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/MeasureTheory/Measure/OpenPos.lean | Continuous.ae_eq_iff_eq | [] | [
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64
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123,
1
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.isBasis_iff_nbhd | [
{
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Mathlib/Logic/Basic.lean | not_ne_iff | [] | [
254,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.pullback_id | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nf : MonoOver X\n⊢ (pullback (𝟙 X)).obj (Quotient.mk'' f) = Quotient.mk'' f",
"state_before": "C : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝... | [
562,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.zero_of_le_dist | [
{
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"tact... | [
419,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_lt_lineMap_iff_of_lt | [
{
"state_after": "k : Type u_1\nE : Type u_2\nPE : Type ?u.56390\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup E\ninst✝¹ : Module k E\ninst✝ : OrderedSMul k E\na a' b b' : E\nr r' : k\nh : r < r'\n⊢ (1 - r) • a + r • b < (1 - r') • a + r' • b ↔ a < b",
"state_before": "k : Type u_1\nE : Type u_2\nPE... | [
88,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.mem_bot | [] | [
75,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.compactConvNhd_subset_inter | [] | [
134,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Data/Set/Basic.lean | Set.mem_ite_univ_right | [] | [
2198,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2196,
1
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_zero | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Continuous.locallyIntegrable | [] | [
253,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_int_cast_map | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R✝\nm n : ℕ\ninst✝³ : Semiring R✝\np✝ q r : R✝[X]\ninst✝² : Semiring S✝\nf✝ : R✝ →+* S✝\nR : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\np : R[X]\ni : ℤ\n⊢ eval (↑i) (map f p) = ↑f... | [
991,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
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Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | AEMeasurable.re | [] | [
51,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
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Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.fg_of_finiteType | [] | [
617,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
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Mathlib/Topology/SubsetProperties.lean | continuous_boolIndicator_iff_clopen | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Type ?u.178896\nπ : ι → Type ?u.178901\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\nX : Type u_1\ninst✝ : TopologicalSpace X\nU : Set X\n⊢ Continuous (boolIndicator U) → IsClopen U\n\ncase mpr\nα : Type u\nβ : Type v\nι : Type ?u.... | [
1670,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
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] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.subgroupOf_range_eq_of_le | [
{
"state_after": "case h\nG : Type ?u.484195\nG' : Type ?u.484198\ninst✝⁶ : Group G\ninst✝⁵ : Group G'\nA : Type ?u.484207\ninst✝⁴ : AddGroup A\nN : Type ?u.484213\nP : Type ?u.484216\ninst✝³ : Group N\ninst✝² : Group P\nK✝ : Subgroup G\nG₁ : Type u_1\nG₂ : Type u_2\ninst✝¹ : Group G₁\ninst✝ : Group G₂\nK : Sub... | [
2697,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2692,
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] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_contract' | [] | [
184,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Antivary.dual_right | [] | [
220,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.nontrivial_iff_two_le | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ Nontrivial (Fin n) ↔ 2 ≤ n",
"tactic": "rcases n with (_ | _ | n) <;>\nsimp [←Nat.one_eq_succ_zero, Fin.nontrivial, not_nontrivial, Nat.succ_le_iff]"
}
] | [
651,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
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] |
Mathlib/Data/Fin/Basic.lean | Fin.val_bit1 | [
{
"state_after": "case zero\nn m : ℕ\ninst✝ : NeZero zero\nk : Fin zero\n⊢ ↑(bit1 k) = bit1 ↑k % zero\n\ncase succ\nn m n✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\nk : Fin (Nat.succ n✝)\n⊢ ↑(bit1 k) = bit1 ↑k % Nat.succ n✝",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\nk : Fin n\n⊢ ↑(bit1 k) = bit1 ↑k % n",
... | [
733,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.piecewise_apply | [] | [
618,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Std/Data/List/Lemmas.lean | List.erase_append_right | [
{
"state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : ¬a ∈ l₁\n⊢ ∀ (b : α), b ∈ l₁ → ¬decide (a = b) = true",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : ¬a ∈ l₁\n⊢ List.erase (l₁ ++ l₂) a = l₁ ++ List.erase l₂ a",
"tactic": "rw [e... | [
1072,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1069,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.isUnit_den | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖↑r‖ ≤ 1\n⊢ ‖↑r.den‖ = 1",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖↑r‖ ≤ 1\n⊢ IsUnit ↑r.den",
"tactic": "rw [isUnit_iff]"
},
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖... | [
103,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.measurableSet_of_null | [] | [
464,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.continuous_of_continuousAt_zero | [
{
"state_after": "R : Type ?u.1410115\nR' : Type ?u.1410118\n𝕜 : Type ?u.1410121\n𝕜₂ : Type ?u.1410124\n𝕜₃ : Type ?u.1410127\n𝕝 : Type u_2\nE : Type u_1\nE₂ : Type ?u.1410136\nE₃ : Type ?u.1410139\nF : Type ?u.1410142\nG : Type ?u.1410145\nι : Type ?u.1410148\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : S... | [
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72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
11
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_toLinearMap | [] | [
726,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Order/SemiconjSup.lean | Function.semiconj_of_isLUB | [
{
"state_after": "α : Type u_1\nβ : Type ?u.7502\nγ : Type ?u.7505\nG : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' => ↑(↑f₁ g')⁻¹ (↑(↑f₂ g') x)) (h x)\ng : G\ny : α\n⊢ IsLUB (range fun g' => ↑(↑f₁ g')⁻¹ (↑(↑f₂ g') (↑(↑f₂ g) y))) (↑(↑f₁ ... | [
110,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.tendsto_of_forall_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.9571\nδ : Type ?u.9574\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nh : ∀ (s : Set β), IsCompact s → IsCompact (f ⁻¹' s)\ns : Set β\nhs : s ... | [
179,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/GeomSum.lean | Odd.geom_sum_pos | [
{
"state_after": "case zero\nα : Type u\nβ : Type ?u.244183\nx : α\ninst✝ : LinearOrderedRing α\nh : Odd Nat.zero\n⊢ 0 < ∑ i in range Nat.zero, x ^ i\n\ncase succ.zero\nα : Type u\nβ : Type ?u.244183\nx : α\ninst✝ : LinearOrderedRing α\nh : Odd (Nat.succ Nat.zero)\n⊢ 0 < ∑ i in range (Nat.succ Nat.zero), x ^ i\... | [
529,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4196\nγ : Type ?u.4199\nδ : Type ?u.4202\ninst✝ : TopologicalSpace α\na : α\n⊢ 𝓝[univ] a = 𝓝 a",
"tactic": "rw [nhdsWithin, principal_univ, inf_top_eq]"
}
] | [
81,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_eq | [] | [
158,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.mul_rpow_of_ne_top | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0∞\nhx : x ≠ ⊤\nhy : y ≠ ⊤\nz : ℝ\n⊢ (x * y) ^ z = x ^ z * y ^ z",
"tactic": "simp [*, mul_rpow_eq_ite]"
}
] | [
505,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_Ioo | [] | [
295,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_union | [] | [
940,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_apply | [
{
"state_after": "no goals",
"state_before": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\ni j : n\n⊢ adjugate A i j = det (updateRow A j (Pi.single i 1))",
"tactic": "rw [adjugate_def, o... | [
219,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.le_mul_ediam_image | [] | [
124,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_add | [] | [
327,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
11
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | isLittleO_coe_const_pow_of_one_lt | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.97427\nβ : Type ?u.97430\nι : Type ?u.97433\nR : Type u_1\ninst✝ : NormedRing R\nr : ℝ\nhr : 1 < r\n⊢ Nat.cast =o[atTop] fun n => r ^ n",
"tactic": "simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr"
}
] | [
212,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.toFun_as_coe | [] | [
188,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
9
] |
Mathlib/Deprecated/Subfield.lean | Preimage.isSubfield | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nS : Set F\nK : Type u_1\ninst✝ : Field K\nf : F →+* K\ns : Set K\nhs : IsSubfield s\nsrc✝ : IsSubring (↑f ⁻¹' s) := RingHom.isSubring_preimage f hs.toIsSubring\na : F\nha : ↑f a ∈ s\n⊢ (↑f a)⁻¹ ∈ s",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nS : Set F... | [
68,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\nx : α\n⊢ ↑normalize (↑normalize x) = ↑normalize x",
"tactic": "simp"
}
] | [
172,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_swap | [] | [
167,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.continuous_dist | [] | [
51,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/GroupTheory/Congruence.lean | Con.zpow | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.99934\nP : Type ?u.99937\ninst✝² : Group M\ninst✝¹ : Group N\ninst✝ : Group P\nc : Con M\nn : ℕ\nw x : M\nh : ↑c w x\n⊢ ↑c (w ^ Int.ofNat n) (x ^ Int.ofNat n)",
"tactic": "simpa only [zpow_ofNat, Int.ofNat_eq_coe] using c.pow n h"
... | [
1240,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
11
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjectionFn_mem | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\np : P\n⊢ ↑s ∩ ↑(mk' p (direction s)ᗮ) ⊆ ↑s"... | [
267,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_eq_sInf_image | [] | [
760,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.eq_iff_eq | [] | [
815,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_submatrix_sum_swap_left | [
{
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Mathlib/Control/Functor.lean | Functor.Comp.map_mk | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | dist_triangle_left | [
{
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204,
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Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.list_prod_map_eq_dProd | [
{
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Mathlib/Analysis/NormedSpace/ConformalLinearMap.lean | IsConformalMap.comp | [
{
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92,
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Mathlib/Data/Set/Sups.lean | Set.Nonempty.of_infs_left | [] | [
279,
26
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Mathlib/LinearAlgebra/Determinant.lean | LinearEquiv.det_mul_det_symm | [
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Mathlib/Data/Real/Sqrt.lean | NNReal.mul_self_sqrt | [
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Mathlib/Data/List/Sigma.lean | List.kreplace_self | [
{
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367,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_le_hausdorffDist_of_mem | [] | [
797,
57
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Iic_of_intervalIntegral_norm_tendsto | [] | [
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68
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Mathlib/Algebra/GroupPower/Basic.lean | pow_bit0 | [] | [
199,
16
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Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_eq_sum_mapIdx | [
{
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187,
16
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Mathlib/Analysis/Complex/Basic.lean | Complex.nnnorm_real | [] | [
186,
29
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Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean | CategoryTheory.Idempotents.app_p_comp | [] | [
49,
25
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPushout.inl_iso_inv | [
{
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243,
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Mathlib/Order/LiminfLimsup.lean | Filter.isBounded_top | [
{
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99
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Mathlib/Control/Traversable/Lemmas.lean | Traversable.traverse_id | [
{
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Mathlib/Order/Filter/Cofinite.lean | Filter.comap_cofinite_le | [] | [
114,
93
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Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.pso_inv | [
{
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Std/Data/List/Basic.lean | List.takeList_eq_takeListTR | [
{
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coe_affineSpan_singleton | [
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707,
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Mathlib/Data/Finset/Image.lean | Finset.Nonempty.image | [] | [
391,
31
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.subset_span_extend | [] | [
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Mathlib/GroupTheory/Sylow.lean | Sylow.ext | [
{
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Mathlib/Data/Real/Sqrt.lean | Real.le_sqrt' | [] | [
309,
43
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308,
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Mathlib/Algebra/CharP/Two.lean | CharTwo.sub_eq_add | [
{
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}
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79
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Mathlib/RingTheory/Ideal/LocalRing.lean | map_mem_nonunits_iff | [] | [
230,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/Topology/Order/Basic.lean | isClosed_le | [] | [
131,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_zero_subset | [] | [
1032,
76
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1030,
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Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | continuousWithinAt_left_of_monotoneOn_of_closure_image_mem_nhdsWithin | [] | [
173,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Algebra/Ring/Defs.lean | mul_neg_one | [
{
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"tactic": "simp"
}
] | [
326,
53
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326,
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Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.charpoly_sub_diagonal_degree_lt | [
{
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Mathlib/Data/Finset/Basic.lean | Finset.mem_insert_self | [] | [
1065,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
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Mathlib/Analysis/Calculus/MeanValue.lean | norm_image_sub_le_of_norm_deriv_le_segment_01 | [
{
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394,
88
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390,
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Mathlib/Algebra/Order/Floor.lean | Int.fract_eq_self | [
{
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] | [
947,
74
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946,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAdjointPair.mul | [
{
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Mathlib/Topology/Algebra/ConstMulAction.lean | continuousOn_const_smul_iff | [] | [
217,
63
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215,
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Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.exists_mulVec_eq_zero_iff' | [
{
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170,
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138,
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioc_of_interval_integral_norm_bounded_left | [] | [
608,
81
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605,
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Mathlib/Algebra/Associated.lean | Associates.dvd_eq_le | [] | [
861,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.swapCore_comm | [
{
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{
... | [
1539,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1535,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | IsAntichain.ordConnected | [
{
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238,
14
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234,
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Mathlib/Data/Nat/Pairing.lean | Nat.pair_eq_pair | [] | [
94,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
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Mathlib/Topology/ContinuousOn.lean | ContinuousOn.fst | [] | [
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38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
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Mathlib/Order/Filter/Basic.lean | Filter.comap_le_comap_iff | [] | [
2270,
90
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2268,
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Mathlib/Algebra/Order/Kleene.lean | kstar_mono | [] | [
246,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.abs_im_le_norm | [
{
"state_after": "K : Type u_1\nE : Type ?u.6631852\ninst✝ : IsROrC K\nz : K\n⊢ ↑im z * ↑im z ≤ ↑normSq z",
"state_before": "K : Type u_1\nE : Type ?u.6631852\ninst✝ : IsROrC K\nz : K\n⊢ abs (↑im z) ≤ ‖z‖",
"tactic": "rw [mul_self_le_mul_self_iff (abs_nonneg _) (norm_nonneg _), abs_mul_abs_self, mul_sel... | [
721,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Iio_subset_Iic_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.66687\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\na : α\n⊢ Iio a ⊆ Iic a",
"tactic": "simpa [← coe_subset] using Set.Iio_subset_Iic_self"
}
] | [
490,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Deprecated/Submonoid.lean | powers.self_mem | [] | [
146,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.encode_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.25349\nσ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α → σ\nh : Primrec fun a => encode (f a)\nn : ℕ\n⊢ encode (Option.map (fun a => encode (f a)) (decode n)) = encode (Option.map f (decode n))... | [
276,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_zero | [
{
"state_after": "no goals",
"state_before": "a✝ : Nat\n⊢ ofNat (a✝ / 0) = 0",
"tactic": "simp"
}
] | [
48,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
46,
25
] |
Mathlib/Data/Nat/Prime.lean | Nat.coprime_or_dvd_of_prime | [
{
"state_after": "p : ℕ\npp : Prime p\ni : ℕ\n⊢ coprime p i ∨ ¬coprime p i",
"state_before": "p : ℕ\npp : Prime p\ni : ℕ\n⊢ coprime p i ∨ p ∣ i",
"tactic": "rw [pp.dvd_iff_not_coprime]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\npp : Prime p\ni : ℕ\n⊢ coprime p i ∨ ¬coprime p i"... | [
684,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
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