file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_symmDiff_eq_zero_iff | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.108610\nγ : Type ?u.108613\nδ : Type ?u.108616\nι : Type ?u.108619\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ s t : Set α\n⊢ ↑↑μ (s ∆ t) = 0 ↔ s =ᵐ[μ] t",
"tactic": "simp [ae_eq_set, symmDiff_def]"
}
] | [
489,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
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Mathlib/Data/Finset/Powerset.lean | Finset.powerset_card_disjiUnion | [
{
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296,
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286,
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Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_prod_self | [
{
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Mathlib/Algebra/Group/Basic.lean | ite_mul_one | [
{
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"tactic": "by_cases h:P <;> simp [h]"
}
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Mathlib/Analysis/Calculus/Deriv/Inv.lean | HasDerivAt.div | [
{
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Mathlib/Topology/Separation.lean | isPreirreducible_iff_subsingleton | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nγ : Type ?u.142380\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space α\nS : Set α\nh : IsPreirreducible S\nx : α\nhx : x ∈ S\ny : α\nhy : y ∈ S\n⊢ x = y",
"state_before": "α : Type u\nβ : Type v\ninst✝³ : Topolog... | [
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1432,
1
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Mathlib/Topology/MetricSpace/Polish.lean | complete_polishSpaceMetric | [
{
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"state_before": "α✝ : Type ?u.841\nβ : Type ?u.844\nα : Type u_1... | [
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Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.exists_disjoint_diff | [
{
"state_after": "ι : Type ?u.9675\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ns t u v : Set α\nh : AEDisjoint μ s t\nx : α\nhx : x ∈ s \\ toMeasurable μ (s ∩ t)\n⊢ x ∈ ?m.10357 h ∧ ¬x ∈ t",
"state_before": "ι : Type ?u.9675\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ns t u v : Set α\nh : ... | [
147,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_comp_le_tsum_of_injective | [] | [
987,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/CompleteLattice.lean | IsGLB.iInf_eq | [] | [
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12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_div | [
{
"state_after": "α : Type ?u.262242\nβ : Type ?u.262245\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : 0 < b → b < a → c ≠ 0\n⊢ (a - b) * c⁻¹ = a * c⁻¹ - b * c⁻¹",
"state_before": "α : Type ?u.262242\nβ : Type ?u.262245\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : 0 < b → b < a → c ≠ 0\n⊢ (a - b) / c = a / c - b / c",
"tactic... | [
1459,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_map'_iff | [
{
"state_after": "no goals",
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"tactic": "rw [Tendsto, Tendsto, map_map]"
}
] | [
2942,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/Injective.lean | Module.Baer.ExtensionOf.ext | [
{
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126,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/Data/Pi/Interval.lean | Pi.Icc_eq | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
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Mathlib/Topology/Separation.lean | tendsto_nhds_unique_of_eventuallyEq | [] | [
974,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/Basic.lean | frontier_sphere | [
{
"state_after": "no goals",
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165,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.prod_factors_gcd_mul_prod_factors_mul | [
{
"state_after": "case inl\nβ : Type u_1\ninst✝ : CommMonoid β\nm : ℕ\nf : ℕ → β\n⊢ Finset.prod (toFinset (factors (gcd m 0))) f * Finset.prod (toFinset (factors (m * 0))) f =\n Finset.prod (toFinset (factors m)) f * Finset.prod (toFinset (factors 0)) f\n\ncase inr\nβ : Type u_1\ninst✝ : CommMonoid β\nm n : ... | [
712,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
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src/lean/Init/Core.lean | heq_of_eq_of_heq | [] | [
637,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.const_mul_right' | [] | [
1518,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1516,
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Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.fromLeftInv_leftInvEquiv_symm | [] | [
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34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearIndependent.finite | [] | [
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92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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Mathlib/Data/List/Sigma.lean | List.exists_of_kerase | [
{
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445,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
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Mathlib/Data/Int/Bitwise.lean | Int.bitwise_or | [
{
"state_after": "case h.h\nm n : ℤ\n⊢ bitwise or m n = lor m n",
"state_before": "⊢ bitwise or = lor",
"tactic": "funext m n"
},
{
"state_after": "case h.h.ofNat.negSucc\nm n : ℕ\n⊢ Nat.bitwise' (fun x y => !(x || !y)) m n = Nat.bitwise' (fun a b => a && !b) n m\n\ncase h.h.negSucc.ofNat\nm n :... | [
238,
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Mathlib/Analysis/Convex/Slope.lean | strictConcaveOn_of_slope_strict_anti_adjacent | [
{
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"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set �... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
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Mathlib/Algebra/Ring/Defs.lean | bit0_eq_two_mul | [] | [
187,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.comp_continuous_iff' | [] | [
536,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_eq | [] | [
381,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/CategoryTheory/Localization/Predicate.lean | CategoryTheory.Localization.comp_liftNatTrans | [
{
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"state_before": "C : Type u_3\nD : Type u_6\ninst✝³ : Category C\ninst✝² : Category D\nL : C ⥤ D\nW : MorphismProperty C\nE : Type u_4\ninst✝¹ : Category E\ninst✝ : Functor.IsLocalization L W\nF₁ F₂ F₃ : C ⥤ E\nF₁' F₂' F₃' : D ⥤ E\nh₁ : Lifting L W F₁ F₁'\nh₂ : Lifting L W F₂ F₂... | [
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Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.uncurry_pre | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nA B X✝ X' Y Y' Z : C\ninst✝² : HasFiniteProducts C\ninst✝¹ : Exponentiable A\nf : B ⟶ A\ninst✝ : Exponentiable B\nX : C\n⊢ CartesianClosed.uncurry ((pre f).app X) = prod.map f (𝟙 (A ⟹ X)) ≫ (exp.ev A).app X",
"tactic": "rw [... | [
291,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.filterSup | [] | [
4143,
100
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4141,
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_differentiable_iff | [] | [
316,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Std/Data/Int/DivMod.lean | Int.mod_lt_of_pos | [] | [
380,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
376,
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Mathlib/Logic/Denumerable.lean | Nat.Subtype.toFunAux_eq | [
{
"state_after": "α : Type ?u.72269\nβ : Type ?u.72272\ns : Set ℕ\ninst✝¹ : Infinite ↑s\ninst✝ : DecidablePred fun x => x ∈ s\nx : ↑s\n⊢ List.length (List.filter (fun x => decide (x ∈ s)) (List.range ↑x)) =\n Finset.card (Finset.filter (fun x => x ∈ s) (Finset.range ↑x))",
"state_before": "α : Type ?u.72... | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
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Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.subset_interior | [] | [
1464,
73
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1463,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_ne_zero | [] | [
2325,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2324,
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Std/Data/Array/Lemmas.lean | Array.getElem_mapIdx | [
{
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"tactic": "simp_all"
}
] | [
215,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
212,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.tsum_eq | [] | [
483,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.boundary_zero | [] | [
106,
55
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105,
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Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.leftUnitor_monoidal | [
{
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.LHom.coe_substructureReduct | [] | [
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732,
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.ofLe_eq_comap_incl | [
{
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lt_wf | [
{
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Mathlib/Algebra/BigOperators/Basic.lean | Fintype.prod_eq_prod_compl_mul | [] | [
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49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.exists_infinite_fiber | [
{
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"tact... | [
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Mathlib/Topology/ContinuousOn.lean | Continuous.if | [] | [
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51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.spanningCoe_top | [] | [
584,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nhds_comap_dist | [] | [
1820,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1818,
1
] |
Std/Data/List/Lemmas.lean | List.mem_nil_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\n⊢ a ∈ [] ↔ False",
"tactic": "simp"
}
] | [
60,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
60,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.not_equiv_zero_const_of_nonzero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nq : ℚ\nhq : q ≠ 0\nh : LimZero (const (padicNorm p) q - 0)\n⊢ LimZero (const (padicNorm (?m.11534 hq h)) q)",
"tactic": "simpa using h"
}
] | [
170,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.map_eq_map' | [
{
"state_after": "case w\nJ : Type w\nC : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nf g : J → C\ninst✝¹ : HasBiproduct f\ninst✝ : HasBiproduct g\np : (b : J) → f b ⟶ g b\n⊢ ∀ (j : J), ι (fun b => f b) j ≫ map p = ι (fun b => f b) j ≫ map' p",
"state_before": "J : Type w\nC : Type u\ninst✝³ :... | [
521,
9
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509,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_def | [] | [
1189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.cons_isPath_iff | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\nh : Adj G u v\np : Walk G v w\n⊢ IsPath (cons h p) ↔ IsPath p ∧ ¬u ∈ support p",
"tactic": "constructor <;> simp (config := { contextual := true ... | [
975,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Data/PFun.lean | PFun.get_prodLift | [] | [
645,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.sInf_upward_closed_eq_succ_iff | [
{
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"state_before": "s : Set ℕ\nhs : ∀ (k₁ k₂ : ℕ), k₁ ≤ k₂ → k₁... | [
116,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_of_forall | [] | [
1263,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_zero | [] | [
61,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_inf_principal_range | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.252749\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\n⊢ comap m (g ⊓ 𝓟 (range m)) = comap m g",
"tactic": "simpa only [le_principal_iff, comap_inf, comap_prin... | [
2220,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2218,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_inj_iff | [] | [
113,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_right_comm | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ a * b * c = a * c * b",
"tactic": "rw [Int.mul_assoc, Int.mul_assoc, Int.mul_comm b]"
}
] | [
404,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
403,
11
] |
Mathlib/Analysis/Convex/Segment.lean | Convex.mem_Ioo | [
{
"state_after": "𝕜 : Type u_1\nE : Type ?u.294082\nF : Type ?u.294085\nG : Type ?u.294088\nι : Type ?u.294091\nπ : ι → Type ?u.294096\ninst✝ : LinearOrderedField 𝕜\nx y z : 𝕜\nh : x < y\n⊢ z ∈ openSegment 𝕜 x y ↔ ∃ a b, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a * x + b * y = z",
"state_before": "𝕜 : Type u_1\nE :... | [
547,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_sSup_of_directedOn | [
{
"state_after": "no goals",
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"tactic": "simp [mem... | [
1168,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1166,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.exists_mem_of_rel_of_mem | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.468460\nδ : Type ?u.468463\nr✝ : α → β → Prop\np : γ → δ → Prop\nr : α → β → Prop\ns : Multiset α\nt : Multiset β\n⊢ ∀ {a : α}, a ∈ 0 → ∃ b, b ∈ 0 ∧ r a b\n\ncase cons\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.468460\nδ : Type ?u.468463\nr✝ : α... | [
2792,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2784,
1
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_smul | [] | [
395,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Set/Function.lean | Set.restrict_ite_compl | [] | [
105,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_sub | [] | [
399,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_Ioo | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.120349\ninst✝ : Fintype ι\na b : ℝ\n⊢ ↑↑volume (Ioo a b) = ofReal (b - a)",
"tactic": "simp [volume_val]"
}
] | [
91,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.append_comm | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.46498\nn n' m : ℕ\ns✝ : Sym α n\na b : α\ns s' : Sym α n'\n⊢ ↑(append s s') = ↑(↑(Sym.cast (_ : n' + n' = n' + n')) (append s' s))",
"state_before": "α : Type u_1\nβ : Type ?u.46498\nn n' m : ℕ\ns✝ : Sym α n\na b : α\ns s' : Sym α n'\n⊢ append s s' = ↑(Sym... | [
511,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_inter_Ico | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.135025\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ a b c d : α\n⊢ Ico a b ∩ Ico c d = Ico (max a c) (min b d)",
"tactic": "rw [← coe_inj, coe_inter, coe_Ico, coe_Ico, coe_Ico, ← inf_eq_min, ← sup_eq_max,\n Set.Ico_... | [
784,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.nodalWeight_eq_eval_nodal_derative | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\nhi : i ∈ s\n⊢ nodalWeight s v i = (eval (v i) (↑derivative (nodal s v)))⁻¹",
"tactic": "rw [eval_nodal_derivative_eval_node_eq hi, nodalWei... | [
570,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_refl | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.141801\nγ : Type ?u.141804\nι : Type ?u.141807\nM : Type u_2\nM' : Type ?u.141813\nN : Type ?u.141816\nP : Type ?u.141819\nG : Type ?u.141822\nH : Type ?u.141825\nR : Type ?u.141828\nS : Type ?u.141831\ninst✝ : Zero M\nl : α →₀ M\nx : α\n⊢ ↑(equivMapDomain (Eq... | [
330,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.forall₃_congr' | [] | [
908,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
11
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | List.measurable_prod' | [
{
"state_after": "case nil\nM : Type u_1\nα : Type u_2\ninst✝² : Monoid M\ninst✝¹ : MeasurableSpace M\ninst✝ : MeasurableMul₂ M\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nl : List (α → M)\nhl✝ : ∀ (f : α → M), f ∈ l → Measurable f\nhl : ∀ (f : α → M), f ∈ [] → Measurable f\n⊢ Measurable (prod [])\n\nc... | [
866,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | disjoint_ball_closedBall_iff | [
{
"state_after": "𝕜 : Type ?u.217236\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx y z : E\nδ ε : ℝ\nhδ : 0 < δ\nhε : 0 ≤ ε\nh : Disjoint (ball x δ) (closedBall y ε)\nhxy : dist x y < δ + ε\n⊢ False",
"state_before": "𝕜 : T... | [
227,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.comp_id | [
{
"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 f id) x✝ = ↑f x✝",
"state_before":... | [
436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.card_modEq_card_fixedPoints | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nG : Type u_2\ninst✝³ : Group G\nhG : IsPGroup p G\nhp : Fact (Nat.Prime p)\nα : Type u_1\ninst✝² : MulAction G α\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑(fixedPoints G α)\n⊢ card α ≡ card ↑(fixedPoints G α) [MOD p]",
"tactic": "classical\n calc\n ca... | [
218,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_le_of_surjective | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.92268\nR : Type u\ninst✝⁶ : Ring R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type v'\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nM₁ : Type v\nin... | [
238,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.uniformContinuous_coe_real | [] | [
40,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | LinearEquiv.coe_toAffineEquiv | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_interior_compacts | [] | [
285,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.of_injective | [] | [
89,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Quot.lean | Quotient.hrecOn'_mk'' | [] | [
722,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec3_eq | [
{
"state_after": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nb₀ b₁ b₂ : α\n⊢ ![b₀, b₁, b₂] = ![b₀, b₁, b₂]",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\na₀ a₁ a₂ b₀ b₁ b₂ : α\nh₀ : a₀ = b₀\nh₁ : a₁ = b₁\nh₂ : a₂ = b₂\n⊢ ![a₀, a₁, ... | [
467,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanExt_hom_app_one | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y Z X' Y' Z' : C\niX : X ≅ X'\niY : Y ≅ Y'\niZ : Z ≅ Z'\nf : X ⟶ Z\ng : Y ⟶ Z\nf' : X' ⟶ Z'\ng' : Y' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iZ.hom\nwg : iY.hom ≫ g' = g ≫ iZ.hom\n⊢ (cospanExt iX iY iZ wf ... | [
426,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.mem_inv_pointwise_smul_iff | [] | [
123,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.inter_eq_zero_iff_disjoint | [
{
"state_after": "α : Type u_1\nβ : Type ?u.495543\nγ : Type ?u.495546\ninst✝ : DecidableEq α\ns t : Multiset α\n⊢ s ∩ t ⊆ 0 ↔ Disjoint s t",
"state_before": "α : Type u_1\nβ : Type ?u.495543\nγ : Type ?u.495546\ninst✝ : DecidableEq α\ns t : Multiset α\n⊢ s ∩ t = 0 ↔ Disjoint s t",
"tactic": "rw [← subs... | [
2971,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2970,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_coe_eq_self_iff_mem_Ioc | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\n⊢ toReal ↑θ = θ ↔ θ ∈ Set.Ioc (-π) π",
"tactic": "rw [toReal_coe_eq_self_iff, ← Set.mem_Ioc]"
}
] | [
537,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_eq_smul_one | [] | [
359,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/CategoryTheory/Adjunction/Evaluation.lean | CategoryTheory.NatTrans.epi_iff_epi_app | [
{
"state_after": "case mp\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : ∀ (a b : C), HasProductsOfShape (a ⟶ b) D\nF G : C ⥤ D\nη : F ⟶ G\n⊢ Epi η → ∀ (c : C), Epi (η.app c)\n\ncase mpr\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : ∀ (a b : C), HasPr... | [
146,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroMorphisms.ext_aux | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\nI J : HasZeroMorphisms C\nw : ∀ (X Y : C), Zero.zero = Zero.zero\nthis : Zero = Zero\n⊢ I = J",
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103,
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94,
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] |
Mathlib/Topology/ContinuousFunction/Basic.lean | map_continuousWithinAt | [] | [
68,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curry_uncurryRight | [
{
"state_after": "case H.h\nR : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : Fin (Nat.succ... | [
1395,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isCompl_span_singleton_orthogonal | [] | [
1246,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
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Mathlib/GroupTheory/Commutator.lean | commutatorElement_one_right | [] | [
48,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.eq_univ_of_forall | [] | [
88,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_one_right | [] | [
275,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
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Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.comp_id | [] | [
1342,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
9
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Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.id_of_comp_right_id | [
{
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"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nf : X ⟶ X\nw : ∀ {Y : C} (g : Y ⟶ X), g ≫ f = g\n⊢ f = 𝟙 X",
"tactic": "convert w (𝟙 X)"
},
{
... | [
239,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLE_comp_ofLEMk | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nB A : C\nX Y : Subobject B\nf : A ⟶ B\ninst✝ : Mono f\nh₁ : X ≤ Y\nh₂ : Y ≤ mk f\n⊢ underlying.map (LE.le.hom h₁ ≫ LE.le.hom h₂) ≫ (underlyingIso f).hom =\n underlying.map (LE.le.hom (_ : X ≤ mk f)) ≫ (underlyi... | [
399,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.card_sections | [
{
"state_after": "no goals",
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Multiset (Multiset α)\n⊢ ∀ ⦃a : Multiset α⦄ {s : Multiset (Multiset α)},\n ... | [
70,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | absorbent_univ | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.141875\nE : Type u_2\nι : Sort ?u.141881\nκ : ι → Sort ?u.141886\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : NormedRing 𝕝\ninst✝⁴ : NormedSpace 𝕜 𝕝\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : SMulWithZero 𝕝 E\ninst✝ : IsScalarTower 𝕜 𝕝 E\ns t u v A B : Set... | [
336,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
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