file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.inf_N | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.even_div | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ Even (m / n) ↔ m % (2 * n) / n = 0",
"tactic": "rw [even_iff_two_dvd, dvd_iff_mod_eq_zero, Nat.div_mod_eq_mod_mul_div, mul_comm]"
}
] | [
183,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Topology/Filter.lean | ContinuousOn.nhds | [] | [
244,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
18
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_empty | [] | [
86,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.eq_of_left | [] | [
135,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.int_cast_def | [] | [
1457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1455,
1
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.neg_re | [] | [
243,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
9
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousOn_univ_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : TopologicalSpace α\nβ : Type u_2\ninst✝ : Preorder β\nf g : α → β\nx : α\ns t : Set α\ny z : β\n⊢ LowerSemicontinuousOn f univ ↔ LowerSemicontinuous f",
"tactic": "simp [LowerSemicontinuousOn, LowerSemicontinuous, lowerSemicontinuousWi... | [
159,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/Analysis/Convex/Normed.lean | isConnected_setOf_sameRay_and_ne_zero | [
{
"state_after": "ι : Type ?u.55149\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\nx : E\nhx : x ≠ 0\n⊢ IsConnected {y | ∃ r, 0 < r ∧ r • x = y}",
"state_before": "ι : Type ?u.55149\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set ... | [
152,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_lt_lowerSemicontinuous_lintegral_ge_of_aemeasurable | [
{
"state_after": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : WeaklyRegular μ\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfmeas : AEMeasurable f\nε : ℝ≥0∞\nε0 : ε ≠ 0\nthis : ε / 2 ≠ 0\n⊢ ∃ g, (∀ (x : α), ↑(f x) < g x) ∧ LowerSemicontinuous g ∧ ... | [
266,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | coprime_sq_sub_sq_add_of_odd_even | [
{
"state_after": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 1\nhn : n % 2 = 0\n⊢ Nat.gcd (Int.natAbs (-(m ^ 2 - n ^ 2))) (Int.natAbs (m ^ 2 + n ^ 2)) = 1",
"state_before": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 1\nhn : n % 2 = 0\n⊢ Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1",
"tactic": "rw [Int.g... | [
359,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
9
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_single_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.58510\nγ : Type ?u.58513\nι : Type ?u.58516\nM : Type u_1\nM' : Type ?u.58522\nN : Type ?u.58525\nP : Type ?u.58528\nG : Type ?u.58531\nH : Type ?u.58534\nR : Type ?u.58537\nS : Type ?u.58540\ninst✝ : Zero M\na a' : α\nb b' : M\nhb : b ... | [
437,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_fst_le_log | [
{
"state_after": "case refine'_1\nb o : Ordinal\nx : Ordinal × Ordinal\n⊢ x ∈ CNF b 0 → x.fst ≤ log b 0\n\ncase refine'_2\nb o✝ : Ordinal\nx : Ordinal × Ordinal\no : Ordinal\nho : o ≠ 0\nH : x ∈ CNF b (o % b ^ log b o) → x.fst ≤ log b (o % b ^ log b o)\n⊢ x ∈ CNF b o → x.fst ≤ log b o",
"state_before": "b o... | [
132,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.coe_max | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.const_div | [] | [
304,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.tendsto_approx | [] | [
207,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
11
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.support_hsum_subset | [
{
"state_after": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\nα : Type u_3\ns : SummableFamily Γ R α\ng : Γ\nhg :\n ∑ i in Set.Finite.toFinset (_ : Set.Finite (Function.support fun a => coeff (toFun s a) g)), coeff (toFun s i) g ≠ 0\n⊢ g ∈ ⋃ (a : α), support (toFun s a)",
... | [
1518,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.ker_prod_ker_le_ker_coprod | [
{
"state_after": "case mk\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂✝ : Type w\nV₂ : Type w'\nM₃✝ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.235722\nM₆ : Type ?u.235725\ninst✝¹² : Semiring R\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M₂✝\ninst✝⁹ : AddCommMonoid M₃✝\ninst✝⁸... | [
514,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.isOpen_generateFrom_of_mem | [] | [
78,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.evalClm_apply | [] | [
1144,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.succ_pred_prime | [] | [
199,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_mul_swap | [] | [
103,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : 0 < c\n⊢ (fun x => x * c) ⁻¹' Ioo a b = Ioo (a / c) (b / c)",
"tactic": "simp [← Ioi_inter_Iio, h]"
}
] | [
536,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mul_const_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.945819\nγ : Type ?u.945822\nδ : Type ?u.945825\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\n⊢ (∫⁻ (a : α), f a ∂μ) * r ≤ ∫⁻ (a : α), f a * r ∂μ",
"tactic": "simp_rw [mul_comm, lintegral_const_mul_le r f]"
}
] | [
742,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.sub_mem_sub | [] | [
372,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_def | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isAdjointPair_iff_compLeft_eq_compRight | [
{
"state_after": "case mp\nR : Type u_1\nM : Type u_2\ninst✝²⁰ : Semiring R\ninst✝¹⁹ : AddCommMonoid M\ninst✝¹⁸ : Module R M\nR₁ : Type ?u.1021599\nM₁ : Type ?u.1021602\ninst✝¹⁷ : Ring R₁\ninst✝¹⁶ : AddCommGroup M₁\ninst✝¹⁵ : Module R₁ M₁\nR₂ : Type ?u.1022211\nM₂ : Type ?u.1022214\ninst✝¹⁴ : CommSemiring R₂\ni... | [
1039,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
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] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_prod | [
{
"state_after": "α✝ : Type ?u.22982\nβ✝ : Type ?u.22985\nγ : Type ?u.22988\nδ : Type ?u.22991\ninst✝² : TopologicalSpace α✝\nα : Type u_1\ninst✝¹ : TopologicalSpace α\nβ : Type u_2\ninst✝ : TopologicalSpace β\ns u : Set α\nt v : Set β\na : α\nb : β\nhu : u ∈ 𝓝[s] a\nhv : v ∈ 𝓝[t] b\n⊢ u ×ˢ v ∈ 𝓝[s] a ×ˢ 𝓝[... | [
312,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.measure_Iio_pos | [] | [
140,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_X | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.inv_coe_int_den | [
{
"state_after": "no goals",
"state_before": "a : ℤ\n⊢ (↑a)⁻¹.den = if a = 0 then 1 else Int.natAbs a",
"tactic": "induction a using Int.induction_on <;>\n simp [← Int.negSucc_coe', Int.negSucc_coe, -neg_add_rev, Rat.inv_neg, Int.ofNat_add_one_out,\n -Nat.cast_succ, inv_coe_nat_den_of_pos, -Int.cast... | [
298,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | sum_eq_tsum_indicator | [] | [
506,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.IsNormal.nfp_fp | [] | [
487,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_congr_set' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Fi... | [
503,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_le_of_infEdist | [
{
"state_after": "ι : Sort ?u.35968\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\nr : ℝ≥0∞\nH1 : ∀ (x : α), x ∈ s → infEdist x t ≤ r\nH2 : ∀ (x : α), x ∈ t → infEdist x s ≤ r\n⊢ (∀ (i : α), i ∈ s → infEdist i t ≤ r) ∧ ∀ (i : α), i ∈ t → ... | [
286,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | ContinuousWithinAt.pow | [] | [
606,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_sup | [] | [
1703,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.div_comp | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Order/Sub/Basic.lean | le_tsub_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.6083\nβ : Type ?u.6086\ninst✝⁸ : Preorder α\ninst✝⁷ : Add α\ninst✝⁶ : Sub α\ninst✝⁵ : OrderedSub α\na✝ b✝ c✝ d : α\nR : Type u_1\ninst✝⁴ : CommSemiring R\ninst✝³ : Preorder R\ninst✝² : Sub R\ninst✝¹ : OrderedSub R\ninst✝ : CovariantClass R R (fun x x... | [
41,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
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] |
src/lean/Init/Data/Nat/Basic.lean | Nat.lt_of_lt_of_le | [] | [
260,
15
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
259,
11
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Ioc_iff_left | [] | [
74,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.dualMap_injective_iff | [
{
"state_after": "K : Type u\ninst✝⁵ : Field K\nV₁ : Type v'\nV₂ : Type v''\ninst✝⁴ : AddCommGroup V₁\ninst✝³ : Module K V₁\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V₂\nf : V₁ →ₗ[K] V₂\n⊢ Function.Injective ↑(dualMap f) → Function.Surjective ↑f",
"state_before": "K : Type... | [
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30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1499,
1
] |
Mathlib/Topology/Constructions.lean | isClosedMap_toDual | [] | [
172,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isAdjointPair_iff_comp_eq_compl₂ | [
{
"state_after": "case mp\nR : Type u_1\nR₁ : Type ?u.286879\nR₂ : Type ?u.286882\nR₃ : Type ?u.286885\nM : Type u_2\nM₁ : Type u_3\nM₂ : Type ?u.286894\nMₗ₁ : Type ?u.286897\nMₗ₁' : Type ?u.286900\nMₗ₂ : Type ?u.286903\nMₗ₂' : Type ?u.286906\nK : Type ?u.286909\nK₁ : Type ?u.286912\nK₂ : Type ?u.286915\nV : Ty... | [
444,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Init/Data/Int/Order.lean | Int.neg_mul_eq_neg_mul_symm | [] | [
64,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.subsingleton | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1530\nr r₁ r₂ : α → α → Prop\nr' : β → β → Prop\ns t : Set α\na✝ b✝ : α\ninst✝ : IsTrichotomous α r\nh : IsAntichain r s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ s\n⊢ a = b",
"state_before": "α : Type u_1\nβ : Type ?u.1530\nr r₁ r₂ : α → α → Prop\nr' : β → β → Prop\ns ... | [
81,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
Mathlib/Data/Complex/Basic.lean | Complex.re_sum | [] | [
1348,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1347,
1
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Mathlib/LinearAlgebra/Determinant.lean | Basis.det_comp_basis | [
{
"state_after": "R : Type ?u.2655796\ninst✝⁹ : CommRing R\nM : Type u_4\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nM' : Type u_2\ninst✝⁶ : AddCommGroup M'\ninst✝⁵ : Module R M'\nι : Type u_3\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ne : Basis ι R M\nA : Type u_1\ninst✝² : CommRing A\ninst✝¹ : Module A M... | [
614,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_smul | [
{
"state_after": "case pos\nR : Type ?u.790939\ninst✝¹² : CommRing R\nM✝ : Type ?u.790945\ninst✝¹¹ : AddCommGroup M✝\ninst✝¹⁰ : Module R M✝\nM' : Type ?u.791530\ninst✝⁹ : AddCommGroup M'\ninst✝⁸ : Module R M'\nι : Type ?u.792072\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ne : Basis ι R M✝\nA : Type ?u.792550\n... | [
273,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
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Mathlib/Computability/TuringMachine.lean | Turing.fun_respects | [
{
"state_after": "no goals",
"state_before": "σ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂\na₁ : σ₁\n⊢ (∀ ⦃a₂ : σ₂⦄,\n (fun a b => tr a = b) a₁ a₂ →\n match f₁ a₁ with\n | some b₁ => ∃ b₂, (fun a b => tr a = b) b₁ b₂ ∧ Reaches₁ f₂ a₂ b₂\n | n... | [
974,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | prevD_comp_left | [] | [
100,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Sign.lean | sign_ne_zero | [] | [
361,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Algebra/Group/Basic.lean | one_mul_eq_id | [] | [
80,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.monotone_lift | [] | [
175,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_sub_eq_add_norm_of_angle_eq_pi | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nh : angle x y = π\n⊢ ‖x‖ ^ 2 - 2 * -(‖x‖ * ‖y‖) + ‖y‖ ^ 2 = (‖x‖ + ‖y‖) ^ 2",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nh : angle x y... | [
274,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.isSplitMono_of_mono | [] | [
242,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/List/Nodup.lean | List.count_eq_one_of_mem | [] | [
200,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.is_integral_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.654670\nB : Type ?u.654673\nS : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\nx y : S\nhx : IsIntegralElem f x\nhy : IsIntegralElem ... | [
513,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Algebra/Group/Prod.lean | MulHom.prod_comp_prodMap | [] | [
405,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.finrank_dualCoannihilator_eq | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁶ : Field K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\nW : Subspace K V\nV₁ : Type ?u.1339846\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : FiniteDimensional K V\ninst✝ : FiniteDimensional K V₁\nΦ : Subspace K (Module.Dual K V)\n⊢ finrank K { x // x... | [
1137,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift'_top | [] | [
246,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_self | [] | [
234,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/Monotone/Basic.lean | Nat.exists_strictMono | [] | [
1028,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.elim_nil | [] | [
85,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.liftHom₂_congr | [
{
"state_after": "no goals",
"state_before": "B : Type u₁\ninst✝¹ : Quiver B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤q C\na b : FreeBicategory B\nf g : a ⟶ b\nη θ : Hom₂ f g\nH : Rel η θ\n⊢ liftHom₂ F η = liftHom₂ F θ",
"tactic": "induction H <;> (dsimp [liftHom₂]; aesop_cat)"
},
{
"state_aft... | [
368,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | sInf_mul | [] | [
87,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_coe_pi | [
{
"state_after": "no goals",
"state_before": "⊢ tan ↑π = 0",
"tactic": "rw [tan_coe, Real.tan_pi]"
}
] | [
793,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | toAdd_list_sum | [
{
"state_after": "ι : Type ?u.994730\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : AddMonoid α\ns : List (Multiplicative α)\n⊢ List.prod s = List.sum s",
"state_before": "ι : Type ?u.994730\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\n... | [
2312,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2311,
1
] |
Mathlib/Data/List/Count.lean | List.length_eq_countp_add_countp | [
{
"state_after": "case nil\nα : Type u_1\nl : List α\np q : α → Bool\n⊢ length [] = countp p [] + countp (fun a => decide ¬p a = true) []\n\ncase cons\nα : Type u_1\nl : List α\np q : α → Bool\nx : α\nh : List α\nih : length h = countp p h + countp (fun a => decide ¬p a = true) h\n⊢ length (x :: h) = countp p (... | [
76,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.mem_properDivisors | [
{
"state_after": "case inl\nn : ℕ\n⊢ n ∈ properDivisors 0 ↔ n ∣ 0 ∧ n < 0\n\ncase inr\nn m : ℕ\nhm : m ≠ 0\n⊢ n ∈ properDivisors m ↔ n ∣ m ∧ n < m",
"state_before": "n m : ℕ\n⊢ n ∈ properDivisors m ↔ n ∣ m ∧ n < m",
"tactic": "rcases eq_or_ne m 0 with (rfl | hm)"
},
{
"state_after": "no goals",
... | [
83,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.mapEquiv.symm | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.mk_coe | [] | [
190,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | derivWithin_csin | [] | [
224,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.one_le_abs | [] | [
137,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.to_subtype_range' | [] | [
288,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.mk_π_app_one | [] | [
596,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedTotalDegree'_eq_bot_iff | [
{
"state_after": "R : Type u_2\nM : Type u_3\ninst✝² : CommSemiring R\nσ : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : SemilatticeSup M\nw : σ → M\np : MvPolynomial σ R\n⊢ (∀ (s : σ →₀ ℕ), coeff s p ≠ 0 → False) ↔ ∀ (d : σ →₀ ℕ), coeff d p = 0",
"state_before": "R : Type u_2\nM : Type u_3\ninst✝² : CommSemi... | [
86,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.restrict_dirac | [
{
"state_after": "case h\nα : Type u_1\nmα : MeasurableSpace α\na : α\ns : Set α\ninst✝¹ : MeasurableSingletonClass α\ninst✝ : Decidable (a ∈ s)\nt : Set α\nht : MeasurableSet t\n⊢ ↑↑(Measure.restrict (Measure.dirac a) s) t = ↑↑(if a ∈ s then Measure.dirac a else 0) t",
"state_before": "α : Type u_1\nmα : M... | [
78,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_Ioc | [] | [
758,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.reverse_reverse | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Cycle α\nx✝ : List α\n⊢ reverse (reverse (Quot.mk Setoid.r x✝)) = Quot.mk Setoid.r x✝",
"tactic": "simp"
}
] | [
563,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.le_stable | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : Type w\nm n : ℕ\nh : m ≤ n\nf : Stream' (Option α)\nal : IsSeq f\n⊢ get? { val := f, property := al } m = none → get? { val := f, property := al } n = none",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\nm n : ℕ\nh : m ≤ n\n⊢ get? s m ... | [
169,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.epi_of_epi_image | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\nX Y : C\nf : X ⟶ Y\ninst✝² : HasImage f\ninst✝¹ : Epi (image.ι f)\ninst✝ : Epi (factorThruImage f)\n⊢ Epi (factorThruImage f ≫ image.ι f)",
"state_before": "C : Type u\ninst✝³ : Category C\nX✝ Y✝ : C\nf✝ : X✝ ⟶ Y✝\nX Y : C\nf : X ⟶ ... | [
479,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.compLeft_id | [
{
"state_after": "case H\nR : Type u_1\nM : Type u_2\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type ?u.513776\nM₁ : Type ?u.513779\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type ?u.514388\nM₂ : Type ?u.514391\ninst✝¹⁰ : CommSemiring R₂\ninst✝⁹... | [
623,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_le_cos_of_nonneg_of_le_pi | [] | [
592,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tendsto_tan_neg_pi_div_two | [
{
"state_after": "case h.e'_3\n\n⊢ tan = fun x => cos⁻¹ x * sin x",
"state_before": "⊢ Tendsto tan (𝓝[Ioi (-(π / 2))] (-(π / 2))) atBot",
"tactic": "convert tendsto_cos_neg_pi_div_two.inv_tendsto_zero.atTop_mul_neg (by norm_num)\n tendsto_sin_neg_pi_div_two using 1"
},
{
"state_after": "no g... | [
1093,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_eq_nat_iff | [] | [
1287,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_eq | [] | [
457,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Data/Sym/Basic.lean | SymOptionSuccEquiv.encode_of_none_mem | [] | [
615,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.int_lt_one_iff | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nm : ℤ\n⊢ ¬padicNorm p ↑m < 1 ↔ padicNorm p ↑m ≤ 1 ∧ ¬padicNorm p ↑m < 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nm : ℤ\n⊢ padicNorm p ↑m < 1 ↔ ↑p ∣ m",
"tactic": "rw [← not_iff_not, ← int_eq_one_iff, eq_iff_le_not_lt]"
},
{
"state_after... | [
299,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_eval₂_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommSemiring R\np q : R[X]\nr : R\n⊢ ↑derivative (eval₂ C q (↑C r)) = eval₂ C q (↑derivative (↑C r)) * ↑derivative q",
"tactic": "rw [eval₂_C, derivative_C, eval₂_zero, zero_... | [
563,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.interedges_biUnion_right | [
{
"state_after": "case a\n𝕜 : Type ?u.10244\nι : Type u_2\nκ : Type ?u.10250\nα : Type u_1\nβ : Type u_3\ninst✝³ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝² : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na✝ : α\nb : β\nδ : 𝕜\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns :... | [
119,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.differentiableOn | [] | [
722,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.inj | [] | [
272,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | dvd_sub_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10914\ninst✝ : NonUnitalRing α\na b c : α\nh : a ∣ b\n⊢ a ∣ b - c ↔ a ∣ c",
"tactic": "rw [sub_eq_add_neg, dvd_add_right h, dvd_neg (α := α)]"
}
] | [
115,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_add_one_eq_top | [
{
"state_after": "α : Type ?u.300385\nβ : Type ?u.300388\nγ : Type ?u.300391\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α → ℝ≥0∞\nf : ℕ → ℝ≥0∞\nhf : f 0 = ⊤ ∨ (∑' (b : ℕ), f (b + 1)) = ⊤\nhf0 : f 0 ≠ ⊤\n⊢ (∑' (n : ℕ), f (n + 1)) = ⊤",
"state_before": "α : Type ?u.300385\nβ : Ty... | [
1035,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.zero_mem | [] | [
47,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/List/MinMax.lean | List.minimum_mem | [] | [
310,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.toMeasure_uniformOfFinset_apply | [] | [
104,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.Integrable.lintegral_lt_top | [] | [
380,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.bounded_iff_bddBelow_bddAbove | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Set ℝ\nbdd : Metric.Bounded s\n⊢ BddBelow s ∧ BddAbove s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Set ℝ\n⊢ Metric.Bounded s → BddBelow s ∧ BddAbove s",
"tactic": "intro bdd"
},
{
"state_after": "case intro\nα : Type u\nβ... | [
188,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
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