file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/CategoryTheory/Limits/Cones.lean | CategoryTheory.Limits.Cone.w | [
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Mathlib/RingTheory/MatrixAlgebra.lean | MatrixEquivTensor.toFunBilinear_apply | [] | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean | Complex.tendsto_abs_tan_atTop | [] | [
54,
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Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.iff_eq_zero_or_one | [
{
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Mathlib/Logic/Equiv/Option.lean | Equiv.removeNone_none | [] | [
142,
26
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141,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.hasSum_integral_iUnion | [] | [
251,
8
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Mathlib/Computability/EpsilonNFA.lean | εNFA.eval_append_singleton | [] | [
138,
36
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Mathlib/Logic/Basic.lean | Ne.ite_eq_left_iff | [] | [
1185,
32
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1184,
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Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_unsym | [] | [
71,
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Mathlib/CategoryTheory/Limits/Final.lean | CategoryTheory.Functor.Final.zigzag_of_eqvGen_quot_rel | [
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407,
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391,
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Images.lean | CategoryTheory.PreservesImage.inv_comp_image_ι_map | [
{
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71,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAtFilter_iff_tendsto | [] | [
264,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_fuzzy | [] | [
928,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/FixedPoints.lean | OrderHom.lfp_le | [] | [
61,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_pos | [] | [
1464,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | continuous_of_const | [] | [
1697,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1695,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.NormNoninc.comp | [] | [
842,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
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Mathlib/Algebra/Star/SelfAdjoint.lean | star_comm_self' | [] | [
63,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GroupPower/Ring.lean | neg_one_sq | [
{
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"tactic": "simp [neg_sq, one_pow]"
}
] | [
225,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Factorization/PrimePow.lean | isPrimePow_iff_factorization_eq_single | [
{
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58,
101
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Mathlib/LinearAlgebra/Span.lean | Submodule.singleton_span_isCompactElement | [
{
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663,
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.Salient.anti | [] | [
396,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_iInf | [] | [
435,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_smul | [] | [
617,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Finset.hasSum | [
{
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180,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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Mathlib/Order/Filter/Pointwise.lean | Filter.mem_one | [] | [
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11
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Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Balanced.ins | [
{
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"tactic": "induction hp generalizing t with\n| root => exact ht.setB... | [
158,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_join | [
{
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Mathlib/Order/Bounds/Basic.lean | AntitoneOn.mem_lowerBounds_image_self | [] | [
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43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_lsmul_apply_le | [] | [
1220,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.concyclic_empty | [] | [
222,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.zero_eq_bot | [] | [
424,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/Data/Complex/Basic.lean | Complex.abs_le_abs_re_add_abs_im | [
{
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}
] | [
1068,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finsupp/Antidiagonal.lean | Finsupp.mem_antidiagonal | [
{
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"tactic": "rcases p with ⟨p₁, p₂⟩"
},
{
"state_after": "no goals",... | [
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88
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49,
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_vadd_left | [
{
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | prod_le_borel_prod | [
{
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1002,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.pow_eq | [] | [
926,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_naturality | [] | [
213,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/RingTheory/GradedAlgebra/Basic.lean | GradedAlgebra.proj_apply | [] | [
230,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/Order/Filter/Extr.lean | IsMinOn.add | [] | [
466,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
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Mathlib/Data/Part.lean | Part.assert_pos | [
{
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474,
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Mathlib/Computability/PartrecCode.lean | Nat.Partrec.rfind' | [
{
"state_after": "f : ℕ →. ℕ\nhf : Partrec f\n⊢ Partrec (unpaired fun a b => Nat.rfind fun n => (fun m => decide (m = 0)) <$> f (Nat.pair a (n + b)))",
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Mathlib/Data/Matrix/Basic.lean | Matrix.reindex_symm | [] | [
2565,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2563,
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Mathlib/Algebra/Invertible.lean | mul_mul_invOf_self_cancel | [
{
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}
] | [
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19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Algebra/Group/Ext.lean | RightCancelMonoid.ext | [] | [
87,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Instances/Discrete.lean | bot_topologicalSpace_eq_generateFrom_of_pred_succOrder | [
{
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58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_lt_one | [
{
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"tactic": "rw [← cast_one, cast_lt, lt_succ_iff, ← bot_eq_zero, le_bot_iff]"
}
] | [
151,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.aemeasurable | [
{
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45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.prod_atBot_atBot_eq | [] | [
1409,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
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Mathlib/Analysis/Convex/StrictConvexSpace.lean | StrictConvexSpace.ofNormAdd | [
{
"state_after": "𝕜 : Type ?u.39174\nE : Type u_1\ninst✝³ : NormedLinearOrderedField 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nh : ∀ (x y : E), ‖x‖ = 1 → ‖y‖ = 1 → ‖x + y‖ = 2 → SameRay ℝ x y\nx : E\nhx : x ∈ sphere 0 1\ny : E\nhy : y ∈ sphere 0 1\nh₂ : ‖x + y‖ = 2\... | [
150,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_zero_subset | [
{
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"tactic": "simp [subset_def, mem_div]"
}
] | [
1274,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.mono_of_source_iso_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ni : X ≅ 0\nZ : C\ng h : Z ⟶ X\nx✝ : g ≫ f = h ≫ f\n⊢ g = h",
"tactic": "rw [zero_of_target_iso_zero g i, zero_of_targ... | [
404,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_right_cancel_iff | [] | [
221,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_div_of_ne_zero | [
{
"state_after": "F : Type ?u.37416\nι : Type ?u.37419\nα : Type u_1\nβ : Type ?u.37425\ninst✝ : DivisionRing α\nm n : ℚ\nmd : ↑m.den ≠ 0\nnn : ↑n.num ≠ 0\nnd : ↑n.den ≠ 0\nthis : ↑n⁻¹.den ∣ n.num\n⊢ ↑(m / n) = ↑m / ↑n",
"state_before": "F : Type ?u.37416\nι : Type ?u.37419\nα : Type u_1\nβ : Type ?u.37425\... | [
190,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.univ_mem' | [] | [
172,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.pellZd_succ_succ | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\nthis : 1 + { re := ↑a, im := 1 } * { re := ↑a, im := 1 } = { re := ↑a, im := 1 } * (2 * ↑a)\n⊢ pellZd a1 (n + 2) + pellZd a1 n = ↑(2 * a) * pellZd a1 (n + 1)",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ pellZd a1 (n + 2) + pellZd a1 n = ↑(2 * a) * pellZd a1 (n +... | [
519,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma1_mem | [
{
"state_after": "case mp\nN✝ N : ℕ\nA : SL(2, ℤ)\n⊢ A ∈ Gamma1 N → ↑(↑A 0 0) = 1 ∧ ↑(↑A 1 1) = 1 ∧ ↑(↑A 1 0) = 0\n\ncase mpr\nN✝ N : ℕ\nA : SL(2, ℤ)\n⊢ ↑(↑A 0 0) = 1 ∧ ↑(↑A 1 1) = 1 ∧ ↑(↑A 1 0) = 0 → A ∈ Gamma1 N",
"state_before": "N✝ N : ℕ\nA : SL(2, ℤ)\n⊢ A ∈ Gamma1 N ↔ ↑(↑A 0 0) = 1 ∧ ↑(↑A 1 1) = 1 ∧ ↑(... | [
197,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.nonempty_Icc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.50\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Finset.Nonempty (Icc a b) ↔ a ≤ b",
"tactic": "rw [← coe_nonempty, coe_Icc, Set.nonempty_Icc]"
}
] | [
50,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_pi | [
{
"state_after": "case a\n𝕜 : Type u\nι : Type v\nι'✝ : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE'✝ : ι'✝ → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝²⁰ : Fintype ι\ninst✝¹⁹ : Fintype ι'✝\ninst✝¹⁸ : NontriviallyNormedField 𝕜\ninst✝¹⁷ : (i : ι) → NormedAddCommGrou... | [
502,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.dom_fintype | [
{
"state_after": "α : Type u_1\nβ : Type ?u.157316\nγ : Type ?u.157319\nδ : Type ?u.157322\nσ : Type u_2\ninst✝⁵ : Primcodable α\ninst✝⁴ : Primcodable β\ninst✝³ : Primcodable γ\ninst✝² : Primcodable δ\ninst✝¹ : Primcodable σ\ninst✝ : Fintype α\nf : α → σ\nl : List α\nleft✝ : List.Nodup l\nm : ∀ (x : α), x ∈ l\n... | [
789,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | smul_vsub_rev_vadd_mem_affineSpan_pair | [] | [
1333,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Algebra/Invertible.lean | mul_right_inj_of_invertible | [] | [
301,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Order/LiminfLimsup.lean | OrderIso.isBoundedUnder_ge_comp | [] | [
260,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.congr_comp | [] | [
705,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_lt_card_fiber_of_nsmul_lt_card | [] | [
380,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_union_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.560456\nγ : Type ?u.560459\nδ : Type ?u.560462\nι : Type ?u.560465\nR : Type ?u.560468\nR' : Type ?u.560471\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ s t ... | [
2756,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2755,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots_sub_C | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\na : R\nhp0 : 0 < degree p\n⊢ degree (p + ↑C (-a)) = degree p",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p ... | [
555,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.131860\nγ : Type ?u.131863\nι : Sort ?u.131866\nι' : Sort ?u.131869\nι₂ : Sort ?u.131872\nκ : ι → Sort ?u.131877\nκ₁ : ι → Sort ?u.131882\nκ₂ : ι → Sort ?u.131887\nκ' : ι' → Sort ?u.131892\nc : Set (Set α)\n⊢ ⋂₀ c = ∅ ↔ ∀ (a : α), ∃ b, ... | [
1214,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | toDual_intCast | [] | [
387,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | eq_natCast | [] | [
259,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_injective | [] | [
187,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Rel.lean | Rel.image_union | [] | [
154,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.inter_of_left | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\na✝ : Fintype ↑s\n⊢ Set.Finite (s ∩ t)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nhs : Set.Finite s\nt : Set α\n⊢ Set.Finite (s ∩ t)",
"tactic": "cases hs"
},
{
"state_aft... | [
744,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/Data/Set/Function.lean | strictMono_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.101627\nι : Sort ?u.101630\nπ : α → Type ?u.101635\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\ns : Set α\n⊢ StrictMono (restrict s f) ↔ StrictMonoOn f s",
"tactic": "simp [Set.restrict, StrictMono, StrictMonoO... | [
1577,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1576,
1
] |
Mathlib/Logic/Basic.lean | Decidable.forall_or_left | [] | [
844,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_lt_ofReal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.22805\nι : Type ?u.22808\ninst✝ : PseudoMetricSpace α\nx y : α\nr : ℝ\n⊢ edist x y < ENNReal.ofReal r ↔ dist x y < r",
"tactic": "rw [edist_dist, ENNReal.ofReal_lt_ofReal_iff_of_nonneg dist_nonneg]"
}
] | [
371,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.le_of_add_le_add_left | [
{
"state_after": "no goals",
"state_before": "d : ℕ\na b c : ℤ√↑d\nh : c + a ≤ c + b\n⊢ a ≤ b",
"tactic": "simpa using Zsqrtd.add_le_add_left _ _ h (-c)"
}
] | [
790,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
11
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_smul_self | [] | [
2188,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2186,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_one | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_mul_of_prime_of_dvd | [
{
"state_after": "p n : ℕ\nhp : Prime p\nh : p ∣ n\nh1 : φ (gcd p n) * φ (p * n) = φ p * φ n * gcd p n\n⊢ φ (p * n) = p * φ n",
"state_before": "p n : ℕ\nhp : Prime p\nh : p ∣ n\n⊢ φ (p * n) = p * φ n",
"tactic": "have h1 := totient_gcd_mul_totient_mul p n"
},
{
"state_after": "p n : ℕ\nhp : Pri... | [
380,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasurableEmbedding.integral_map | [
{
"state_after": "case pos\nα : Type u_2\nE : Type u_3\nF : Type ?u.1387726\n𝕜 : Type ?u.1387729\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\nins... | [
1557,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.Valid.le_endPos | [
{
"state_after": "no goals",
"state_before": "cs cs' : List Char\n⊢ { byteIdx := utf8ByteSize.go cs } ≤ endPos { data := cs ++ cs' }",
"tactic": "simp [Nat.le_add_right]"
}
] | [
158,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
157,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | midpoint_le_right | [] | [
160,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/AssocList.lean | Std.AssocList.replace_toList | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\ninst✝ : BEq α\na : α\nb : β\nkey✝ : α\nvalue✝ : β\ntail✝ : AssocList α β\ntail_ih✝ :\n toList (replace a b tail✝) = List.replaceF (fun x => bif x.fst == a then some (a, b) else none) (toList tail✝)\n⊢ toList\n (match key✝ == a with\n | true => ... | [
167,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
164,
9
] |
Mathlib/Data/Bundle.lean | Bundle.pullbackTotalSpaceEmbedding_snd | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/GroupTheory/Torsion.lean | CommGroup.primaryComponent.isPGroup | [] | [
347,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_pow_unitClosedBall | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Topology/Maps.lean | Embedding.continuous_iff | [] | [
246,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_multiset_prod | [
{
"state_after": "case mk\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nm : Multiset R[X]\nL : List R[X]\n⊢ ¬0 ∈ Quot.mk Setoid.r L → roots (prod (Quot.mk Setoid.r L)) = Multiset.bind (Quot.mk Setoid.r L) roots",
"state_before": "R : Type u\nS : Ty... | [
696,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Analysis/Convex/Jensen.lean | le_sup_of_mem_convexHull | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.35552\nβ : Type u_3\nι : Type ?u.35558\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : LinearOrderedAddCommGroup β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSMul 𝕜 β\ns✝ : Set E\nf : E → β\nt... | [
95,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | PrincipalIdealRing.mem_submonoid_of_factors_subset_of_units_subset | [
{
"state_after": "case intro\nR : Type u\nM : Type v\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : IsPrincipalIdealRing R\ns : Submonoid R\na : R\nha : a ≠ 0\nhfac : ∀ (b : R), b ∈ factors a → b ∈ s\nhunit : ∀ (c : Rˣ), ↑c ∈ s\nc : Rˣ\nhc : Multiset.prod (factors a) * ↑c = a\n⊢ a ∈ s",
"state_before": ... | [
298,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.nsmul | [] | [
638,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.aeval_comp_bind₁ | [
{
"state_after": "case hf\nσ : Type u_4\nτ : Type u_3\nR : Type u_1\nS : Type u_2\nT : Type ?u.1067210\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S\ninst✝¹ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\ninst✝ : Algebra R S\nf : τ → S\ng : σ → MvPolynomial τ R\ni✝ : σ\n⊢ ↑(AlgHom.comp (aeval f) (bind₁ g)) (X ... | [
319,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.isIso_iff_mk_eq_top | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nX Y : C\nf : X ⟶ Y\ninst✝ : Mono f\nh : mk f = ⊤\n⊢ IsIso (ofMkLEMk f (𝟙 Y) (_ : mk f ≤ ⊤))",
"state_before": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nX Y : C\nf : X ⟶... | [
264,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
src/lean/Init/Data/List/Basic.lean | List.mapTR_loop_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\nas : List α\nbs : List β\n⊢ mapTR.loop f as bs = reverse bs ++ map f as",
"tactic": "induction as generalizing bs with\n| nil => simp [mapTR.loop, map]\n| cons a as ih =>\n simp [mapTR.loop, map]\n rw [ih (f a... | [
190,
8
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
183,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.natPred_le_natPred | [] | [
67,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_eq_linear_combination | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type ?u.282378\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι✝ : Type ?u.283028\ns✝ : Finset ι✝\nι₂ : Type ?u.283034\ns₂ : Finset ι₂\nι : Type u_1\ns : Finset ι\nw : ι → k\np : ι → V\nhw : Fi... | [
468,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_subset_vsub_left | [] | [
1523,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_submatrix | [] | [
2397,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2394,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_equiv_eq_map_symm | [] | [
2513,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2511,
1
] |
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