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/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.equiv_trans | [] | [
176,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.coe_mul | [] | [
552,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
9
] |
Mathlib/Algebra/Field/Basic.lean | add_div' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7271\nK : Type ?u.7274\ninst✝ : DivisionSemiring α\na✝ b✝ c✝ d a b c : α\nhc : c ≠ 0\n⊢ b + a / c = (b * c + a) / c",
"tactic": "rw [add_div, mul_div_cancel _ hc]"
}
] | [
66,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_sub_eq_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c✝ : α\nn : ℤ\na b c : α\n⊢ toIcoMod hp a (b - c) = toIcoMod hp (a + c) b - c",
"tactic": "simp_rw [toIcoMod, toIcoDiv_sub_eq_toIcoDiv_add, sub_right_comm]"
}
] | [
533,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | linearIndependent_iff_card_le_finrank_span | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\nι : Type u_1\ninst✝ : Fintype ι\nb : ι → V\n⊢ LinearIndependent K b ↔ Fintype.card ι ≤ Set.finrank K (Set.range b)",
"tactic": "rw [linearIndependent_iff_card_eq_f... | [
450,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.vertical_strip | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b C : ℝ\nf g : ℂ → E\nz : ℂ\nhfd : DiffContOnCl ℂ f (re ⁻¹' Ioo a b)\nhB :\n ∃ c,\n c < π / (b - a) ∧\n ∃ B, f =O[comap (Abs.abs ∘ im) atTop ⊓ 𝓟 (re ⁻¹' Ioo a b)] fun z => expR (B * expR (c * Abs.abs z.im))\nhle_... | [
306,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Order/OrderIsoNat.lean | WellFounded.iSup_eq_monotonicSequenceLimit | [
{
"state_after": "α : Type u_1\ninst✝ : CompleteLattice α\nh : WellFounded fun x x_1 => x > x_1\na : ℕ →o α\nm : ℕ\n⊢ ↑a m ≤ monotonicSequenceLimit a",
"state_before": "α : Type u_1\ninst✝ : CompleteLattice α\nh : WellFounded fun x x_1 => x > x_1\na : ℕ →o α\n⊢ iSup ↑a = monotonicSequenceLimit a",
"tact... | [
262,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.ae_mem_imp_eq_mk | [] | [
1252,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.zpow_mem_zpowers | [] | [
57,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.toConvexCone_top | [] | [
538,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.neg_neg | [] | [
374,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.pairwise_cons | [] | [
3751,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3748,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_succ_eq_comp_left | [] | [
809,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Order/CompleteLattice.lean | biSup_const | [
{
"state_after": "α : Type u_2\nβ : Type ?u.100367\nβ₂ : Type ?u.100370\nγ : Type ?u.100373\nι✝ : Sort ?u.100376\nι' : Sort ?u.100379\nκ : ι✝ → Sort ?u.100384\nκ' : ι' → Sort ?u.100389\ninst✝ : CompleteLattice α\nf g s✝ t : ι✝ → α\na✝ b : α\nι : Type u_1\na : α\ns : Set ι\nhs : Set.Nonempty s\nthis : Nonempty ↑... | [
1225,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Data/Set/Image.lean | Set.Nonempty.of_image | [] | [
456,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.77892\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.77904\nι : Sort ?u.77907\nκ : ι → Sort ?u.77912\ninst✝³ : CompleteLattice α\ninst✝² : CompleteLattice β\ninst✝¹ : CompleteLattice γ\ninst✝ : CompleteLattice δ\ng : CompleteLatticeHom β γ\nf... | [
777,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | hasFDerivWithinAt_of_restrictScalars | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝⁹ : NontriviallyNormedField 𝕜'\ninst✝⁸ : NormedAlgebra 𝕜 𝕜'\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedSpace 𝕜' E\ninst✝⁴ : IsScalarTower 𝕜 𝕜' E\nF : Type u_3\ninst✝³ : ... | [
95,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.irreducible_aux2 | [
{
"state_after": "p q : ℤ[X]\nk m m' n : ℕ\nhkm : k < m\nhmn : m < n\nhkm' : k < m'\nhmn' : m' < n\nu v w : ℤˣ\nhp : p = trinomial k m n ↑u ↑v ↑w\nhq : q = trinomial k m' n ↑u ↑v ↑w\nh : p * mirror p = q * mirror q\nf : ℤ[X] → ℤ[X] := fun p => { toFinsupp := Finsupp.filter (Set.Ioo (k + n) (n + n)) p.toFinsupp ... | [
281,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Measurable.fract | [] | [
59,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/RingTheory/FiniteType.lean | Module.Finite.injective_of_surjective_endomorphism | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : M →ₗ[R] M\nhfg : Finite R M\nf_surj : Surjective ↑f\nx✝ : Module R[X] M := modulePolynomialOfEndo f\n⊢ Function.Injective ↑f",
"state_before": "R : Type u_1\ninst✝² : CommRing R\nM : Type u_2\... | [
693,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_op | [] | [
1486,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1484,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.has_cofiltered_limits_of_has_filtered_colimits_op | [] | [
285,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.one_comp | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.const_mul | [] | [
1490,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1488,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_fst | [] | [
768,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.succ_pred | [
{
"state_after": "no goals",
"state_before": "a : Nat\nh : a ≠ 0\n⊢ succ (pred a) = a",
"tactic": "induction a with\n| zero => contradiction\n| succ => rfl"
},
{
"state_after": "no goals",
"state_before": "case zero\nh : zero ≠ 0\n⊢ succ (pred zero) = zero",
"tactic": "contradiction"
}... | [
567,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
564,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_congr_fun | [
{
"state_after": "α : Type u_1\nβ : Type ?u.294994\nγ : Type ?u.294997\nδ : Type ?u.295000\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\nhfg : ∀ᵐ (x : α) ∂μ, x ∈ s → f x = g x\n⊢ (fun x => f x) =ᵐ[Measure.restrict μ s] fun a => g a",
"state_before": "α : Type u_1\... | [
335,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Init/CcLemmas.lean | ne_of_ne_of_eq | [] | [
125,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/GroupTheory/Subgroup/Saturated.lean | AddSubgroup.ker_saturated | [
{
"state_after": "A₁ : Type u_1\nA₂ : Type u_2\ninst✝² : AddCommGroup A₁\ninst✝¹ : AddCommGroup A₂\ninst✝ : NoZeroSMulDivisors ℕ A₂\nf : A₁ →+ A₂\nn : ℕ\ng : A₁\nhg : n • g ∈ AddMonoidHom.ker f\n⊢ n = 0 ∨ g ∈ AddMonoidHom.ker f",
"state_before": "A₁ : Type u_1\nA₂ : Type u_2\ninst✝² : AddCommGroup A₁\ninst✝... | [
69,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_eq | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.769930\n𝕜 : Type ?u.769933\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
821,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.sum_coord_apply_eq_one | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.112987\nk : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝⁴ : AddCommGroup V\ninst✝³ : AffineSpace V P\ninst✝² : Ring k\ninst✝¹ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni j : ι\ne : ι ≃ ι'\ninst✝ : Fintype ι\nq : P\nhq : q ∈ affineSpan k (range ↑b)\n⊢ ∑ i : ι,... | [
212,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_le_of_liminf_slope_right_lt_deriv_boundary' | [
{
"state_after": "E : Type ?u.193\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.289\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf f' : ℝ → ℝ\na b : ℝ\nhf : ContinuousOn f (Icc a b)\nhf' : ∀ (x : ℝ), x ∈ Ico a b → ∀ (r : ℝ), f' x < r → ∃ᶠ (z : ℝ) in 𝓝[Ioi x] x, slope f x z <... | [
127,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\na : AddMonoidAlgebra R ℕ\n⊢ { toFinsupp := a } = 0 ↔ a = 0",
"tactic": "rw [← ofFinsupp_zero, ofFinsupp_inj]"
}
] | [
281,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.unique_on | [] | [
278,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_concat | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' : List α\nhd : α\ntl : List α\n⊢ rotate (hd :: tl) 1 = tl ++ [hd]",
"tactic": "simp"
}
] | [
511,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_add_subset | [] | [
1122,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.map_inf_fixedPoints_le | [] | [
252,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.comm' | [] | [
94,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Order/Floor.lean | subsingleton_floorRing | [
{
"state_after": "F : Type ?u.312400\nα✝ : Type ?u.312403\nβ : Type ?u.312406\nα : Type u_1\ninst✝ : LinearOrderedRing α\nH₁ H₂ : FloorRing α\n⊢ H₁ = H₂",
"state_before": "F : Type ?u.312400\nα✝ : Type ?u.312403\nβ : Type ?u.312406\nα : Type u_1\ninst✝ : LinearOrderedRing α\n⊢ Subsingleton (FloorRing α)",
... | [
1626,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1621,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.zneg_bit1 | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.658372\nn : ZNum\n⊢ -ZNum.bit1 n = ZNum.bitm1 (-n)",
"tactic": "cases n <;> rfl"
}
] | [
1082,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.conjCle_apply | [] | [
374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.alternatingFaceMapComplex_obj_d | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.d\n (ChainComplex.of (fun n => X.obj [n].op) (AlternatingFaceMapComplex.objD X)\n (_ : ∀ (n : ℕ), AlternatingFaceMapComplex.objD X (n + 1) ≫ AlternatingFaceMapComplex.objD ... | [
186,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.toEquiv_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.8291\nδ : Type ?u.8294\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : UniformSpace δ\ne : α ≃ β\nh₁ : UniformContinuous e.toFun\nh₂ : UniformContinuous e.invFun\ne' : α ≃ β\nh₁' : Uniform... | [
55,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_reflect | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na : α\ng f✝ : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\nk m n : ℕ\nh : m ≤ n + 1\nthis : ∀ (i : ℕ), i < m → i ≤ n\n⊢ ∏ j in Ico k m, f (n - j) = ∏ j in Ico (n + 1 - m) (n + 1 - k), f j",
"state_before": "α : Type u\nβ : Type v\nγ : Type... | [
164,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | Right.pow_lt_one_of_lt | [
{
"state_after": "β : Type ?u.94928\nA : Type ?u.94931\nG : Type ?u.94934\nM : Type u_1\nR : Type ?u.94940\ninst✝² : Monoid M\ninst✝¹ : Preorder M\ninst✝ : CovariantClass M M (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\nn✝ : ℕ\nx : M\nhn : 0 < n✝\nh : x < 1\nn : ℕ\nx✝ : Nat.succ 0 ≤ n\nih : x ^ n < 1\n⊢ x ... | [
222,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.exists_isSubordinate_of_locallyFinite_of_prop | [
{
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.gc_map_comap | [] | [
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1653,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.isHomogeneous | [] | [
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20
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Mathlib/Order/Heyting/Basic.lean | sup_sdiff_cancel_right | [] | [
581,
29
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isClosed_iff_of_mem | [
{
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230,
90
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Mathlib/LinearAlgebra/Dual.lean | Basis.toDualEquiv_apply | [] | [
413,
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Mathlib/Algebra/Order/Group/Abs.lean | dist_bdd_within_interval | [] | [
367,
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Mathlib/RingTheory/Ideal/Basic.lean | one_not_mem_nonunits | [] | [
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Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.Represents.congr_fun | [] | [
97,
26
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Mathlib/Data/List/Basic.lean | List.takeWhile_idem | [
{
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3670,
63
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.vanishingIdeal_univ | [
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Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.diff_ae_eq_left | [] | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isOrtho_smul_right | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_biUnion | [] | [
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Std/Data/Int/Lemmas.lean | Int.subNatNat_of_lt | [] | [
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Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decay | [
{
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.coe_addHom_mk | [] | [
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264,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.centralizer_eq_top_iff_subset | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.mono_of_isLimit_parallelFamily | [] | [
660,
58
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Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.forget_map | [] | [
228,
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Mathlib/Data/Part.lean | Part.bind_assoc | [
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Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.iff_not_exists_isMinBadSeq | [
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Mathlib/LinearAlgebra/Dimension.lean | basis_le_span' | [
{
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Std/Data/List/Lemmas.lean | List.length_pos | [] | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mod_self | [
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1058,
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Mathlib/Algebra/Order/Group/DenselyOrdered.lean | le_of_forall_lt_one_mul_le | [] | [
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.abs_lt_one | [] | [
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.prod_eq_top_iff | [
{
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Mathlib/Algebra/GroupPower/Basic.lean | Commute.zpow_left | [] | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.one_of_succ | [] | [
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.comm_tmul | [
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Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | IsOpenMap.coverPreserving | [
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Mathlib/Data/List/Chain.lean | List.chain_iff_get | [
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.continuous | [] | [
433,
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432,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_eq_empty_iff | [] | [
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51
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_coe' | [] | [
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime.eq_of_mul_eq_zero | [] | [
227,
39
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223,
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Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.IsInitial.isIso_to | [] | [
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35
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Mathlib/RingTheory/FinitePresentation.lean | AlgHom.FiniteType.of_finitePresentation | [] | [
494,
46
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493,
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Mathlib/Topology/Constructions.lean | inducing_sigma_map | [
{
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Std/Data/String/Lemmas.lean | String.Pos.addString_byteIdx | [] | [
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Mathlib/Data/Real/NNReal.lean | Real.toNNReal_zero | [] | [
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_empty | [
{
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Mathlib/GroupTheory/GroupAction/Group.lean | Commute.smul_right_iff | [] | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_const_vadd | [] | [
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_univ | [] | [
573,
40
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.zero_trim | [
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56
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Mathlib/Algebra/Order/Group/Defs.lean | lt_mul_inv_iff_mul_lt | [
{
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Mathlib/GroupTheory/GroupAction/Defs.lean | IsCentralScalar.unop_smul_eq_smul | [
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr_iff | [] | [
116,
81
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.card_eq | [
{
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.pseudoZero_def | [] | [
250,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nW X Y Z : C\nf : X ⟶ Y\ng : X ⟶ Z\ng' : Z ⟶ W\ninst✝² : HasPushout f g\ninst✝¹ : HasPushout pushout.inr g'\ninst✝ : HasPushout f (g ≫ g')\n⊢ pushout.inr ≫ (pushoutLeftPushoutInrIso f g g').inv = ... | [
2234,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2232,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | OrderIso.map_ciInf | [] | [
1356,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_eq_sub_div | [
{
"state_after": "case hc\nb a : Nat\nh₁ : 0 < b\nh₂ : b ≤ a\n⊢ 0 < b ∧ b ≤ a",
"state_before": "b a : Nat\nh₁ : 0 < b\nh₂ : b ≤ a\n⊢ a / b = (a - b) / b + 1",
"tactic": "rw [div_eq a, if_pos]"
},
{
"state_after": "no goals",
"state_before": "case hc\nb a : Nat\nh₁ : 0 < b\nh₂ : b ≤ a\n⊢ 0 <... | [
290,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
289,
1
] |
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