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/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.bot_orthogonal_eq_top | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.89112\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nK : Submodule 𝕜 E\n⊢ ⊤ ≤ ⊤ᗮᗮ",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.89112... | [
203,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.bind_right | [] | [
1078,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.succ_pred_iff_is_succ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.85057\nβ : Type ?u.85060\nγ : Type ?u.85063\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nx✝ : ∃ a, o = succ a\na : Ordinal\ne : o = succ a\n⊢ succ (pred o) = o",
"tactic": "simp only [e, pred_succ]"
}
] | [
204,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.formPerm_eq_formPerm_iff | [
{
"state_after": "α✝ : Type ?u.33186\ninst✝¹ : DecidableEq α✝\ns✝ s'✝ : Cycle α✝\nα : Type u_1\ninst✝ : DecidableEq α\ns s' : Cycle α\nhs : Nodup s\nhs' : Nodup s'\n⊢ formPerm s hs = formPerm s' hs' ↔ s = s' ∨ length s ≤ 1 ∧ length s' ≤ 1",
"state_before": "α✝ : Type ?u.33186\ninst✝¹ : DecidableEq α✝\ns✝ s'... | [
206,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
8
] |
Std/Data/Nat/Lemmas.lean | Nat.max_eq_right | [
{
"state_after": "no goals",
"state_before": "a b : Nat\nh : a ≤ b\n⊢ max a b = b",
"tactic": "simp [Nat.max_def, h, Nat.not_lt.2 h]"
}
] | [
211,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
210,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.smul_comp | [] | [
1510,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.hasPrev | [
{
"state_after": "no goals",
"state_before": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ Iterator.hasPrev it = true ↔ l ≠ []",
"tactic": "simp [Iterator.hasPrev, h.pos, Nat.pos_iff_ne_zero]"
}
] | [
573,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
572,
1
] |
Mathlib/Topology/Separation.lean | strictMono_nhdsSet | [] | [
701,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.lt_to_int | [
{
"state_after": "α : Type ?u.981446\nm n : ZNum\nh : ↑m < ↑n\n⊢ ↑m < ↑n ↔ Ordering.lt = Ordering.lt",
"state_before": "α : Type ?u.981446\nm n : ZNum\nh : Ordering.casesOn Ordering.lt (↑m < ↑n) (m = n) (↑n < ↑m)\n⊢ ↑m < ↑n ↔ Ordering.lt = Ordering.lt",
"tactic": "simp at h"
},
{
"state_after": ... | [
1398,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ι_matrix | [
{
"state_after": "case w\nJ : Type\ninst✝⁴ : Fintype J\nK : Type\ninst✝³ : Fintype K\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasFiniteBiproducts C\nf : J → C\ng : K → C\nm : (j : J) → (k : K) → f j ⟶ g k\nj : J\nj✝ : K\n⊢ (ι f j ≫ matrix m) ≫ π (fun k => g k) j✝ = (lift fun k => m... | [
840,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.hasLimitsOfShape_of_reflective | [] | [
365,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | IsCompact.uniformContinuousOn_of_continuous | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.42243\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace β\ns : Set α\nf : α → β\nhs : IsCompact s\nhf : ContinuousOn f s\n⊢ UniformContinuous (restrict s f)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.42243\ninst✝¹ : UniformSpace α\ninst✝... | [
185,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.eigenspace_zero | [
{
"state_after": "no goals",
"state_before": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End R M\n⊢ eigenspace f 0 = LinearMap.ker f",
"tactic": "simp [eigenspace]"
}
] | [
71,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.mk_ordinal_out | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.219951\nβ : Type ?u.219954\nγ : Type ?u.219957\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ card (type (?m.220055 o)) = card o",
"tactic": "rw [Ordinal.type_lt]"
}
] | [
1324,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.exists_iff | [] | [
248,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.bot_mul_coe_of_pos | [] | [
953,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_add_nat | [] | [
1659,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1658,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.or_not_self | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (x : Bool), (x || !x) = true",
"tactic": "decide"
}
] | [
256,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mem_frange | [
{
"state_after": "α : Type u_1\nβ : Type ?u.481748\nγ : Type ?u.481751\nι : Type ?u.481754\nM : Type u_2\nM' : Type ?u.481760\nN : Type ?u.481763\nP : Type ?u.481766\nG : Type ?u.481769\nH : Type ?u.481772\nR : Type ?u.481775\nS : Type ?u.481778\ninst✝ : Zero M\nf : α →₀ M\ny : M\n⊢ (∃ a, a ∈ f.support ∧ ↑f a =... | [
991,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_id_mem_convexHull | [] | [
233,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.associated_eq_self_apply | [
{
"state_after": "no goals",
"state_before": "S : Type u_3\nR : Type u_1\nR₁ : Type ?u.429167\nM : Type u_2\ninst✝⁷ : Ring R\ninst✝⁶ : CommRing R₁\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : Module R₁ M\ninst✝² : CommSemiring S\ninst✝¹ : Algebra S R\ninst✝ : Invertible 2\nB₁ : BilinForm R M\nQ :... | [
810,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Data/List/Perm.lean | List.forall₂_comp_perm_eq_perm_comp_forall₂ | [
{
"state_after": "case h.h\nα : Type uu\nβ : Type vv\nl₁✝ l₂ : List α\nγ : Type ?u.38852\nδ : Type ?u.38855\nr : α → β → Prop\np : γ → δ → Prop\nl₁ : List α\nl₃ : List β\n⊢ (Forall₂ r ∘r Perm) l₁ l₃ = (Perm ∘r Forall₂ r) l₁ l₃",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\nγ : Type ?u.38852\nδ... | [
368,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2519860\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑re (inner x y) = (‖x‖ * ‖x‖ + 2 * ↑re (inner x y) + ‖y‖ * ‖y‖ -... | [
1139,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.image_symm_image | [] | [
89,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Order/ModularLattice.lean | inf_covby_of_covby_sup_left | [] | [
180,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_sub_le' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.981881\nγ : Type ?u.981884\nδ : Type ?u.981887\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhf : AEMeasurable f\n⊢ (∫⁻ (x : α), g x ∂μ) ≤ (∫⁻ (x : α), g x - f x ∂μ) + ∫⁻ (x : α), f x ∂μ",
"state_before": "α : Type u_1\nβ : Type ?u.981881\nγ : Type ?u.9... | [
929,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nonempty.left | [] | [
512,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | Equiv.transLocalEquiv_eq_trans | [] | [
812,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Init/IteSimp.lean | if_false_left_eq_and | [
{
"state_after": "no goals",
"state_before": "p : Prop\nh : Decidable p\nq : Prop\n⊢ (if p then False else q) = (¬p ∧ q)",
"tactic": "by_cases p <;> simp [h]"
}
] | [
40,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Data/Int/NatPrime.lean | Int.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul | [
{
"state_after": "p : ℕ\np_prime : Nat.Prime p\nm n : ℤ\nk l : ℕ\nhpm : ↑(p ^ k) ∣ m\nhpn : ↑(p ^ l) ∣ n\nhpmn : ↑(p ^ (k + l + 1)) ∣ m * n\nhpm' : p ^ k ∣ natAbs m\nhpn' : p ^ l ∣ natAbs n\n⊢ p ^ (k + l + 1) ∣ natAbs (m * n)",
"state_before": "p : ℕ\np_prime : Nat.Prime p\nm n : ℤ\nk l : ℕ\nhpm : ↑(p ^ k) ... | [
36,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedComponent_eq | [] | [
100,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.mk_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoMetricSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nK : ℝ≥0\nf : α → β\nx y : α\nr : ℝ\nh : ∀ (x y : α), dist (f x) (f y) ≤ dist x y\n⊢ ∀ (x y : α), dist (f x) (f y) ≤ ↑1 * dist... | [
320,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
11
] |
Mathlib/Topology/Semicontinuous.lean | IsClosed.upperSemicontinuousWithinAt_indicator | [] | [
775,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.card_interedges_add_card_interedges_compl | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.3694\nι : Type ?u.3697\nκ : Type ?u.3700\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\ns : Finset α\nt : Finset β... | [
85,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/Order.lean | setOf_isOpen_sup | [] | [
945,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean | CategoryTheory.Pretriangulated.comp_dist_triangle_mor_zero₁₂ | [
{
"state_after": "case intro\nC : Type u\ninst✝⁹ : Category C\ninst✝⁸ : HasZeroObject C\ninst✝⁷ : HasShift C ℤ\ninst✝⁶ : Preadditive C\ninst✝⁵ : ∀ (n : ℤ), Functor.Additive (shiftFunctor C n)\nD : Type u₂\ninst✝⁴ : Category D\ninst✝³ : HasZeroObject D\ninst✝² : HasShift D ℤ\ninst✝¹ : Preadditive D\ninst✝ : ∀ (n... | [
133,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_st_of_exists_st | [] | [
350,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Uniform.continuousOn_iff'_left | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.202052\ninst✝¹ : UniformSpace α\ninst✝ : TopologicalSpace β\nf : β → α\ns : Set β\n⊢ ContinuousOn f s ↔ ∀ (b : β), b ∈ s → Tendsto (fun x => (f x, f b)) (𝓝[s] b) (𝓤 α)",
"tactic": "simp [Conti... | [
1956,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_smul_top_iff | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.157879\nG : Type ?u.157882\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nI J : Ideal R\nN✝ P : Submodule R M\nS : Set R\nT : Set M\nM' : Type w\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R M'\nN : Submodule R M\nx : { x // x ∈ N }\... | [
339,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Real.lean | cauchySeq_of_edist_le_of_summable | [
{
"state_after": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nf : ℕ → α\nd : ℕ → ℝ≥0\nhf : ∀ (n : ℕ), edist (f n) (f (Nat.succ n)) ≤ ↑(d n)\nhd : Summable d\nε : ℝ≥0\nεpos : 0 < ε\n⊢ ∃ N, ∀ (n : ℕ), N ≤ n → edist (f n) (f N) < ↑ε",
"state_before": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nf : ℕ → α\nd : ... | [
43,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Std/Data/AssocList.lean | Std.AssocList.isEmpty_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : AssocList α β\n⊢ isEmpty l = List.isEmpty (toList l)",
"tactic": "cases l <;> simp [*, isEmpty, List.isEmpty]"
}
] | [
44,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
43,
9
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mker_inr | [
{
"state_after": "case h\nM : Type u_2\nN : Type u_1\nP : Type ?u.144954\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.144975\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type ?u.144999\nmc : MonoidHomClass F M N\nx : N\n⊢ x ∈ mker (inr M N) ... | [
1242,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.inr_fst | [] | [
825,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.le_set | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.110781\nβ : Type ?u.110784\nγ : Type ?u.110787\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : Ordinal → Ordinal\no : Ordinal\nH : IsNormal f\np : Set Ordinal\np0 : Set.Nonempty p\nb : Ordinal\nH₂ : ∀ (o : Ordinal), b ≤ o ↔ ∀ (a : Ordinal)... | [
463,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_eq_pi_div_two | [] | [
245,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.diff | [] | [
564,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
11
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.inf_apply | [] | [
532,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Algebra/Associated.lean | associated_unit_mul_right_iff | [] | [
516,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | ContDiffWithinAt.arctan | [] | [
223,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Set.Finite.summable_compl_iff | [] | [
889,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.Equivalence_mk'_counit | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | Filter.IsBoundedUnder.smul_tendsto_zero | [] | [
108,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun | [
{
"state_after": "case h.e'_5.h.e'_6\nα : Type u_1\nβ : Type ?u.1531711\nι : Type ?u.1531714\nE : Type u_2\nF : Type ?u.1531720\n𝕜 : Type ?u.1531723\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\nf : { x // x ∈ simpleFunc E p μ }\n⊢ ↑↑f = AEEq... | [
625,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | derivWithin_zpow | [] | [
108,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_product_left | [
{
"state_after": "F : Type ?u.55319\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nι : Type ?u.55331\nκ : Type ?u.55334\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns✝ s₁ s₂ : Finset β\nf✝ g : β → α\na : α\ns : Finset β\nt : Finset γ\nf : β × γ → α\n⊢ (∀ (a : β) (b : γ), a ∈ s → b ∈ t → f (a, b) ≤ sup s fun i =>... | [
178,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/PrimeIdeal.lean | Order.Ideal.IsPrime.mem_or_mem | [
{
"state_after": "P : Type u_1\ninst✝ : SemilatticeInf P\nx✝ y✝ : P\nI : Ideal P\nhI : IsPrime I\nx y : P\n⊢ ¬x ∈ I ∧ ¬y ∈ I → ¬x ⊓ y ∈ I",
"state_before": "P : Type u_1\ninst✝ : SemilatticeInf P\nx✝ y✝ : P\nI : Ideal P\nhI : IsPrime I\nx y : P\n⊢ x ⊓ y ∈ I → x ∈ I ∨ y ∈ I",
"tactic": "contrapose!"
},... | [
130,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.sSup_def | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8808\ns : Set (Setoid α)\n⊢ (EqvGen.Setoid fun x y => ∃ r, r ∈ s ∧ Rel r x y) = EqvGen.Setoid (⨆ (a : Setoid α) (_ : a ∈ s), Rel a)",
"state_before": "α : Type u_1\nβ : Type ?u.8808\ns : Set (Setoid α)\n⊢ sSup s = EqvGen.Setoid (sSup (Rel '' s))",
"tactic": "r... | [
244,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | ULift.algebraMap_eq | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nontrivial_univ | [] | [
2557,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2555,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.ext | [
{
"state_after": "C : Type u_1\ninst✝³ : Category C\nD : Type u_3\ninst✝² : Category D\nE : Type ?u.5750\ninst✝¹ : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type ?u.5802\ninst✝ : Category A\nG : C ⥤ D\nH✝ H : CoverDense K G\nℱ : SheafOfTypes K\nX : D\ns ... | [
116,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/List/Basic.lean | List.drop_left | [] | [
2148,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2146,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_mul_aleph | [
{
"state_after": "no goals",
"state_before": "o₁ o₂ : Ordinal\n⊢ aleph o₁ * aleph o₂ = aleph (max o₁ o₂)",
"tactic": "rw [Cardinal.mul_eq_max (aleph0_le_aleph o₁) (aleph0_le_aleph o₂), max_aleph_eq]"
}
] | [
566,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_smul | [] | [
141,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.card_comap_dvd_of_injective | [
{
"state_after": "α : Type u_2\ninst✝³ : Group α\ns t : Subgroup α\nH : Type u_1\ninst✝² : Group H\nK : Subgroup H\ninst✝¹ : Fintype { x // x ∈ K }\nf : α →* H\ninst✝ : Fintype { x // x ∈ comap f K }\nhf : Injective ↑f\nthis : Fintype { x // x ∈ map f (comap f K) }\n⊢ card { x // x ∈ comap f K } ∣ card { x // x... | [
832,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.revzip_powersetAux_lemma | [
{
"state_after": "α✝ : Type ?u.31102\nα : Type u\ninst✝ : DecidableEq α\nl : List α\nl' : List (Multiset α)\nH : ∀ ⦃x : Multiset α × Multiset α⦄, x ∈ revzip l' → x.fst + x.snd = ↑l\nthis : Forall₂ (fun p s => p = (s, ↑l - s)) (revzip l') (List.map Prod.fst (revzip l'))\n⊢ revzip l' = List.map (fun x => (x, ↑l -... | [
154,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_left | [] | [
118,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
11
] |
Mathlib/Topology/PathConnected.lean | Path.map_symm | [] | [
435,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nndist_coe_le_nndist | [] | [
245,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.exists_mk' | [] | [
580,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Set/Prod.lean | AntitoneOn.set_prod | [] | [
449,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.apply_mem_map₂ | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : AddCommMonoid P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N →ₗ[R] P\nm : M... | [
56,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.130759\nι : Type ?u.130762\ninst✝ : CompleteLattice α\nf g : Filter β\np q : β → Prop\nu v : β → α\nh : ∀ (x : β), p x → q x\na : α\nha : a ∈ {a | ∀ᶠ (x : β) in f, q x → u x ≤ a}\n⊢ ∀ (x : β), (q x → u x ≤ a) → p x → u x ≤... | [
858,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Ordered.insertNew | [] | [
310,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
308,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.le_order_add | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\n⊢ ∀ (i : ℕ), ↑i < min (order φ) (order ψ) → ↑(coeff R i) (φ + ψ) = 0",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\n⊢ min (order φ) (order ψ) ≤ order (φ + ψ)",
"tactic": "refine' le_order _ _ _"
}... | [
2343,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2341,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.comap_exp_comap_abs_atTop | [
{
"state_after": "no goals",
"state_before": "⊢ comap re (comap Real.exp atTop) = comap re atTop",
"tactic": "rw [Real.comap_exp_atTop]"
}
] | [
430,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Data/Set/Basic.lean | Set.monotone_setOf | [] | [
2930,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2929,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_pos | [] | [
866,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | neg_of_mul_neg_right | [] | [
825,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.apply_symm_apply | [] | [
396,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.irreducible_of_factor | [] | [
470,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_antiperiod_eq | [] | [
533,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.is_integral_of_is_integral_mul_unit | [
{
"state_after": "case intro.intro\nR : Type u_2\nA : Type ?u.738556\nB : Type ?u.738559\nS : Type u_1\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\nr : R\nhr : ↑f r * y = 1\np : R[X]\np_monic : Monic p\nhp :... | [
613,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiable_sinh | [] | [
123,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_mul_monic | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ : R[X]\nι : Type ?u.692387\np q : R[X]\nhq : Monic q\nH : leadingCoeff p = 0\n⊢ leadingCoeff (p * q) = leadingCoeff p",
"tactic": "rw [H, leadingCoeff_eq_zero.1 H, zero_mul, leadingCoeff... | [
1016,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_mul_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.25998\nm : Type u_2\nn : Type u_3\np : Type ?u.26007\nα : Type ?u.26010\nR : Type u_1\nS : Type ?u.26016\ninst✝⁴ : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype p\ninst✝¹ : AddCommMonoid R\ninst✝ : CommSemigroup R\nA : Matrix m n R\nB : Matrix n m ... | [
152,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.toNat_append | [
{
"state_after": "case mk\nm : ℕ\nb : Bool\nxs : List Bool\nP : List.length xs = m\n⊢ Bitvec.toNat ({ val := xs, property := P }++ₜb ::ᵥ Vector.nil) =\n Bitvec.toNat { val := xs, property := P } * 2 + Bitvec.toNat (b ::ᵥ Vector.nil)",
"state_before": "m : ℕ\nxs : Bitvec m\nb : Bool\n⊢ Bitvec.toNat (xs++ₜ... | [
55,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.comp_comp | [] | [
204,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_target_subset_range | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_1\nM : Type u_2\nH : Type u_4\nE' : Type ?u.140773\nM' : Type ?u.140776\nH' : Type ?u.140779\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : Topologic... | [
847,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Data/Finset/Functor.lean | Finset.map_traverse | [
{
"state_after": "α β γ : Type u\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : CommApplicative F\ninst✝ : CommApplicative G\ng : α → G β\nh : β → γ\ns : Finset α\n⊢ Functor.map h <$> Multiset.toFinset <$> Multiset.traverse g s.val =\n Multiset.toFinset <$> Multiset.traverse... | [
220,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_one | [] | [
314,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/Char.lean | Char.ofNat_toNat | [
{
"state_after": "c : Char\nh : isValidCharNat (toNat c)\n⊢ ofNatAux (toNat c) h = c",
"state_before": "c : Char\nh : isValidCharNat (toNat c)\n⊢ ofNat (toNat c) = c",
"tactic": "rw [Char.ofNat, dif_pos h]"
},
{
"state_after": "no goals",
"state_before": "c : Char\nh : isValidCharNat (toNat ... | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/CategoryTheory/Category/GaloisConnection.lean | CategoryTheory.Adjunction.gc | [] | [
50,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.vecMul_transpose | [
{
"state_after": "case h\nl : Type ?u.916992\nm : Type u_2\nn : Type u_1\no : Type ?u.917001\nm' : o → Type ?u.917006\nn' : o → Type ?u.917011\nR : Type ?u.917014\nS : Type ?u.917017\nα : Type v\nβ : Type w\nγ : Type ?u.917024\ninst✝¹ : NonUnitalCommSemiring α\ninst✝ : Fintype n\nA : Matrix m n α\nx : n → α\nx✝... | [
1937,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1935,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.coe_prodComm | [] | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.Tendsto.const_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.97009\nγ : Type ?u.97012\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf : Filter α\nm : α → ℝ≥0∞\na b : ℝ≥0∞\nhm : Tendsto m f (𝓝 b)\nhb : b ≠ 0 ∨ a ≠ ⊤\nthis : a = 0\n⊢ Tendsto (fun b => a * m b) f (𝓝 (a * b))"... | [
379,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
11
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_monoidHom_injective | [] | [
555,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivWithinAt.mul_const' | [] | [
401,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.tendsto_comp | [] | [
950,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.map_eq_desc'_lift_right | [
{
"state_after": "no goals",
"state_before": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nX' Y' Z' : A\nf' : X' ⟶ Y'\ng' : Y' ⟶ Z'\nw' : f' ≫ g' = 0\nα : Arrow.mk f ⟶ Arrow.mk f'\nβ : Arrow.mk g ⟶ Arrow.mk g'\nh : α.right = β.left\n⊢ (kernel.ι g ≫ α.ri... | [
290,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.