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/Data/PEquiv.lean | PEquiv.mem_single | [] | [
347,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.coe_zsmul | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.card_le_univ | [] | [
267,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | MonoidHom.dfinsupp_prod_apply | [] | [
2263,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2261,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_inj | [] | [
170,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.mem_irrefl | [] | [
1557,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
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Mathlib/Data/Multiset/Pi.lean | Multiset.Pi.cons_ne | [] | [
49,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_range_findGreatest | [] | [
1567,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1565,
1
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.integrable | [] | [
515,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
11
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_coe_ne_top_iff_summable | [
{
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"state_before": "α : Type ?u.233118\nβ : Type u_1\nγ : Type ?u.233124\na b c d : ℝ≥0∞\nr p q : ℝ... | [
789,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.zero_le | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nI : FractionalIdeal S P\nx : P\nhx : x ∈ 0\n⊢ x ∈ I",
"state_before": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P... | [
400,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
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Mathlib/Topology/Algebra/ConstMulAction.lean | isClosedMap_smul | [] | [
262,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.ofFunction_le | [
{
"state_after": "case zero\nα : Type u_1\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\ns : Set α\nf : ℕ → Set α := fun i => Nat.casesOn i s fun x => ∅\n⊢ Nat.zero ≠ 0 → m (f Nat.zero) = 0\n\ncase succ\nα : Type u_1\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\ns : Set α\nf : ℕ → Set α := fun i => Nat.casesOn i s fun x => ∅\ni... | [
707,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernelZeroIsoSource_hom | [] | [
334,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_le_replicate | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.91808\nγ : Type ?u.91811\na : α\nk n : ℕ\n⊢ replicate k a ≤ replicate n a ↔ List.replicate k a <+ List.replicate n a",
"tactic": "rw [← replicate_le_coe, coe_replicate]"
}
] | [
969,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
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Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.trace_zero | [
{
"state_after": "no goals",
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167,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | dvd_normalize_iff | [] | [
199,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.star_eq_conjTranspose | [] | [
2343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2342,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.val_one | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_eq_empty_iff | [
{
"state_after": "no goals",
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1202,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.of_isNonZero | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np : Poly\nh : isNonZero [] = true\n⊢ denote ctx [] > 0",
"tactic": "contradiction"
},
{
"state_after": "case inl\nctx : Context\np✝ : Poly\nk : Nat\nv : Var\np : List (Nat × Var)\nhe : (v == fixedVar) = true\nh : k > 0\n⊢ denote ctx p ... | [
637,
50
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
630,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | sigmaFinsuppEquivDfinsupp_add | [
{
"state_after": "case h.h\nι : Type u_3\nR : Type ?u.76301\nM : Type ?u.76304\nη : ι → Type u_2\nN : Type u_1\ninst✝¹ : Semiring R\ninst✝ : AddZeroClass N\nf g : (i : ι) × η i →₀ N\ni✝ : ι\na✝ : η i✝\n⊢ ↑(↑(↑sigmaFinsuppEquivDfinsupp (f + g)) i✝) a✝ =\n ↑(↑(↑sigmaFinsuppEquivDfinsupp f + ↑sigmaFinsuppEquivD... | [
347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_equiv_symm | [
{
"state_after": "no goals",
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"tactic": "rw [map_map, e.self_comp_symm, map_id, map_comap_of_surjective e.surjective]"
}
] | [
2533,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2531,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_add_erase | [
{
"state_after": "case ofFinsupp\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ (↑(monomial n) (coeff { toFinsupp := toFinsupp✝ } n) + erase n { toFinsupp := toFinsupp✝ }).toFinsupp =\n { toFinsupp := toFinsupp✝ }.toFinsupp",
"state_before": "R... | [
1044,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Order/GaloisConnection.lean | Nat.galoisConnection_mul_div | [] | [
456,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.bijective | [] | [
206,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
11
] |
Mathlib/Data/Nat/Parity.lean | Nat.even_or_odd' | [
{
"state_after": "no goals",
"state_before": "m n✝ n : ℕ\n⊢ ∃ k, n = 2 * k ∨ n = 2 * k + 1",
"tactic": "simpa only [← two_mul, exists_or, Odd, Even] using even_or_odd n"
}
] | [
83,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/PathConnected.lean | Path.target | [] | [
129,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap_int_eq | [] | [
782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_mk' | [] | [
285,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.conj_neg | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.one_kronecker_one | [] | [
344,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.all_eq_allTR | [
{
"state_after": "no goals",
"state_before": "f : Nat → Bool\nn✝ n : Nat\n⊢ (all f n && allTR.loop f (0 + n) 0) = all f (0 + n)",
"tactic": "simp [allTR.loop]"
},
{
"state_after": "f : Nat → Bool\nn✝ m n : Nat\n⊢ (all f n && f n && allTR.loop f (succ (m + n)) m) = all f (succ (m + n))",
"sta... | [
758,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
751,
10
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.549105\nι : Type ?u.549108\ninst✝¹ : PseudoMetricSpace α\nγ : Type w\ninst✝ : MetricSpace γ\nx y : γ\n⊢ dist x y ≠ 0 ↔ x ≠ y",
"tactic": "simpa only [not_iff_not] using dist_eq_zero"
}
] | [
2860,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2859,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ite_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s s' : Set α\n⊢ Set.ite ∅ s s' = s'",
"tactic": "simp [Set.ite]"
}
] | [
2279,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2279,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.sum_sq_le_of_mem_box | [
{
"state_after": "α : Type ?u.502797\nβ : Type ?u.502800\nn d k N : ℕ\nx : Fin n → ℕ\nhx : ∀ (i : Fin n), x i < d\n⊢ ∑ i : Fin n, x i ^ 2 ≤ n * (d - 1) ^ 2",
"state_before": "α : Type ?u.502797\nβ : Type ?u.502800\nn d k N : ℕ\nx : Fin n → ℕ\nhx : x ∈ box n d\n⊢ ∑ i : Fin n, x i ^ 2 ≤ n * (d - 1) ^ 2",
... | [
203,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Control/EquivFunctor.lean | EquivFunctor.mapEquiv_trans | [
{
"state_after": "no goals",
"state_before": "f : Type u₀ → Type u₁\ninst✝ : EquivFunctor f\nα β : Type u₀\ne : α ≃ β\nγ : Type u₀\nab : α ≃ β\nbc : β ≃ γ\nx : f α\n⊢ ↑((mapEquiv f ab).trans (mapEquiv f bc)) x = ↑(mapEquiv f (ab.trans bc)) x",
"tactic": "simp [mapEquiv, map_trans']"
}
] | [
88,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | HasStrictDerivAt.arctan | [] | [
136,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/List/Count.lean | List.count_le_count_map | [
{
"state_after": "α : Type u_2\nl✝ : List α\ninst✝¹ : DecidableEq α\nβ : Type u_1\ninst✝ : DecidableEq β\nl : List α\nf : α → β\nx : α\n⊢ countp (fun x_1 => x_1 == x) l ≤ countp ((fun x_1 => x_1 == f x) ∘ f) l",
"state_before": "α : Type u_2\nl✝ : List α\ninst✝¹ : DecidableEq α\nβ : Type u_1\ninst✝ : Decida... | [
334,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Std/Data/List/Lemmas.lean | List.diff_sublist | [] | [
1531,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1525,
1
] |
Mathlib/NumberTheory/Liouville/Basic.lean | Liouville.exists_one_le_pow_mul_dist | [
{
"state_after": "Z : Type u_1\nN : Type u_2\nR : Type u_3\ninst✝ : PseudoMetricSpace R\nd : N → ℝ\nj : Z → N → R\nf : R → R\nα : R\nε M : ℝ\nd0 : ∀ (a : N), 1 ≤ d a\ne0 : 0 < ε\nB : ∀ ⦃y : R⦄, y ∈ closedBall α ε → dist (f α) (f y) ≤ dist α y * M\nL : ∀ ⦃z : Z⦄ ⦃a : N⦄, j z a ∈ closedBall α ε → 1 ≤ d a * dist (... | [
121,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasInitial C\n⊢ zeroIsoInitial.inv = 0",
"tactic": "ext"
}
] | [
324,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/Countable/Basic.lean | Function.Embedding.countable | [] | [
46,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
11
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | LinearEquiv.coe_isometryOfInner | [] | [
1310,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_eq_neg_one_mul | [
{
"state_after": "n : Nat\n⊢ -↑(succ n) = -[n+1]",
"state_before": "n : Nat\n⊢ -↑(succ n) = -[1 * n+1]",
"tactic": "rw [Nat.one_mul]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ -↑(succ n) = -[n+1]",
"tactic": "rfl"
},
{
"state_after": "n : Nat\n⊢ - -[n+1] = ofNat... | [
531,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
528,
11
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_eq_pi_single | [] | [
342,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.leftMulMatrix_eq_repr_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : Ring S\ninst✝² : Algebra R S\nm : Type u_3\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nb : Basis m R S\nx : S\ni j : m\n⊢ ↑(leftMulMatrix b) x i j = ↑(↑b.repr (x * ↑b j)) i",
"tactic": "rw [leftMulMat... | [
895,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.ProbabilityMeasure.tendsto_measure_of_null_frontier_of_tendsto | [
{
"state_after": "Ω✝ : Type ?u.40691\ninst✝³ : MeasurableSpace Ω✝\nΩ : Type u_1\nι : Type u_2\nL : Filter ι\ninst✝² : MeasurableSpace Ω\ninst✝¹ : PseudoEMetricSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nμ : ProbabilityMeasure Ω\nμs : ι → ProbabilityMeasure Ω\nμs_lim : Tendsto μs L (𝓝 μ)\nE : Set Ω\nE_nullbdry : (... | [
427,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_eq_pi_div_two_iff | [
{
"state_after": "case pos\nz : ℂ\nh₀ : z = 0\n⊢ arg z = π / 2 ↔ z.re = 0 ∧ 0 < z.im\n\ncase neg\nz : ℂ\nh₀ : ¬z = 0\n⊢ arg z = π / 2 ↔ z.re = 0 ∧ 0 < z.im",
"state_before": "z : ℂ\n⊢ arg z = π / 2 ↔ z.re = 0 ∧ 0 < z.im",
"tactic": "by_cases h₀ : z = 0"
},
{
"state_after": "case neg.mp\nz : ℂ\nh... | [
261,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | MulOpposite.nndist_unop | [] | [
1667,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1667,
1
] |
Mathlib/Order/Antichain.lean | isStrongAntichain_insert | [] | [
331,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_eq_coe | [
{
"state_after": "case hp\nm n : Nat\n⊢ ∀ (i n : Nat), ↑i = ↑(n + i) - ↑n\n\ncase hn\nm n : Nat\n⊢ ∀ (i m : Nat), -[i+1] = ↑m - ↑(m + i + 1)",
"state_before": "m n : Nat\n⊢ subNatNat m n = ↑m - ↑n",
"tactic": "apply subNatNat_elim m n fun m n i => i = m - n"
},
{
"state_after": "case hp\nm n✝ i ... | [
512,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
504,
11
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubgroup_mono | [] | [
555,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.trivial_eq_bot | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_mul | [
{
"state_after": "R : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nrc : RingHomClass F R S\nf : F\nI J : Ideal R\nK L : Ideal S\nr : R\nhri : r ∈ I\ns : R\nhsj : s ∈ J\n⊢ ↑f r * ↑f s ∈ map f I * map f J",
"state_before": "R : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : CommRing ... | [
1790,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1780,
1
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Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.next_nat_succ | [] | [
138,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/Basic.lean | lt_of_eq_of_lt | [] | [
187,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.one_def | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_image | [] | [
473,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.expNear_succ | [
{
"state_after": "n : ℕ\nx r : ℝ\n⊢ x * x ^ n * ((↑(Nat.factorial n))⁻¹ * (↑n + 1)⁻¹) * r = x ^ n * (↑(Nat.factorial n))⁻¹ * (x * (↑n + 1)⁻¹ * r)",
"state_before": "n : ℕ\nx r : ℝ\n⊢ expNear (n + 1) x r = expNear n x (1 + x / (↑n + 1) * r)",
"tactic": "simp [expNear, range_succ, mul_add, add_left_comm, ... | [
1759,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1756,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_apply_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : DecidableEq ι\nb : Basis ι R M\ni : ι\nm : M\n⊢ ↑(↑(toDual b) (↑b i)) m = ↑(↑b.repr m) i",
"tactic": "rw [← b.toDual... | [
328,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | has_deriv_within_taylorWithinEval_at_Icc | [] | [
230,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.mul_left_inj | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b✝ c✝ u a : αˣ\nb c : α\nh : b * ↑a = c * ↑a\n⊢ b = c",
"tactic": "simpa only [mul_inv_cancel_right] using congr_arg (fun x : α => x * ↑(a⁻¹ : αˣ)) h"
}
] | [
317,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurableSet_prod | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.84459\nδ : Type ?u.84462\nδ' : Type ?u.84465\nι : Sort uι\ns✝ t✝ u : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nmγ : MeasurableSpace γ\ns : Set α\nt : Set β\nh : s ×ˢ t = ∅\n⊢ MeasurableSet (s ×ˢ t) ↔ MeasurableSet s ∧ MeasurableSet ... | [
738,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.mkContinuous_norm_le | [] | [
768,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Topology/Filter.lean | Filter.Tendsto.nhds | [] | [
227,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
11
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.fst_comp_quotientInfEquivQuotientProd | [
{
"state_after": "case h\nR : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nI J : Ideal R\ncoprime : I ⊔ J = ⊤\n⊢ RingHom.comp (RingHom.comp (RingHom.fst (R ⧸ I) (R ⧸ J)) ↑(quotientInfEquivQuotientProd I J coprime))\n (Quotient.mk (I ⊓ J)) =\n RingHom.comp (Quotient.factor (I ⊓ J) I (_ ... | [
534,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Init/Data/Fin/Basic.lean | Fin.eq_of_veq | [
{
"state_after": "case refl\nn iv : ℕ\nilt₁ jlt₁ : iv < n\n⊢ { val := iv, isLt := ilt₁ } = { val := iv, isLt := jlt₁ }",
"state_before": "n iv : ℕ\nilt₁ : iv < n\njv : ℕ\njlt₁ : jv < n\nh : { val := iv, isLt := ilt₁ }.val = { val := jv, isLt := jlt₁ }.val\n⊢ { val := iv, isLt := ilt₁ } = { val := jv, isLt :... | [
15,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
14,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toOpens_top | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.C_apply | [] | [
724,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootSet_mapsTo | [
{
"state_after": "R : Type u\nS✝ : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝⁹ : CommRing R\ninst✝⁸ : IsDomain R\np✝ q : R[X]\ninst✝⁷ : CommRing T\np : T[X]\nS : Type u_1\nS' : Type u_2\ninst✝⁶ : CommRing S\ninst✝⁵ : IsDomain S\ninst✝⁴ : Algebra T S\ninst✝³ : CommRing S'\ninst✝² : IsDomain S'\ninst✝¹ : Algebra T... | [
976,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_zero | [
{
"state_after": "case pos\na : Ordinal\nh : a = 0\n⊢ a ^ 0 = 1\n\ncase neg\na : Ordinal\nh : ¬a = 0\n⊢ a ^ 0 = 1",
"state_before": "a : Ordinal\n⊢ a ^ 0 = 1",
"tactic": "by_cases h : a = 0"
},
{
"state_after": "no goals",
"state_before": "case pos\na : Ordinal\nh : a = 0\n⊢ a ^ 0 = 1",
... | [
56,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Real.continuousAt_rpow | [] | [
260,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivaryOn_toDual_left | [] | [
279,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.nontrivial_of_not_isZero | [] | [
746,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_add_nat | [] | [
2514,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2513,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_right_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.72761\nα : Type u_1\nβ : Type ?u.72767\nπ : ι → Type ?u.72772\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ b ∆ c = a ∆ c ∆ b",
"tactic": "simp_rw [symmDiff_assoc, symmDiff_comm]"
}
] | [
489,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.left_triangle | [
{
"state_after": "case w.h\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nx✝ : C\n⊢ (whiskerRight adj.unit F ≫ whiskerLeft F adj.counit).app x✝ = (𝟙 (𝟭 C ⋙ F)).app x✝",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u... | [
183,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two | [] | [
1449,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.copy_eq | [] | [
429,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_sub_iff_add_le | [
{
"state_after": "no goals",
"state_before": "x y k : Nat\nh : k ≤ y\n⊢ x ≤ y - k ↔ x + k ≤ y",
"tactic": "rw [← Nat.add_sub_cancel x k, Nat.sub_le_sub_right_iff h, Nat.add_sub_cancel]"
}
] | [
465,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
464,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.comap_op_mul | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM✝ N✝ P Q : Submodule R A\nm n : A\nM N : Submodule R Aᵐᵒᵖ\n⊢ comap (↑(opLinearEquiv R)) (M * N) = comap (↑(opLinearEquiv R)) N * comap (↑(opLine... | [
318,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.uniqueProd_symm_apply | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.le_div_two_iff_lt_neg | [
{
"state_after": "n : ℕ\nhn : Fact (n % 2 = 1)\nx : ZMod n\nhx0 : x ≠ 0\nnpos : NeZero n\n⊢ val x ≤ n / 2 ↔ n / 2 < val (-x)",
"state_before": "n : ℕ\nhn : Fact (n % 2 = 1)\nx : ZMod n\nhx0 : x ≠ 0\n⊢ val x ≤ n / 2 ↔ n / 2 < val (-x)",
"tactic": "haveI npos : NeZero n :=\n ⟨by\n rintro rfl\n simp... | [
814,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.comp_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf fab : α → β\nfbc : β → γ\nga ga' : α → α\ngb gb' : β → β\ngc gc' : γ → γ\nhab : Semiconj fab ga gb\nhbc : Semiconj fbc gb gc\nx : α\n⊢ (fbc ∘ fab) (ga x) = gc ((fbc ∘ fab) x)",
"tactic": "simp only [comp_apply, hab... | [
58,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.ne_zero_iff | [] | [
123,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
11
] |
Mathlib/Order/Heyting/Hom.lean | map_bihimp | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.33397\nδ : Type ?u.33400\ninst✝² : HeytingAlgebra α\ninst✝¹ : HeytingAlgebra β\ninst✝ : HeytingHomClass F α β\nf : F\na b : α\n⊢ ↑f (a ⇔ b) = ↑f a ⇔ ↑f b",
"tactic": "simp_rw [bihimp, map_inf, map_himp]"
... | [
197,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/Group/Defs.lean | pow_zero | [] | [
630,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Order/Filter/CountableInter.lean | EventuallyLE.countable_bInter | [
{
"state_after": "ι✝ : Sort ?u.5259\nα : Type u_2\nβ : Type ?u.5265\nl : Filter α\ninst✝ : CountableInterFilter l\nι : Type u_1\nS : Set ι\nhS : Set.Countable S\ns t : (i : ι) → i ∈ S → Set α\nh : ∀ (i : ι) (hi : i ∈ S), s i hi ≤ᶠ[l] t i hi\n⊢ (⋂ (x : ↑S), s ↑x (_ : ↑x ∈ S)) ≤ᶠ[l] ⋂ (x : ↑S), t ↑x (_ : ↑x ∈ S)"... | [
120,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/List/Infix.lean | List.subset_insert | [] | [
498,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_model_space_eq_id | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nM : Type ?u.234410\nH : Type ?u.234413\nE' : Type ?u.234416\nM' : Type ?u.234419\nH' : Type ?u.234422\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝... | [
1283,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.restrictScalars_closedBall | [] | [
1098,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.prod_comap_inr | [
{
"state_after": "case h\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.303059\nM₆ : Type ?u.303062\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\... | [
575,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.mk_add_moveLeft_inl | [] | [
1503,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
1
] |
Mathlib/Data/List/Basic.lean | List.replicate_add | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.17053\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nm n : ℕ\na : α\n⊢ replicate (m + n) a = replicate m a ++ replicate n a",
"tactic": "induction m <;> simp [*, zero_add, succ_add, replicate]"
}
] | [
441,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_of_mul | [] | [
150,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.compl_mem_sets | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.205\nπ : ι → Type ?u.210\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nhs : IsCompact s\nf : Filter α\nhf : ¬sᶜ ∈ f\n⊢ ∃ a, a ∈ s ∧ ¬sᶜ ∈ 𝓝 a ⊓ f",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.205\nπ : ι → Type ?u.210\ni... | [
81,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | properSpace_of_compact_closedBall_of_le | [] | [
2166,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2163,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_transpose | [
{
"state_after": "case a.h\nl : Type ?u.49070\nm : Type ?u.49073\nn : Type u_1\no : Type ?u.49079\nm' : o → Type ?u.49084\nn' : o → Type ?u.49089\nR : Type ?u.49092\nS : Type ?u.49095\nα : Type v\nβ : Type w\nγ : Type ?u.49102\ninst✝¹ : DecidableEq n\ninst✝ : Zero α\nv : n → α\ni j : n\n⊢ (diagonal v)ᵀ i j = di... | [
469,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.toList_inj | [] | [
200,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
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