ℝ\nhx : x ∈ s\ny : ℝ\nhy : y ∈ s\nz : ℝ≥0\nhz : z ∈ Icc (toNNReal x) (toNNReal y)\n⊢ z ∈ toNNReal '' s",
"state_before": "s : Set ℝ\nt : Set ℝ≥0\nh : OrdConnected s\n⊢ OrdConnected (toNNReal '' s)",
"tactic": "refine' ⟨ball_image_iff.2 fu... | [
1038,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.coe_det | [
{
"state_after": "case h\nR : Type ?u.298780\ninst✝¹⁰ : CommRing R\nM : Type u_1\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nM' : Type ?u.299371\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nι : Type ?u.299913\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Fintype ι\ne : Basis ι R M\nA : Type u_2\ninst✝³ : CommRing A\... | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.mem_falling | [
{
"state_after": "𝕜 : Type ?u.13760\nα : Type u_1\ninst✝¹ : LinearOrderedField 𝕜\ninst✝ : DecidableEq α\nk : ℕ\n𝒜 : Finset (Finset α)\ns : Finset α\n⊢ (∃ v, v ∈ 𝒜 ∧ s ⊆ v ∧ card s = k) ↔ (∃ t, t ∈ 𝒜 ∧ s ⊆ t) ∧ card s = k",
"state_before": "𝕜 : Type ?u.13760\nα : Type u_1\ninst✝¹ : LinearOrderedField �... | [
136,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.IsPrimitive.primPart_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nhp : IsPrimitive p\n⊢ primPart p = p",
"tactic": "rw [← one_mul p.primPart, ← C_1, ← hp.content_eq_one, ← p.eq_C_content_mul_primPart]"
}
] | [
293,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Konig.lean | TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system | [
{
"state_after": "no goals",
"state_before": "J✝ : Type v\ninst✝⁵ : SmallCategory J✝\nJ : Type u\ninst✝⁴ : SmallCategory J\nF : J ⥤ TopCat\ninst✝³ : IsCofilteredOrEmpty J\ninst✝² : ∀ (j : J), Nonempty ↑(F.obj j)\ninst✝¹ : ∀ (j : J), CompactSpace ↑(F.obj j)\ninst✝ : ∀ (j : J), T2Space ↑(F.obj j)\n⊢ Nonempty ... | [
171,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.continuousOn_derivWithin | [] | [
2139,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2137,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Wrepr_equiv | [
{
"state_after": "case mk\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\na : (P F).A\nf : PFunctor.B (P F) a → WType (P F).B\nih : ∀ (a : PFunctor.B (P F) a), Wequiv (Wrepr (f a)) (f a)\n⊢ Wequiv (Wrepr (WType.mk a f)) (WType.mk a f)",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\... | [
242,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : 0 < c\n⊢ (fun x x_1 => x * x_1) c ⁻¹' Ioo a b = Ioo (a / c) (b / c)",
"tactic": "simp [← Ioi_inter_Iio, h]"
}
] | [
622,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_algebraMap | [] | [
607,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/CategoryTheory/Bicategory/Functor.lean | CategoryTheory.Pseudofunctor.to_oplax_mapId | [] | [
479,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Topology/Order/Basic.lean | countable_setOf_covby_left | [
{
"state_after": "case h.e'_2.h.h.e'_2.h.h.h.e'_2.h.h.a\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\ne_1✝² e_1✝¹ : α = αᵒᵈ\nx✝¹ : α\ne_1✝ : α = αᵒᵈ\nx✝ : α\n⊢ x✝ ⋖ x✝¹ ↔ x✝¹ ⋖ x✝",
"state_before": "α : ... | [
1426,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarAlgHom.ext_adjoin_singleton | [] | [
775,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
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