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/Filter/Basic.lean | Filter.NeBot.ne | [] | [
498,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/CategoryTheory/Monoidal/NaturalTransformation.lean | CategoryTheory.MonoidalNatTrans.comp_toNatTrans_lax | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.mem_localTriv_source | [] | [
702,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nφ : G ≃g G'\nv : V\nv' : V'\nC : ConnectedComponent G\nu : V\n⊢ connectedComponentMk G (↑(Iso.symm φ) v') = connectedComponentMk G u ↔\n connectedComponentMk G' v' = map (RelEmbedding.toRel... | [
2088,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2084,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_add' | [
{
"state_after": "case inl\ny z : ℝ\nh : y + z ≠ 0\nhx : 0 ≤ 0\n⊢ 0 ^ (y + z) = 0 ^ y * 0 ^ z\n\ncase inr\nx y z : ℝ\nhx : 0 ≤ x\nh : y + z ≠ 0\npos : 0 < x\n⊢ x ^ (y + z) = x ^ y * x ^ z",
"state_before": "x y z : ℝ\nhx : 0 ≤ x\nh : y + z ≠ 0\n⊢ x ^ (y + z) = x ^ y * x ^ z",
"tactic": "rcases hx.eq_or_... | [
185,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.target_eq | [
{
"state_after": "𝕜 : Type u_3\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_2\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\n⊢ I.target = ↑I '' I.source",
"state_before": "𝕜 : Type u_3\ninst✝³ : NontriviallyNormedField ... | [
254,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_mul_lt_one_iff_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ a * b⁻¹ < 1 ↔ a < b",
"tactic": "rw [← mul_lt_mul_iff_right b, inv_mul_cancel_right, one_mul]"
}
] | [
322,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_covby_of_not_isMin | [] | [
633,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_one | [
{
"state_after": "M : Type u_2\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_1\ninst✝¹ : CommMonoid N\nP : Type ?u.730830\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx : M\n⊢ ↑(toMap f) x * ↑1⁻¹ = ↑(toMap f) x",
"state_before": "M : Type u_2\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_1\ni... | [
721,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.tendsto_iff_ptendsto_univ | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nl₁ : Filter α\nl₂ : Filter β\nf : α → β\n⊢ Tendsto f l₁ l₂ ↔ Tendsto f (l₁ ⊓ 𝓟 Set.univ) l₂",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl₁ : Filter α\nl₂ : Filter β\nf : α → β\n⊢ Tendsto f l₁ l₂ ↔ PTendsto (PFun.res f Set.univ) l₁ l₂",
"t... | [
254,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Iio | [] | [
178,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_three | [
{
"state_after": "x : ℝ\nh₁ : (2 * cos (π / 3) - 1) ^ 2 * (2 * cos (π / 3) + 2) = 0\n⊢ cos (π / 3) = 1 / 2",
"state_before": "x : ℝ\n⊢ cos (π / 3) = 1 / 2",
"tactic": "have h₁ : (2 * cos (π / 3) - 1) ^ 2 * (2 * cos (π / 3) + 2) = 0 := by\n have : cos (3 * (π / 3)) = cos π := by\n congr 1\n ring\n... | [
857,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Order/Disjoint.lean | disjoint_sup_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : OrderBot α\na b c : α\n⊢ Disjoint (a ⊔ b) c ↔ Disjoint a c ∧ Disjoint b c",
"tactic": "simp only [disjoint_iff, inf_sup_right, sup_eq_bot_iff]"
}
] | [
188,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_log | [] | [
220,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.clm_apply | [] | [
144,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.trans_wbtw_right_ne | [] | [
524,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_of_add_const_right | [] | [
704,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.range_dualMap_mkQ_eq | [
{
"state_after": "case h\nR : Type u_1\nM : Type u_2\nM' : Type ?u.1403652\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M'\ninst✝ : Module R M'\nW : Submodule R M\nφ : Dual R M\n⊢ φ ∈ LinearMap.range (LinearMap.dualMap (mkQ W)) ↔ φ ∈ dualAnnihilator W",
"state_be... | [
1251,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.dvd_lcm_right | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\nhxy : gcd x y = 0\n⊢ y ∣ 0",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\nhxy : gcd x y = 0\n⊢ y ∣ lcm x y",
"tactic": "rw [lcm, hxy, div_zero]"
},
{
"state_after... | [
268,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.id_comp | [
{
"state_after": "case h\nR : Type u\nL₁ : Type v\nL₂ : Type w\nL₃ : Type w₁\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L₁\ninst✝⁴ : LieAlgebra R L₁\ninst✝³ : LieRing L₂\ninst✝² : LieAlgebra R L₂\ninst✝¹ : LieRing L₃\ninst✝ : LieAlgebra R L₃\nf : L₁ →ₗ⁅R⁆ L₂\nx✝ : L₁\n⊢ ↑(comp id f) x✝ = ↑f x✝",
"state_before":... | [
442,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_or_equiv_or_gt_or_fuzzy | [
{
"state_after": "case inl.inl\nx y : PGame\nh₁ : x ≤ y\nh₂ : y ≤ x\n⊢ x < y ∨ (x ≈ y) ∨ y < x ∨ x ‖ y\n\ncase inl.inr\nx y : PGame\nh₁ : x ≤ y\nh₂ : x ⧏ y\n⊢ x < y ∨ (x ≈ y) ∨ y < x ∨ x ‖ y\n\ncase inr.inl\nx y : PGame\nh₁ : y ⧏ x\nh₂ : y ≤ x\n⊢ x < y ∨ (x ≈ y) ∨ y < x ∨ x ‖ y\n\ncase inr.inr\nx y : PGame\nh₁ ... | [
999,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ -π < π / 2 ∧ π / 2 ≤ π",
"tactic": "constructor <;> linarith [pi_pos]"
}
] | [
614,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.le_def | [] | [
92,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_subtype_eq | [] | [
334,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorph.map_nhds_eq | [] | [
119,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/List/Join.lean | List.join_reverse | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.18738\nL : List (List α)\n⊢ join (reverse L) = reverse (join (map reverse L))",
"tactic": "simpa [reverse_reverse, map_reverse] using congr_arg List.reverse (reverse_join L.reverse)"
}
] | [
230,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_list_prod | [] | [
907,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
11
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.rightAdjointMate_id | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nX : C\ninst✝ : HasRightDual X\n⊢ 𝟙 Xᘁ = 𝟙 Xᘁ",
"tactic": "simp only [rightAdjointMate, MonoidalCategory.tensor_id, Category.id_comp,\n coevaluation_evaluation_assoc, Category.comp_id, Iso.inv_... | [
187,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | bounded_iff_forall_norm_le' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.98865\n𝕜 : Type ?u.98868\nα : Type ?u.98871\nι : Type ?u.98874\nκ : Type ?u.98877\nE : Type u_1\nF : Type ?u.98883\nG : Type ?u.98886\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
676,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.ne_of_gt | [] | [
31,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
31,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_inj | [] | [
444,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_univ | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.128288\ninst✝ : Fintype ι\nr : ℝ≥0\n⊢ ↑r = ↑↑volume (Icc 0 ↑r)",
"tactic": "simp"
}
] | [
107,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.iIsOrtho_def | [] | [
786,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.smul_vec2 | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nR : Type u_1\ninst✝ : SMul R α\nx : R\na₀ a₁ : α\n⊢ x • ![a₀, a₁] = ![x • a₀, x • a₁]",
"tactic": "rw [smul_cons, smul_cons, smul_empty]"
}
] | [
480,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | powMonoidWithZeroHom_apply | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.edist_equiv_symm_single_same | [
{
"state_after": "no goals",
"state_before": "p : ℝ≥0∞\n𝕜 : Type ?u.494939\n𝕜' : Type ?u.494942\nι : Type u_1\nα : ι → Type ?u.494950\nβ : ι → Type u_2\ninst✝⁹ : Fintype ι\ninst✝⁸ : Fact (1 ≤ p)\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : NormedField 𝕜'\ninst✝⁵ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝⁴ : (... | [
876,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_eq_bot_of_injective | [
{
"state_after": "R : Type u_4\nR₁ : Type ?u.1268464\nR₂ : Type u_5\nR₃ : Type ?u.1268470\nR₄ : Type ?u.1268473\nS : Type ?u.1268476\nK : Type ?u.1268479\nK₂ : Type ?u.1268482\nM : Type u_1\nM' : Type ?u.1268488\nM₁ : Type ?u.1268491\nM₂ : Type u_2\nM₃ : Type ?u.1268497\nM₄ : Type ?u.1268500\nN : Type ?u.126850... | [
1448,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | toDfinsupp_support | [
{
"state_after": "case a\nι : Type u_1\nR : Type ?u.2193\nM : Type u_2\ninst✝² : DecidableEq ι\ninst✝¹ : Zero M\ninst✝ : (m : M) → Decidable (m ≠ 0)\nf : ι →₀ M\na✝ : ι\n⊢ a✝ ∈ Dfinsupp.support (Finsupp.toDfinsupp f) ↔ a✝ ∈ f.support",
"state_before": "ι : Type u_1\nR : Type ?u.2193\nM : Type u_2\ninst✝² : ... | [
102,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.edist_efixedPoint_le | [
{
"state_after": "case h.e'_4.h.e'_5\nα : Type u_1\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\nhf : ContractingWith K f\nx : α\nhx : edist x (f x) ≠ ⊤\n⊢ edist x (f x) = edist x (f x) * ↑K ^ 0",
"state_before": "α : Type u_1\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : ... | [
147,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Order/Atoms.lean | GaloisCoinsertion.isCoatom_iff' | [] | [
783,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_nat_cast | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\nn : ℕ\n⊢ ↑(x ^ ↑n) = ↑(x ^ n)",
"tactic": "simpa only [coe_rpow, coe_pow] using Real.rpow_nat_cast x n"
}
] | [
131,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_add_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.129440\nα : Type u_1\nβ : Type ?u.129446\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na✝¹ a✝ : α\nz a : ℤ\n⊢ a ≤ ⌊a✝ + ↑z⌋ ↔ a ≤ ⌊a✝⌋ + z",
"tactic": "rw [le_floor, ← sub_le_iff_le_add, ← sub_le_iff_le_add, le_floor, Int.cast_sub]"... | [
726,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_series_hasSum_exp' | [] | [
437,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.isPositive_one | [] | [
84,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.map_smulₛₗ | [] | [
500,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
11
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.iSup_adj | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nf : ι → Subgraph G\n⊢ Adj (⨆ (i : ι), f i) a b ↔ ∃ i, Adj (f i) a b",
"tactic": "simp [iSup]"
}
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400,
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399,
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.of_unique_max_ideal | [] | [
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_bot | [] | [
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Mathlib/Topology/Order/Basic.lean | Filter.Tendsto.max_left | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.coe_tanLocalHomeomorph_symm | [] | [
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Mathlib/Topology/Algebra/Order/T5.lean | Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic | [
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.pre_eq | [
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Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_right | [
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Mathlib/Data/Complex/Basic.lean | Complex.I_re | [] | [
302,
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Mathlib/Order/WithBot.lean | WithTop.ofDual_le_iff | [] | [
813,
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Mathlib/Analysis/Calculus/MeanValue.lean | StrictMonoOn.exists_slope_lt_deriv_aux | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.map_id | [] | [
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_int_eq_addSubgroup_closure | [] | [
202,
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Std/Data/Int/DivMod.lean | Int.fdiv_eq_ediv_of_dvd | [
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.ne_empty_of_mem | [] | [
164,
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_extendDomain | [
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284,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_map | [
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Mathlib/Topology/Order.lean | IsOpen.mono | [] | [
244,
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.map_mk_eq_bot_of_le | [
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111,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.leftInverse_symm | [] | [
360,
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Mathlib/Order/Concept.lean | gc_intentClosure_extentClosure | [] | [
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48
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Mathlib/Algebra/Periodic.lean | Function.Periodic.const_inv_smul₀ | [
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Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.map_Hσ | [
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207,
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src/lean/Init/Data/Nat/Basic.lean | Nat.succ_mul | [
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85
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Mathlib/Data/Set/Lattice.lean | Set.preimage_iUnion | [
{
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Mathlib/Data/Rat/Order.lean | Rat.abs_def | [
{
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309,
42
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300,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_toNat_of_infinite | [] | [
1739,
36
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1738,
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Mathlib/Topology/FiberBundle/Constructions.lean | Pullback.continuous_proj | [
{
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322,
20
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320,
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Std/Data/List/Lemmas.lean | List.range_zero | [] | [
1926,
49
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Mathlib/Data/Set/Lattice.lean | Set.sInter_prod_sInter | [
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Mathlib/Data/PNat/Basic.lean | PNat.add_coe | [] | [
125,
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Mathlib/Logic/Basic.lean | imp_iff_right_iff | [] | [
177,
87
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177,
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Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.average_eq_integral_normalize | [
{
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395,
68
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389,
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Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.exists_root_sum_quadratic | [
{
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101,
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Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_self | [
{
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59,
41
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.extend_eq | [] | [
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63
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.of_isIso_fac_right | [
{
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Mathlib/Algebra/Group/Opposite.lean | isUnit_unop | [] | [
485,
27
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Mathlib/Algebra/CharZero/Lemmas.lean | bit1_eq_bit1 | [] | [
142,
24
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141,
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Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.dvd_pow_natDegree_of_aeval_eq_zero | [] | [
190,
30
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186,
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Mathlib/Computability/Primrec.lean | Primrec.option_casesOn | [
{
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Mathlib/Init/Algebra/Classes.lean | antisymm | [] | [
270,
26
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_down' | [
{
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810,
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796,
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | ne₁₂_of_not_collinear | [
{
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29
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.liftp_iff | [
{
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117,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.exists_ge | [] | [
772,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
11
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.SeparationQuotient.uniformContinuous_lift | [
{
"state_after": "case pos\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : SeparatedSpace β\nf : α → β\nhf : UniformContinuous f\n⊢ UniformContinuous (lift f)\n\ncase neg\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α\ninst✝² ... | [
388,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.discreteSieve_mem | [] | [
47,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | tendsto_const_smul_iff | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.30275\nα : Type u_2\nβ : Type u_1\nG : Type u_3\ninst✝³ : TopologicalSpace α\ninst✝² : Group G\ninst✝¹ : MulAction G α\ninst✝ : ContinuousConstSMul G α\nf : β → α\nl : Filter β\na : α\nc : G\nh : Tendsto (fun x => c • f x) l (𝓝 (c • a))\n⊢ Tendsto f... | [
201,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.add_div_of_dvd_right | [
{
"state_after": "no goals",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhca : c ∣ a\nh : c = 0\n⊢ (a + b) / c = a / c + b / c",
"tactic": "simp [h]"
},
{
"state_after": "m n a✝ b✝ c✝ d a b c : ℕ\nhca : c ∣ a\nh : ¬c = 0\n⊢ b % c < c",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhca : c ∣ a\nh... | [
473,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
11
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.201083\nβ : Type ?u.201086\ninst✝² : LinearOrderedField α\ninst✝¹ : DivisionRing β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nx : β\nhx : x ≠ 0\n⊢ ¬LimZero (const abv x)",
"tactic": "rwa [const_limZero]"
}
] | [
651,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Deprecated/Group.lean | Multiplicative.isGroupHom | [] | [
472,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_bot | [] | [
835,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.submodule_span_single | [
{
"state_after": "R M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nF F' : Filtration I M\nh : Stable F\n⊢ Submodule.span { x // x ∈ reesAlgebra I } ↑(Filtration.submodule F) = Filtration.submodule F",
"state_before": "R M : Type u\ninst✝² : CommRing R\ninst✝¹ : Ad... | [
320,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.not_lt_zero | [] | [
420,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
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