file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Sym/Basic.lean | Sym.replicate_right_inj | [] | [
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57
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Mathlib/Data/List/Sigma.lean | List.not_eq_key | [
{
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Std/Data/Int/DivMod.lean | Int.fdiv_neg' | [] | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_ne_zero | [
{
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Mathlib/Data/Nat/Prime.lean | Nat.Prime.one_lt | [] | [
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Mathlib/Computability/TuringMachine.lean | Turing.Tape.nth_zero | [] | [
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.map_map | [
{
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Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.liftP_iff' | [
{
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Mathlib/Data/List/ProdSigma.lean | List.sigma_cons | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.prob_compl_eq_one_iff | [
{
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Mathlib/Algebra/Order/Floor.lean | Nat.floor_congr | [
{
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1501,
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Mathlib/Init/Algebra/Classes.lean | eqv_lt_iff_eq | [] | [
428,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
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Mathlib/Analysis/Normed/Group/Basic.lean | pi_nnnorm_const' | [] | [
2541,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2540,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_bot | [] | [
1018,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
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Mathlib/Algebra/FreeMonoid/Count.lean | FreeMonoid.countp_apply | [] | [
77,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Std/Data/Int/DivMod.lean | Int.add_emod_eq_add_emod_left | [
{
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436,
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Mathlib/Topology/Inseparable.lean | IsOpen.not_specializes | [] | [
124,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Mathlib/Topology/Algebra/Ring/Basic.lean | mulLeft_continuous | [] | [
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37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/LiminfLimsup.lean | Filter.isCobounded_le_of_bot | [] | [
235,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Order/Minimal.lean | maximals_union | [
{
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... | [
153,
52
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.valuation_zero | [] | [
1038,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_id' | [] | [
707,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.length_add | [] | [
662,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_copy | [] | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Instances/Real.lean | Real.tendsto_inv | [] | [
112,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edge_mem_incidenceSet_iff | [] | [
847,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineSubspace.subtypeₐᵢ_linearIsometry | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
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Mathlib/Order/Iterate.lean | Function.Commute.iterate_pos_lt_iff_map_lt' | [] | [
206,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.omega_le_of_isLimit | [] | [
2447,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Gluing.lean | Metric.glueDist_triangle | [
{
"state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝² : MetricSpace X\ninst✝¹ : MetricSpace Y\nΦ✝ : Z → X\nΨ✝ : Z → Y\nε✝ : ℝ\ninst✝ : Nonempty Z\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\nH : ∀ (p q : Z), abs (dist (Φ p) (Φ q) - dist (Ψ p) (Ψ q)) ≤ 2 * ε\nx : Y\ny z : X\n⊢ glueDist Ψ Φ ε (Sum.swap (Sum.inr x)) (Sum.... | [
155,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.sumAssoc_apply_inr | [] | [
367,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
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Mathlib/Data/Int/ModEq.lean | Int.mod_mul_left_mod | [] | [
325,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Algebra/Basic.lean | Algebra.coe_linearMap | [] | [
437,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
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] |
Mathlib/Data/Finmap.lean | Finmap.toFinmap_cons | [] | [
525,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
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Mathlib/Data/Real/NNReal.lean | NNReal.lt_div_iff | [] | [
841,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
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Mathlib/Analysis/LocallyConvex/Basic.lean | absorbs_union | [] | [
96,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.realSize_tail | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns : Heap α\n⊢ realSize (Option.getD (tail? le s) nil) = realSize s - 1",
"state_before": "α : Type u_1\nle : α → α → Bool\ns : Heap α\n⊢ realSize (tail le s) = realSize s - 1",
"tactic": "simp only [Heap.tail]"
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{
"state_after": "no goals",
... | [
258,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_injective_isCommutative | [
{
"state_after": "G : Type u_2\nG' : Type u_1\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.427007\ninst✝¹ : AddGroup A\nH K : Subgroup G\nf : G' →* G\nhf : Injective ↑f\ninst✝ : IsCommutative H\na b : { x // x ∈ comap f H }\nthis :\n { val := ↑f ↑a, property := (_ : ↑a ∈ comap f H) } * { val := ↑f ↑b, pro... | [
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.mk_type | [] | [
137,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
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] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.map | [] | [
351,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.enum_typein | [] | [
526,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
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Mathlib/Topology/PathConnected.lean | Path.symm_range | [
{
"state_after": "case h\nX : Type u_1\nY : Type ?u.114634\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx✝ y z : X\nι : Type ?u.114649\nγ✝ : Path x✝ y\na b : X\nγ : Path a b\nx : X\n⊢ x ∈ range ↑(symm γ) ↔ x ∈ range ↑γ",
"state_before": "X : Type u_1\nY : Type ?u.114634\ninst✝¹ : TopologicalSpa... | [
198,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lt_wf | [
{
"state_after": "case intro\nα✝ : Type ?u.98794\nβ : Type ?u.98797\nγ : Type ?u.98800\nr✝ : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na✝ : Ordinal\nα : Type u_1\nr : α → α → Prop\nwo : IsWellOrder α r\na x : α\nx✝ : ∀ (y : α), r y x → Acc r y\nIH : ∀ (y : α), r y x → Acc (fun x x_1 => x < x_1) (typei... | [
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.seq_apply | [] | [
406,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
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Std/Data/List/Lemmas.lean | List.getLastD_eq_getLast? | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\n⊢ getLastD l a = Option.getD (getLast? l) a",
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}
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Mathlib/Deprecated/Group.lean | Units.coe_isMonoidHom | [] | [
429,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbent.subset | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.6565\nE : Type u_2\nι : Sort ?u.6571\nκ : ι → Sort ?u.6576\ninst✝¹ : SeminormedRing 𝕜\ninst✝ : SMul 𝕜 E\ns t u v A B : Set E\nhA : Absorbent 𝕜 A\nhAB : A ⊆ B\nx : E\n⊢ (∃ r, 0 < r ∧ ∀ (a : 𝕜), r ≤ ‖a‖ → x ∈ a • A) → ∃ r, 0 < r ∧ ∀ (a : 𝕜), r ≤ ‖a‖ → x ∈ a • B",... | [
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98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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] |
Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | FundamentalGroupoid.comp_eq | [] | [
333,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Maps.lean | QuotientMap.surjective | [] | [
322,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
11
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.coe_toHomeomorph | [] | [
513,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
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] |
Mathlib/Topology/Algebra/UniformGroup.lean | TendstoUniformlyOn.mul | [] | [
498,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
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] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_nil | [] | [
102,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_le_of_deriv_right_le_deriv_boundary | [] | [
231,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_succ | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Topology/Separation.lean | minimal_nonempty_closed_eq_singleton | [] | [
270,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
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Mathlib/SetTheory/Game/PGame.lean | PGame.Relabelling.le | [] | [
1111,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.coe_id | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.map_congr | [] | [
391,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | ContDiffWithinAt.log | [] | [
172,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_neg_index | [] | [
1749,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1746,
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] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.sup_mul | [] | [
253,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_mul_mul_le_card_div_mul_card_div | [
{
"state_after": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA✝ B✝ C✝ A B C : Finset α\n⊢ card (A * C) * card B⁻¹ ≤ card (A * B⁻¹) * card (B⁻¹ * C)",
"state_before": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA✝ B✝ C✝ A B C : Finset α\n⊢ card (A * C) * card B ≤ card (A / B) ... | [
168,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2553374\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑re (inner x y) = (‖x‖ * ‖x‖ + ‖y‖ * ‖y‖ - (‖x‖ * ‖x‖ - 2 * ↑re ... | [
1146,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_empty | [] | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_image_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ncard (f '' s) ≤ ncard s",
"tactic": "classical\nrw [ncard_eq_toFinset_card s hs]\nconvert @Finset.card_image_le _ _ hs.toFinset f _\nsimp only\nrw [@nca... | [
240,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Memℒp.exists_boundedContinuous_integral_rpow_sub_le | [
{
"state_after": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : NormalSpace α\ninst✝³ : BorelSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\nμ : Measure α\np✝ : ℝ≥0∞\ninst✝¹ : NormedSpace ℝ E\ninst✝ : Measure.WeaklyRegular μ\np : ℝ\nhp : 0 < p\nf : α → E\nhf : Memℒp f (EN... | [
305,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.biUnionIndex_mem | [
{
"state_after": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nhJ : J ∈ biUnion π πi\n⊢ Exists.choose (_ : ∃ J', J' ∈ π ∧ J ∈ πi J') ∈ π",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (... | [
365,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_of_subset_right | [] | [
944,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixedPoints_submonoid_sup | [] | [
98,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.sUnion_singleton | [
{
"state_after": "no goals",
"state_before": "x y : ZFSet\n⊢ y ∈ ⋃₀ {x} ↔ y ∈ x",
"tactic": "simp_rw [mem_sUnion, mem_singleton, exists_eq_left]"
}
] | [
1093,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.next | [
{
"state_after": "l m₁ : List Char\nc : Char\nm₂ r : List Char\n⊢ (if\n { byteIdx := utf8Len l } + { byteIdx := utf8Len m₁ } =\n { byteIdx := utf8Len l + (utf8Len m₁ + (utf8Len m₂ + csize c)) } then\n { byteIdx := utf8Len m₁ }\n else\n {\n byteIdx :=\n (String.next {... | [
838,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
829,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.measurableSet_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.380860\nδ : Type ?u.380863\nδ' : Type ?u.380866\nι : Sort uι\ns✝ t u : Set α\nmα : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nf : α → β\ng : β → γ\nhf : MeasurableEmbedding f\ns : Set β\n⊢ Me... | [
1110,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.cutMap_self | [
{
"state_after": "case h\nF : Type ?u.9231\nα : Type u_1\nβ : Type ?u.9237\nγ : Type ?u.9240\ninst✝¹ : LinearOrderedField α\ninst✝ : DivisionRing β\na✝ a₁ a₂ : α\nb : β\nq : ℚ\na x✝ : α\n⊢ x✝ ∈ cutMap α a ↔ x✝ ∈ Iio a ∩ range Rat.cast",
"state_before": "F : Type ?u.9231\nα : Type u_1\nβ : Type ?u.9237\nγ : ... | [
130,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.mk_center | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.mul_sub_lt_image_sub_of_lt_deriv | [
{
"state_after": "E : Type ?u.396205\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.396301\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nC : (fun x => ℝ) 1\nhf'_gt : ∀ (x : ℝ)... | [
804,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.binaryRec_zero | [
{
"state_after": "C : ℕ → Sort u\nz : C 0\nf : (b : Bool) → (n : ℕ) → C n → C (bit b n)\n⊢ (if n0 : 0 = 0 then Eq.mpr (_ : C 0 = C 0) z\n else\n let n' := div2 0;\n let_fun _x := (_ : bit (bodd 0) (div2 0) = 0);\n Eq.mpr (_ : C 0 = C (bit (bodd 0) n')) (f (bodd 0) n' (binaryRec z f n'))) =\n ... | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.294661\nγ : Type ?u.294664\nδ : Type ?u.294667\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nh : ∀ (a : α), f a = g a\n⊢ (∫⁻ (a : α), f a ∂μ) = ∫⁻ (a : α), g a ∂μ",
"tactic": "simp only [h]"
}
] | [
324,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorLeftHomEquiv_tensor_id_comp_evaluation | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\ninst✝² : MonoidalCategory C\nX Y : C\ninst✝¹ : HasLeftDual X\ninst✝ : HasLeftDual Y\nf : X ⟶ Y\n⊢ (λ_ ᘁY).inv ≫ (η_ (ᘁX) X ⊗ 𝟙 ᘁY) ≫ (α_ (ᘁX) X ᘁY).hom ≫ (𝟙 ᘁX ⊗ (f ⊗ 𝟙 ᘁY) ≫ ε_ (ᘁY) Y) =\n ((λ_ ᘁY).inv ≫ (η_ (ᘁX) X ⊗ 𝟙 ᘁY) ≫ ((𝟙 ᘁX ⊗ f) ⊗ 𝟙 ᘁY) ≫ (α_... | [
523,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | Subspace.closedComplemented_of_quotient_finiteDimensional | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.131964\nG : Type ?u.131967\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : NormedSpace 𝕜 G\nin... | [
144,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioc_subset_closure_interior | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na✝ b : α\ns : Set α\na : α\n⊢ Ioc a a ⊆ closure (interior (Ioc a a))\n\ncase inr\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace... | [
2319,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2312,
1
] |
Mathlib/Topology/List.lean | List.tendsto_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.10411\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β✝\nβ : Type u_1\nf : List α → β\nr : List α → Filter β\nh_nil : Tendsto f (pure []) (r [])\nh_cons : ∀ (l : List α) (a : α), Tendsto f (𝓝 l) (r l) → Tendsto (fun p => f (p.... | [
112,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/Filter.lean | Filter.continuous_nhds | [] | [
222,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | dist_partial_sum' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.910337\nι : Type ?u.910340\ninst✝ : SeminormedAddCommGroup α\nr C : ℝ\nf u : ℕ → α\nn : ℕ\n⊢ dist (∑ k in Finset.range n, u k) (∑ k in Finset.range (n + 1), u k) = ‖u n‖",
"tactic": "simp [dist_eq_norm', sum_range_succ]"
}
] | [
417,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | ufm_of_gcd_of_wfDvdMonoid | [] | [
186,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.isoLimitCone_inv_π | [
{
"state_after": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ F : J ⥤ C\ninst✝ : HasLimit F\nt : LimitCone F\nj : J\n⊢ lift F t.cone ≫ π F j = t.cone.π.app j",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC :... | [
264,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.mkRat_eq | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Compare.lean | cmp_eq_eq_iff | [] | [
235,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nonempty.inl | [] | [
499,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.size_pos | [
{
"state_after": "n : ℕ\n⊢ 2 ^ 0 ≤ n ↔ 0 < n",
"state_before": "n : ℕ\n⊢ 0 < size n ↔ 0 < n",
"tactic": "rw [lt_size]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 2 ^ 0 ≤ n ↔ 0 < n",
"tactic": "rfl"
}
] | [
162,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.coe_punitProd | [] | [
523,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
9
] |
Mathlib/Order/Lattice.lean | Monotone.inf | [] | [
1080,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
11
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_drop_succ | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.116361\nα : Type ?u.116364\nM : Type ?u.116367\nN : Type ?u.116370\nP : Type ?u.116373\nM₀ : Type ?u.116376\nG : Type u_1\nR : Type ?u.116382\ninst✝ : Group G\nx : G\nxs : List G\nx✝ : 0 < length (x :: xs)\n⊢ prod (drop (0 + 1) (x :: xs)) = (nthLe (x... | [
436,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.PInfty_add_QInfty | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\n⊢ PInfty + (𝟙 K[X] - PInfty) = 𝟙 K[X]",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\n⊢ PInfty + QInfty = 𝟙 K[X]",
"tactic": "dsimp only [QInfty]"
... | [
164,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Order/Monoid/WithZero/Defs.lean | WithZero.coe_lt_coe | [] | [
66,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.eq_one_iff | [
{
"state_after": "G : Type u\ninst✝¹ : Group G\nN✝ : Subgroup G\nnN✝ : Subgroup.Normal N✝\nH : Type v\ninst✝ : Group H\nN : Subgroup G\nnN : Subgroup.Normal N\nx : G\n⊢ x⁻¹ * 1 ∈ N ↔ x ∈ N",
"state_before": "G : Type u\ninst✝¹ : Group G\nN✝ : Subgroup G\nnN✝ : Subgroup.Normal N✝\nH : Type v\ninst✝ : Group H... | [
124,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_smul_measure | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.579678\nγ : Type ?u.579681\nδ : Type ?u.579684\nι : Type ?u.579687\nR : Type u_1\nR' : Type ?u.579693\nm0 : MeasurableSpace α\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\np ... | [
2868,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2866,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.freeGroupCongr_refl | [] | [
872,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Algebra/CharZero/Quotient.lean | QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff | [
{
"state_after": "R : Type u_1\ninst✝¹ : DivisionRing R\ninst✝ : CharZero R\np : R\nψ θ : R ⧸ AddSubgroup.zmultiples p\nn : ℕ\nhz : n ≠ 0\n⊢ (∃ k, ψ = θ + ↑(↑k • (p / ↑n))) ↔ ∃ k, ψ = θ + ↑(↑k • (p / ↑n))",
"state_before": "R : Type u_1\ninst✝¹ : DivisionRing R\ninst✝ : CharZero R\np : R\nψ θ : R ⧸ AddSubgr... | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_preimage_singleton | [] | [
2017,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2015,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_inj | [] | [
96,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
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