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/NumberTheory/Padics/RingHoms.lean | PadicInt.ker_toZMod | [
{
"state_after": "case h\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx✝ x : ℤ_[p]\n⊢ x ∈ RingHom.ker toZMod ↔ x ∈ maximalIdeal ℤ_[p]",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx : ℤ_[p]\n⊢ RingHom.ker toZMod = maximalIdeal ℤ_[p]",
"tactic": "ext x"
},
{
"state_after": "cas... | [
296,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Set/Sups.lean | Set.singleton_sups | [] | [
148,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.range_eq_univ | [] | [
40,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.subset_closure | [] | [
481,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.transpose | [
{
"state_after": "α : Type u_2\nβ : Type ?u.3659\nm : Type ?u.3662\nn : Type u_1\nA✝ : Matrix n n α\ninst✝¹ : Star α\ninst✝ : Star β\nA : Matrix n n α\nh : IsHermitian A\n⊢ (Matrix.map Aᵀ star)ᵀ = Aᵀ",
"state_before": "α : Type u_2\nβ : Type ?u.3659\nm : Type ?u.3662\nn : Type u_1\nA✝ : Matrix n n α\ninst✝¹... | [
76,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.mk_mem_sigmaLift | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nγ : ι → Type u_1\ninst✝ : DecidableEq ι\nf : ⦃i : ι⦄ → α i → β i → Finset (γ i)\ni : ι\na : α i\nb : β i\nx : γ i\n⊢ (∃ a_1,\n a_1 ∈\n f ((_ : { fst := i, snd := a }.fst = { fst := i, snd := a }.fst) ▸ { fst := i, snd := a }.snd)\... | [
152,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_mem_vsub | [] | [
613,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.congr | [] | [
198,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumDiffSubset_apply_inl | [] | [
370,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Topology/Sheaves/PresheafOfFunctions.lean | TopCat.presheafToType_obj | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | nonempty_omegaLimit_of_isCompact_absorbing | [
{
"state_after": "case intro.intro\nτ : Type u_1\nα : Type u_3\nβ : Type u_2\nι : Type ?u.74453\ninst✝¹ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\ninst✝ : NeBot f\nc : Set β\nhc₁ : IsCompact c\nhs : Set.Nonempty s\nv : Set τ\nhv₁ : v ∈ f\nhv₂ : closure (image2 ϕ v s) ⊆ c\n⊢ Set.Nonempty... | [
325,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_neg | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.324499\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.324508\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf✝ g f : NormedAddGroupHom V₁ V₂\n⊢ ‖-f‖ = ‖f‖",
... | [
470,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.pell_eq | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\npn : xz a1 n * xz a1 n - ↑(Pell.d a1) * yz a1 n * yz a1 n = 1 := pell_eqz a1 n\n⊢ ↑(xn a1 n * xn a1 n) - ↑(Pell.d a1 * yn a1 n * yn a1 n) = 1",
"tactic": "repeat' rw [Int.ofNat_mul]; exact pn"
},
{
"state_after": "a : ℕ\na1 ... | [
249,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_eq_iff | [] | [
301,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_eq_norm_mul_iff | [
{
"state_after": "case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3212961\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\ny : E\n⊢ inner 0 y = ↑‖0‖ * ↑‖y‖ ↔ ↑‖y‖ • 0 = ↑‖0‖ • y\n\ncase in... | [
1675,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1670,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.prime_mul_iff | [
{
"state_after": "no goals",
"state_before": "a b : ℕ\n⊢ Prime (a * b) ↔ Prime a ∧ b = 1 ∨ Prime b ∧ a = 1",
"tactic": "simp only [iff_self_iff, irreducible_mul_iff, ← irreducible_iff_nat_prime, Nat.isUnit_iff]"
}
] | [
230,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | DifferentiableAt.star | [] | [
72,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.PInfty_comp_πSummand_id | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX : SimplicialObject C\ns : Splitting X\ninst✝ : Preadditive C\nn : ℕ\n⊢ HomologicalComplex.Hom.f PInfty n ≫ πSummand s (IndexSet.id [n].op) =\n 𝟙 (X.obj [n].op) ≫ πSummand s (IndexSet.id [n].op)",
"state_before": "C : ... | [
137,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_add | [] | [
59,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.sup_prod | [] | [
1698,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1697,
1
] |
Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nW X Y Z : C\n⊢ (α_ W (X ⊗ Y) Z).inv ≫ ((α_ W X Y).inv ⊗ 𝟙 Z) ≫ (α_ (W ⊗ X) Y Z).hom = (𝟙 W ⊗ (α_ X Y Z).hom) ≫ (α_ W X (Y ⊗ Z)).inv",
"tactic": "coherence"
}
] | [
62,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_assoc | [] | [
627,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.map_ringChar | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\ninst✝³ : CommMonoid R✝\nR' : Type v\ninst✝² : CommMonoidWithZero R'\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nχ : MulChar R R'\n⊢ ↑χ ↑(ringChar R) = 0",
"tactic": "rw [ringChar.Nat.cast_ringChar, χ.map_zero]"
}
] | [
280,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Topology/Basic.lean | interior_union_isClosed_of_interior_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns t : Set α\nh₁ : IsClosed s\nh₂ : interior t = ∅\nx : α\nx✝ : x ∈ interior (s ∪ t)\nu : Set α\nhu₁ : IsOpen u\nhu₂ : u ⊆ s ∪ t\nhx₁ : x ∈ u\nhx₂ : ¬x... | [
381,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.one_toNat | [
{
"state_after": "no goals",
"state_before": "α β : Type u\n⊢ ↑toNat 1 = 1",
"tactic": "rw [← toNat_cast 1, Nat.cast_one]"
}
] | [
1756,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1756,
1
] |
Mathlib/Algebra/Module/Torsion.lean | AddMonoid.isTorsion_iff_isTorsion_nat | [
{
"state_after": "case refine'_1\nR : Type ?u.754879\nM : Type u_1\ninst✝ : AddCommMonoid M\nh : IsTorsion M\nx : M\n⊢ ∃ a, a • x = 0\n\ncase refine'_2\nR : Type ?u.754879\nM : Type u_1\ninst✝ : AddCommMonoid M\nh : Module.IsTorsion ℕ M\nx : M\n⊢ IsOfFinAddOrder x",
"state_before": "R : Type ?u.754879\nM : ... | [
838,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_iInter₂ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.42954\nβ : Type ?u.42957\nγ : Type u_1\nι : Sort u_2\nι' : Sort ?u.42966\nι₂ : Sort ?u.42969\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.42979\nκ₂ : ι → Sort ?u.42984\nκ' : ι' → Sort ?u.42989\nx : γ\ns : (i : ι) → κ i → Set γ\n⊢ (x ∈ ⋂ (i : ι) (j : κ i), s i... | [
156,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.inv_injective | [] | [
156,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_iff_ordConnected | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type ?u.282167\nF : Type ?u.282170\nβ : Type ?u.282173\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\n⊢ Convex 𝕜 s ↔ OrdConnected s",
"tactic": "simp_rw [convex_iff_segment_subset, segment_eq_uIcc, ordConnected_iff_uIcc_subset]"
}
] | [
583,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_pow | [] | [
211,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.uniformContinuous_quotient | [] | [
299,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.congr_mono | [] | [
879,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_zero | [] | [
837,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/NumberTheory/Primorial.lean | primorial_add_dvd | [
{
"state_after": "m n : ℕ\nh : n ≤ m\np : ℕ\nhp : (m + 1 ≤ p ∧ p < m + n + 1) ∧ Nat.Prime p\n⊢ p ∣ Nat.choose (m + n) m",
"state_before": "m n : ℕ\nh : n ≤ m\np : ℕ\nhp : p ∈ filter Nat.Prime (Ico (m + 1) (m + n + 1))\n⊢ p ∣ Nat.choose (m + n) m",
"tactic": "rw [mem_filter, mem_Ico] at hp"
},
{
... | [
70,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Parity.lean | Odd.pow_pos_iff | [] | [
495,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_submatrix | [] | [
170,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_eq_bot_iff | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
1018,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffWithinAt.inter' | [] | [
315,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Real.norm_two | [] | [
1738,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1737,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.ext_of_adjoin_eq_top | [] | [
177,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_nonneg_of_mem_Icc | [
{
"state_after": "x : ℝ\nhx : x ∈ closure (Ioo 0 π)\n⊢ 0 ≤ sin x",
"state_before": "x : ℝ\nhx : x ∈ Icc 0 π\n⊢ 0 ≤ sin x",
"tactic": "rw [← closure_Ioo pi_ne_zero.symm] at hx"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ∈ closure (Ioo 0 π)\n⊢ 0 ≤ sin x",
"tactic": "exa... | [
421,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_toMul | [] | [
2235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2234,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.fderiv_aeval | [] | [
187,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
11
] |
Mathlib/Order/Monotone/Monovary.lean | Monovary.dual_left | [] | [
208,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.bot_ne_zero | [] | [
322,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | DifferentiableOn.rpow | [] | [
445,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.closure_eq | [] | [
762,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_subset | [] | [
1822,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1821,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Group.lean | le_mul_ciInf | [] | [
29,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.iUnion_of_chain | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.10523\nπ : ι → Type ?u.10528\ninst✝³ : TopologicalSpace α\ns✝ t u v : Set α\ninst✝² : LinearOrder β\ninst✝¹ : SuccOrder β\ninst✝ : IsSuccArchimedean β\ns : β → Set α\nH : ∀ (n : β), IsPreconnected (s n)\nK : ∀ (n : β), Set.Nonempty (s n ∩ s (succ n))\ni✝ j i... | [
245,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubVSubWeights_apply_of_ne | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type ?u.424095\nP : Type ?u.424098\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.424754\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\ni j t : ι\nhi : t ≠ i\nhj : t ≠ j\n⊢... | [
696,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.map_apply | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.evaln_complete | [
{
"state_after": "case intro\nc : Code\nn x : ℕ\nh✝ : x ∈ eval c n\nk : ℕ\nh : x ∈ evaln (k + 1) c n\n⊢ ∃ k, x ∈ evaln k c n\n\nc : Code\nn x : ℕ\nh : x ∈ eval c n\n⊢ ∃ k, x ∈ evaln (k + 1) c n",
"state_before": "c : Code\nn x : ℕ\nh : x ∈ eval c n\n⊢ ∃ k, x ∈ evaln k c n",
"tactic": "rsuffices ⟨k, h⟩ :... | [
925,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_of_compactSpace | [] | [
2450,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2449,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_mem_Icc | [] | [
628,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_strictMono | [
{
"state_after": "a b : Ordinal\n⊢ a < b → beth a < beth b",
"state_before": "⊢ StrictMono beth",
"tactic": "intro a b"
},
{
"state_after": "case h\na✝ b : Ordinal\nIH : ∀ (k : Ordinal), k < b → ∀ ⦃a : Ordinal⦄, a < k → beth a < beth k\na : Ordinal\n⊢ a < b → beth a < beth b",
"state_before"... | [
444,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.sum_hom | [] | [
415,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Topology/ContinuousFunction/Polynomial.lean | polynomialFunctions_separatesPoints | [
{
"state_after": "R : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : TopologicalSemiring R\nX : Set R\nx y : ↑X\nh : x ≠ y\n⊢ (fun f => ↑f) (↑↑(toContinuousMapOnAlgHom X) Polynomial.X) x ≠\n (fun f => ↑f) (↑↑(toContinuousMapOnAlgHom X) Polynomial.X) y",
"state_before": "R : Type ... | [
160,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_mul_sqrt_lt_succ' | [] | [
187,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.ennreal_tsum' | [
{
"state_after": "case h.e'_5.h\nα : Type u_2\nβ : Type ?u.2920454\nγ : Type ?u.2920457\nγ₂ : Type ?u.2920460\nδ : Type ?u.2920463\nι✝ : Sort y\ns t u : Set α\ninst✝¹ : MeasurableSpace α\nι : Type u_1\ninst✝ : Countable ι\nf : ι → α → ℝ≥0∞\nh : ∀ (i : ι), Measurable (f i)\nx : α\n⊢ tsum (fun i => f i) x = ∑' (i... | [
1939,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1936,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | abs_circleMap_zero | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.5687\ninst✝ : NormedAddCommGroup E\nR θ : ℝ\n⊢ ↑Complex.abs (circleMap 0 R θ) = Abs.abs R",
"tactic": "simp [circleMap]"
}
] | [
119,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Pi/Algebra.lean | Sum.elim_one_mulSingle | [
{
"state_after": "no goals",
"state_before": "I : Type u\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : I → Type v₁\ng : I → Type v₂\nh : I → Type v₃\nx y : (i : I) → f i\ni✝ : I\na a' : α → γ\nb b' : β → γ\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : One γ\ni : β\nc : γ\n⊢ Sum.elim 1 (Pi.mulSin... | [
461,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.false_eq_true_eq_False | [
{
"state_after": "no goals",
"state_before": "⊢ ¬false = true",
"tactic": "decide"
}
] | [
69,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V W X✝ Y Z X X' : C\nf : X ⟶ X'\n⊢ f ≫ (λ_ X').inv = (λ_ X).inv ≫ (𝟙 tensorUnit' ⊗ f)",
"tactic": "simp"
}
] | [
263,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_def | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.655\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np✝ q : MvPolynomial σ R\ninst✝ : DecidableEq σ\np : MvPolynomial σ R\n⊢ (Finset.sup (support p) fun s => ↑toMultiset s) = Finset.sup (support p) fun s => ↑toMultiset s",
"stat... | [
95,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_sup | [] | [
486,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.SatelliteConfig.exists_normalized_aux1 | [
{
"state_after": "E : Type u_1\ninst✝ : NormedAddCommGroup E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastr : r a (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin (Nat.succ N)\ninej : i ≠ j\nah :\n ∀ (i j : Fin (Nat.succ N)),\n i ≠ j → r a i ≤ ‖c a i - c a j‖ ∧ r a j ≤ τ * r a i... | [
385,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Algebra/BigOperators/NatAntidiagonal.lean | Finset.Nat.prod_antidiagonal_swap | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.4624\ninst✝¹ : CommMonoid M\ninst✝ : AddCommMonoid N\nn : ℕ\nf : ℕ × ℕ → M\n⊢ ∏ p in antidiagonal n, f (Prod.swap p) = ∏ p in antidiagonal n, f p",
"tactic": "conv_lhs => rw [← map_swap_antidiagonal, Finset.prod_map]"
}
] | [
41,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_addEquiv_refl | [] | [
236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.comp | [] | [
2917,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2916,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_sub | [] | [
349,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_mono | [] | [
936,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Algebra/Hom/Group.lean | injective_iff_map_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.229687\nβ : Type ?u.229690\nM : Type ?u.229693\nN : Type ?u.229696\nP : Type ?u.229699\nG✝ : Type ?u.229702\nH✝ : Type ?u.229705\nF : Type u_3\ninst✝⁴ : Group G✝\ninst✝³ : CommGroup H✝\nG : Type u_1\nH : Type u_2\ninst✝² : Group G\ninst✝¹ : MulOneCla... | [
1572,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.index_some | [] | [
398,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.isThreeCycle_sq | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ g : Perm α\nht : IsThreeCycle g\n⊢ Nat.coprime 2 (_root_.orderOf g)",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ g : Perm α\nht : IsThreeCycle g\n⊢ IsThreeCycle (g * g)",
"tactic": "rw [← pow_tw... | [
620,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_iUnion_null_iff' | [] | [
281,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.Lp_add_le_hasSum | [
{
"state_after": "ι : Type u\ns : Finset ι\nf g : ι → ℝ≥0\nA B : ℝ≥0\np : ℝ\nhp : 1 ≤ p\nhf : HasSum (fun i => f i ^ p) (A ^ p)\nhg : HasSum (fun i => g i ^ p) (B ^ p)\nhp' : p ≠ 0\n⊢ ∃ C, C ≤ A + B ∧ HasSum (fun i => (f i + g i) ^ p) (C ^ p)",
"state_before": "ι : Type u\ns : Finset ι\nf g : ι → ℝ≥0\nA B :... | [
544,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Dynamics/Minimal.lean | eq_empty_or_univ_of_smul_invariant_closed | [] | [
117,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Set/Basic.lean | SetCoe.exists | [] | [
193,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.ofPowerSeries_apply_coeff | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : StrictOrderedSemiring Γ\nx : PowerSeries R\nn : ℕ\n⊢ coeff (↑(ofPowerSeries Γ R) x) ↑n = ↑(PowerSeries.coeff R n) x",
"tactic": "simp [ofPowerSeries_apply]"
}
] | [
1190,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1189,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basis.lean | Basis.ext_multilinear | [
{
"state_after": "case intro\nR : Type u_2\nι : Type u_1\nn : ℕ\nM : Fin n → Type ?u.28551\nM₂ : Type u_3\nM₃ : Type u_4\ninst✝⁷ : CommSemiring R\ninst✝⁶ : AddCommMonoid M₂\ninst✝⁵ : AddCommMonoid M₃\ninst✝⁴ : (i : Fin n) → AddCommMonoid (M i)\ninst✝³ : (i : Fin n) → Module R (M i)\ninst✝² : Module R M₂\ninst✝¹... | [
69,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_eq | [] | [
1791,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1790,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.exists_most_significant_bit | [
{
"state_after": "case z\nn : ℕ\nh✝ : n ≠ 0\nh : 0 ≠ 0\n⊢ ∃ i, testBit 0 i = true ∧ ∀ (j : ℕ), i < j → testBit 0 j = false\n\ncase f\nn✝ : ℕ\nh✝ : n✝ ≠ 0\nb : Bool\nn : ℕ\nhn : n ≠ 0 → ∃ i, testBit n i = true ∧ ∀ (j : ℕ), i < j → testBit n j = false\nh : bit b n ≠ 0\n⊢ ∃ i, testBit (bit b n) i = true ∧ ∀ (j : ℕ... | [
113,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.elim | [] | [
83,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.splitMin_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx✝ ls : ℕ\nll : Ordnode α\nlx : α\nlr : Ordnode α\nx : α\nr : Ordnode α\n⊢ splitMin' (node ls ll lx lr) x r = (findMin' (node ls ll lx lr) x, eraseMin (node x✝ (node ls ll lx lr) x r))",
"tactic": "rw [splitMin', splitMin_eq ls ll lx lr, findMi... | [
612,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Topology/Order/Basic.lean | IsLUB.frequently_mem | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : LinearOrder α\ninst✝² : LinearOrder β\ninst✝¹ : OrderTopology α\ninst✝ : OrderTopology β\na : α\ns : Set α\nha : IsLUB s a\na' : α\nha' : a' ∈ s\n⊢ ∃ᶠ (x : α) in 𝓝[Iic a] a, x ∈ ... | [
1966,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1958,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.quot_mk_to_coe'' | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Group/Basic.lean | one_div_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.25306\nG : Type ?u.25309\ninst✝ : DivisionMonoid α\na b c : α\n⊢ 1 / (a / b) = b / a",
"tactic": "simp"
}
] | [
419,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.ker_le_ker_completion | [
{
"state_after": "case intro.mk\nG : Type u_1\ninst✝² : SeminormedAddCommGroup G\nH : Type u_2\ninst✝¹ : SeminormedAddCommGroup H\nK : Type ?u.15971\ninst✝ : SeminormedAddCommGroup K\nf : NormedAddGroupHom G H\ng : G\nh₀ : ↑f g = 0\n⊢ ↑(toAddMonoidHom (NormedAddGroupHom.comp toCompl (incl (ker f)))) { val := g,... | [
171,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.factorThruImage_eq | [
{
"state_after": "no goals",
"state_before": "Δ Δ'' : SimplexCategory\nφ : Δ ⟶ Δ''\ne : Δ ⟶ image φ\ninst✝¹ : Epi e\ni : image φ ⟶ Δ''\ninst✝ : Mono i\nfac : e ≫ i = φ\n⊢ factorThruImage φ = e",
"tactic": "rw [← cancel_mono i, fac, ← image_ι_eq fac, image.fac]"
}
] | [
798,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.functorPullback_mem | [] | [
181,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
src/lean/Init/Control/Lawful.lean | ExceptT.seqLeft_eq | [
{
"state_after": "α β ε : Type u\nm : Type u → Type v\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : ExceptT ε m α\ny : ExceptT ε m β\n⊢ (do\n let a ← x\n let _ ← y\n pure a) =\n do\n let f ← const β <$> x\n f <$> y",
"state_before": "α β ε : Type u\nm : Type u → Type v\ninst✝¹ : Mona... | [
153,
47
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
143,
11
] |
Mathlib/Analysis/Normed/Group/Basic.lean | coe_normGroupSeminorm | [] | [
735,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Logic/Relation.lean | Relation.eq_comp | [] | [
146,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.map_finsupp_sum | [] | [
1120,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | dist_div_right | [
{
"state_after": "no goals",
"state_before": "M : Type u\nG : Type v\nX : Type w\ninst✝² : DivInvMonoid M\ninst✝¹ : PseudoMetricSpace M\ninst✝ : IsometricSMul Mᵐᵒᵖ M\na b c : M\n⊢ dist (a / c) (b / c) = dist a b",
"tactic": "simp only [div_eq_mul_inv, dist_mul_right]"
}
] | [
387,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_monomial | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.601563\na : R\nn : ℕ\nha : a = 0\n⊢ leadingCoeff (↑(monomial n) a) = a\n\ncase neg\nR : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.601563\na : R\nn... | [
799,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.div_dvd_of_dvd | [] | [
460,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_sqrt_of_multiplicity_odd | [
{
"state_after": "m : ℤ\nhm : 0 < m\np : ℕ\nhp : Fact (Nat.Prime p)\nHpv : Part.get (multiplicity (↑p) m) (_ : multiplicity.Finite (↑p) m) % 2 = 1\n⊢ 1 ≠ 0",
"state_before": "m : ℤ\nhm : 0 < m\np : ℕ\nhp : Fact (Nat.Prime p)\nHpv : Part.get (multiplicity (↑p) m) (_ : multiplicity.Finite (↑p) m) % 2 = 1\n⊢ P... | [
100,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.adherence_nhdset | [] | [
164,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
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