file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/CategoryTheory/Abelian/Projective.lean | CategoryTheory.projective_of_preservesFiniteColimits_preadditiveCoyonedaObj | [
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Mathlib/Order/Bounds/Basic.lean | image2_lowerBounds_upperBounds_subset_upperBounds_image2 | [
{
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Mathlib/Data/Rat/Cast.lean | Rat.cast_eq_zero | [
{
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] | [
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97
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Mathlib/Order/Filter/Basic.lean | Filter.comap_iInf | [] | [
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26
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2188,
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Mathlib/Data/List/Basic.lean | List.findIdx_nil | [] | [
1143,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
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Mathlib/Data/Real/NNReal.lean | NNReal.mul_eq_mul_left | [
{
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718,
42
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Mathlib/Order/Bounds/Basic.lean | OrderTop.bddAbove | [] | [
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Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.id_apply | [] | [
549,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Group/Basic.lean | isOpenMap_div_left | [] | [
1163,
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Mathlib/RingTheory/Finiteness.lean | Module.Finite.trans | [
{
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625,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Logic.lean | Or.symm | [] | [
247,
50
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.equalizerSubobject_factors | [
{
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"tactic": "simp"
}
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72,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_injective | [] | [
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31
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioi_eq_Ioi | [] | [
1296,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_congr_ae | [] | [
380,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformly.prod | [] | [
320,
39
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316,
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Mathlib/Data/Set/Prod.lean | Set.Nonempty.fst | [] | [
314,
84
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314,
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Mathlib/Order/Monotone/Monovary.lean | monovaryOn_toDual_left | [] | [
269,
10
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Mathlib/Order/Filter/AtTopBot.lean | Filter.comap_embedding_atTop | [] | [
1337,
74
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1332,
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Mathlib/Analysis/Normed/Group/Basic.lean | pi_nnnorm_le_iff' | [] | [
2479,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_add_edgeDensity_compl | [
{
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149,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.coeff_eq_b | [] | [
111,
15
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_compL_le | [] | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Nilpotent.lean | isNilpotent_of_finite_tFAE | [
{
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Mathlib/Data/List/Perm.lean | List.mem_permutations | [] | [
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89
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Mathlib/Order/Monotone/Monovary.lean | Antivary.symm | [] | [
387,
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386,
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Mathlib/Data/MvPolynomial/Polynomial.lean | MvPolynomial.eval_polynomial_eval_finSuccEquiv | [
{
"state_after": "R : Type u_1\nn : ℕ\nx : Fin n → R\ninst✝ : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n⊢ eval₂ (RingHom.comp (eval x) (RingHom.comp (Polynomial.evalRingHom q) (RingHom.comp Polynomial.C C)))\n (fun s => ↑(eval x) (Polynomial.eval q (Fin.cases Polynomial.... | [
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_zero | [] | [
394,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
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Std/Data/String/Lemmas.lean | String.extract_zero_endPos | [
{
"state_after": "c : Char\ncs : List Char\n⊢ { data := extract.go₁ (c :: cs) 0 0 { byteIdx := utf8Len cs + csize c } } = { data := c :: cs }",
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"tactic": "simp [extract, Nat.ne... | [
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inl_fst | [] | [
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
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Mathlib/Data/Set/Ncard.lean | Set.Infinite.ncard | [] | [
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Mathlib/Topology/Paracompact.lean | refinement_of_locallyCompact_sigmaCompact_of_nhds_basis_set | [
{
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.prod_mono | [] | [
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Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearEquiv.ofInjectiveEndo_left_inv | [] | [
993,
62
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Mathlib/Data/Holor.lean | HolorIndex.take_take | [
{
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"tactic": "simp [assocRight, take, cast_type, List.take_take, Nat.le_add_r... | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.comp_inj | [
{
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Mathlib/Data/Set/Ncard.lean | Set.ncard_inter_le_ncard_right | [] | [
311,
49
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Mathlib/Algebra/CharP/Basic.lean | add_pow_char_pow_of_commute | [
{
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"state_before": "R : Type u_1\ninst✝¹ : Semiring R\np n : ℕ\nhp : Fact... | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_bot | [
{
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}
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744,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_mul_cancel_right | [
{
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"tactic": "rw [← mul_mk'_one_eq_mk', ... | [
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96
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Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | MeasureTheory.SimpleFunc.edist_nearestPt_le | [
{
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.order_zero | [] | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIxxMod_trans | [
{
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_weightedVSubVSubWeights | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_typein_succ | [
{
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.sum_right | [] | [
435,
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433,
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Mathlib/Topology/VectorBundle/Basic.lean | Bundle.zeroSection_proj | [] | [
385,
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384,
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableAt_fst | [] | [
177,
35
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176,
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Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean | CategoryTheory.Limits.hasLimit_of_equalizer_and_product | [] | [
122,
49
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Mathlib/Order/Monotone/Basic.lean | Function.update_mono | [] | [
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82
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1191,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_eq_card | [] | [
245,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map.id | [
{
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1
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsSeparable.closure | [
{
"state_after": "case intro.intro\nα : Type u\nt : TopologicalSpace α\ns c : Set α\nc_count : Set.Countable c\nhs : s ⊆ _root_.closure c\n⊢ IsSeparable (_root_.closure s)",
"state_before": "α : Type u\nt : TopologicalSpace α\ns : Set α\nhs : IsSeparable s\n⊢ IsSeparable (_root_.closure s)",
"tactic": "... | [
402,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.eraseMax_aux | [
{
"state_after": "α : Type u_1\ninst✝ : Preorder α\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nH : Valid' o₁ (Ordnode.node s l x r) o₂\nthis : Ordnode.node s l x r = Ordnode.node' l x r\n⊢ Valid' o₁ (eraseMax (Ordnode.node' l x r)) ↑(findMax' x r) ∧\n size (Ordnode.node' l x ... | [
1399,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1389,
1
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.exists_disjoint_closedBall_covering_ae_aux | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝⁵ : MetricSpace α\nβ : Type u\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : HasBesicovitchCovering α\nμ : MeasureTheory.Measure α\ninst✝ : SigmaFinite μ\nf : α → Set ℝ\ns : Set α\nhf : ∀ (x : α), ... | [
846,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_mk_iff_exists_subset | [
{
"state_after": "α✝ β : Type u\nc : Cardinal\nα : Type u\ns : Set α\n⊢ (∃ p, (#↑p) = c) ↔ ∃ s_1, (#↑(Subtype.val '' s_1)) = c",
"state_before": "α✝ β : Type u\nc : Cardinal\nα : Type u\ns : Set α\n⊢ c ≤ (#↑s) ↔ ∃ p, p ⊆ s ∧ (#↑p) = c",
"tactic": "rw [le_mk_iff_exists_set, ← Subtype.exists_set_subtype]"... | [
2226,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2223,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_bot | [] | [
301,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nx y : α\n⊢ Pos (const y - const x) ↔ x < y",
"tactic": "rw [← const_sub, const_pos, sub_pos]"
}
] | [
784,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_gcd_helper_2' | [] | [
55,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/CategoryTheory/Adjunction/Reflective.lean | CategoryTheory.unitCompPartialBijective_symm_natural | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝³ : Category C\ninst✝² : Category D\ninst✝¹ : Category E\ni : D ⥤ C\ninst✝ : Reflective i\nA B B' : C\nh : B ⟶ B'\nhB : B ∈ Functor.essImage i\nhB' : B' ∈ Functor.essImage i\nf : i.obj ((leftAdjoint i).obj A) ⟶ B\n⊢ ↑(... | [
155,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.closure_prime_cycle_swap | [
{
"state_after": "case intro.intro.intro\nι : Type ?u.3022349\nα : Type u_1\nβ : Type ?u.3022355\ninst✝² : DecidableEq α\ninst✝¹ : Finite β\ninst✝ : Fintype α\nσ τ : Perm α\nh0 : Nat.Prime (Fintype.card α)\nh1 : IsCycle σ\nh2 : support σ = univ\nx y : α\nh4 : x ≠ y\nh5 : τ = swap x y\n⊢ closure {σ, τ} = ⊤",
... | [
1694,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ici_eq_Ici | [] | [
1272,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.degree_basisDivisor_self | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝ : Field F\nx y : F\n⊢ degree (basisDivisor x x) = ⊥",
"tactic": "rw [basisDivisor_self, degree_zero]"
}
] | [
158,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_anti_mono | [] | [
181,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformly_extend_exists | [] | [
441,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_le_of_left_le | [
{
"state_after": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidablePred ((fun x x_1 => x ≤ x_1) c)\nhac : a ≤ c\n⊢ (Finset.Ico c b).val = Ico c b",
"state_before": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidablePred... | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.div_div_self | [
{
"state_after": "case intro\nn k l w✝ : ℕ\nhm : n * w✝ ≠ 0\n⊢ n * w✝ / (n * w✝ / n) = n",
"state_before": "m n k l : ℕ\nh : n ∣ m\nhm : m ≠ 0\n⊢ m / (m / n) = n",
"tactic": "rcases h with ⟨_, rfl⟩"
},
{
"state_after": "case intro\nn k l w✝ : ℕ\nhm : n ≠ 0 ∧ w✝ ≠ 0\n⊢ n * w✝ / (n * w✝ / n) = n",... | [
466,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
11
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.map_cons | [
{
"state_after": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nl : ListBlank Γ\na : Γ\n⊢ cons (head (map f (cons a l))) (tail (map f (cons a l))) = cons (PointedMap.f f a) (map f l)",
"state_before": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ :... | [
415,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | dist_partial_sum_le_of_le_geometric | [
{
"state_after": "α : Type u_1\nβ : Type ?u.580401\nι : Type ?u.580404\ninst✝ : SeminormedAddCommGroup α\nr C : ℝ\nf : ℕ → α\nhf : ∀ (n : ℕ), ‖f n‖ ≤ C * r ^ n\nn : ℕ\n⊢ ‖f n‖ ≤ C * r ^ n",
"state_before": "α : Type u_1\nβ : Type ?u.580401\nι : Type ?u.580404\ninst✝ : SeminormedAddCommGroup α\nr C : ℝ\nf : ... | [
387,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_mul_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\na0 : a ≠ 0\n⊢ natDegree (p * ↑C a) = natDegree p",
"tactic": "simp only [natDegree, degree_mul_C a0]"
}
] | [
336,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.induction_on | [] | [
164,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
11
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_mul_iff_right | [] | [
96,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.normalize_eq_mk' | [] | [
100,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.fromBlocks | [
{
"state_after": "α : Type u_2\nβ : Type ?u.5694\nm : Type u_1\nn : Type u_3\nA✝ : Matrix n n α\ninst✝ : InvolutiveStar α\nA : Matrix m m α\nB : Matrix m n α\nC : Matrix n m α\nD : Matrix n n α\nhA : IsHermitian A\nhBC : Bᴴ = C\nhD : IsHermitian D\nhCB : Cᴴ = B\n⊢ IsHermitian (Matrix.fromBlocks A B C D)",
"... | [
117,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | DifferentiableOn.hasFPowerSeriesOnBall | [] | [
592,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
11
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biprod.lift_desc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nX Y : C\ninst✝ : HasBinaryBiproduct X Y\nT U : C\nf : T ⟶ X\ng : T ⟶ Y\nh : X ⟶ U\ni : Y ⟶ U\n⊢ lift f g ≫ desc h i = f ≫ h + g ≫ i",
"tactic": "simp [biprod.lift_eq, bipr... | [
464,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Computability/Partrec.lean | Computable.bind_decode_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.145328\nσ : Type u_1\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → β → Option σ\nhf : Computable₂ fun a n => Option.bind (decode n) (f a)\nn : ℕ\n⊢ (Part.bind ↑(Option.bind (decode (Nat.unpair n).... | [
658,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_lt_iff_coeff_zero | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.703639\nf : R[X]\nn : ℕ\n⊢ (∀ (m : ℕ), n ≤ m → coeff f m = 0) → degree f < ↑n",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.703639\nf :... | [
1092,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Iso.map_adj_iff | [] | [
1921,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1920,
1
] |
Mathlib/Order/WithBot.lean | WithBot.wellFounded_gt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.121527\nγ : Type ?u.121530\nδ : Type ?u.121533\ninst✝ : Preorder α\nh : WellFounded fun x x_1 => x > x_1\na : WithBot α\n⊢ Acc (fun x x_1 => x < x_1) (↑WithBot.toDual a) → Acc (fun x x_1 => x > x_1) a",
"state_before": "α : Type u_1\nβ : Type ?u.121527\nγ : Type ?... | [
1294,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_mono_endpoints | [] | [
76,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_eq_iInter_thickening | [
{
"state_after": "case hs\nι : Sort ?u.142608\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx : α\nδ : ℝ\nδ_nn : 0 ≤ δ\nE : Set α\n⊢ ∀ (ε : ℝ), δ < ε → Set.Nonempty (Ioi δ ∩ Ioc δ ε)",
"state_before": "ι : Sort ?u.142608\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\n... | [
1335,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator_subset | [] | [
230,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_inv | [
{
"state_after": "ι : Type ?u.2113579\nα : Type u_1\nβ : Type ?u.2113585\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝ y✝ : α\nf : Perm α\nx y : α\n⊢ y =\n if SameCycle f x (if SameCycle f⁻¹ x y then ↑f⁻¹ y else y) then ↑f (if SameCycle f⁻¹ x y then ↑f⁻¹ y else y)\n else if SameCycle f⁻¹ x... | [
979,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.typesGrothendieckTopology_eq_canonical | [
{
"state_after": "⊢ typesGrothendieckTopology ∈ Sheaf.finestTopologySingle '' Set.range yoneda.toPrefunctor.obj",
"state_before": "⊢ typesGrothendieckTopology = Sheaf.canonicalTopology (Type u)",
"tactic": "refine' le_antisymm subcanonical_typesGrothendieckTopology (sInf_le _)"
},
{
"state_after... | [
196,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.self | [] | [
1268,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.find_min' | [] | [
915,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Topology/ContinuousOn.lean | eventuallyEq_nhdsWithin_of_eqOn | [] | [
436,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.Chain.eq_nil_of_irrefl | [
{
"state_after": "case H0\nα : Type u_1\nr : α → α → Prop\ns : Cycle α\ninst✝¹ : IsTrans α r\ninst✝ : IsIrrefl α r\nh✝ : Chain r s\nh : Chain r Cycle.nil\n⊢ Cycle.nil = Cycle.nil\n\ncase HI\nα : Type u_1\nr : α → α → Prop\ns : Cycle α\ninst✝¹ : IsTrans α r\ninst✝ : IsIrrefl α r\nh✝ : Chain r s\na : α\nl : List ... | [
1032,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Algebra/Hom/Group.lean | AddMonoid.coe_one | [] | [
1366,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_assoc | [
{
"state_after": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns t u v : Finset α\n⊢ ∀ (a b c : Finset α), a ○ b ○ c ≤ a ○ (b ○ c)",
"state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\n... | [
543,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Algebra/Group/Opposite.lean | MulOpposite.commute_op | [] | [
259,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Monotone/Basic.lean | Antitone.dual | [] | [
225,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
11
] |
Mathlib/Data/Option/Basic.lean | Option.iget_of_mem | [] | [
309,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.sum_repr_symm | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.817499\n𝕜 : Type u_2\ninst✝⁹ : IsROrC 𝕜\nE : Type u_3\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.817528\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type ?u.817546\ninst✝⁴ ... | [
445,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.toEquiv_injective | [] | [
153,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.prod_fst | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | NormedSpace.exists_lt_norm | [
{
"state_after": "case intro\nα : Type ?u.319308\nβ : Type ?u.319311\nγ : Type ?u.319314\nι : Type ?u.319317\n𝕜 : Type ?u.319320\nE : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : Nontrivial E\nc : ℝ\nx : E\nhx : x ≠ 0\n⊢ ∃ x, c < ‖x‖",
"st... | [
433,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vadd_mem_mk' | [] | [
470,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_eq_image | [] | [
603,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
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