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 |
|---|---|---|---|---|---|---|
Std/Data/String/Lemmas.lean | String.next'_eq | [] | [
311,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
311,
9
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.cantor' | [
{
"state_after": "α β : Type u\na b : Cardinal\nhb✝ : 1 < b\nhb : 2 ≤ b\n⊢ a < b ^ a",
"state_before": "α β : Type u\na b : Cardinal\nhb : 1 < b\n⊢ a < b ^ a",
"tactic": "rw [← succ_le_iff, (by norm_cast : succ (1 : Cardinal) = 2)] at hb"
},
{
"state_after": "no goals",
"state_before": "α β ... | [
1395,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/Data/List/Infix.lean | List.suffix_iff_eq_drop | [] | [
218,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.symm | [
{
"state_after": "p q : ℝ\nh : IsConjugateExponent p q\n⊢ 1 < p / (p - 1)",
"state_before": "p q : ℝ\nh : IsConjugateExponent p q\n⊢ 1 < q",
"tactic": "rw [h.conj_eq]"
},
{
"state_after": "no goals",
"state_before": "p q : ℝ\nh : IsConjugateExponent p q\n⊢ 1 < p / (p - 1)",
"tactic": "ex... | [
96,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
11
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.neg_empty | [] | [
577,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.pred_sub | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k n m : ℕ\n⊢ pred n - m = pred (n - m)",
"tactic": "rw [← Nat.sub_one, Nat.sub_sub, one_add, sub_succ]"
}
] | [
320,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.map_unique | [
{
"state_after": "α : Type u_1\ninst✝¹ : UniformSpace α\npkg : AbstractCompletion α\nβ : Type u_2\ninst✝ : UniformSpace β\npkg' : AbstractCompletion β\nf✝ f : α → β\ng : pkg.space → pkg'.space\nhg : UniformContinuous g\nh : ∀ (a : α), coe pkg' (f a) = g (coe pkg a)\na : α\n⊢ AbstractCompletion.map pkg pkg' f (c... | [
215,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_right_inj | [] | [
124,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Inseparable.lean | not_inseparable_iff_exists_open | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.28647\nZ : Type ?u.28650\nα : Type ?u.28653\nι : Type ?u.28656\nπ : ι → Type ?u.28661\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X... | [
293,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_congr_nnnorm_ae | [
{
"state_after": "α : Type u_1\nE : Type ?u.1276212\nF : Type u_2\nG : Type ?u.1276218\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → F\nhfg : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ = ‖g x‖₊\nthis : (fun x => ↑‖f ... | [
367,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.toSubmodule_eq_top | [] | [
804,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.mul_pos_mem_iff | [
{
"state_after": "case mp.intro.left\na t : ℝ\nha : 0 < a\nh₁ : 0 ≤ a * t\nh₂ : a * t ≤ 1\n⊢ 0 ≤ t\n\ncase mp.intro.right\na t : ℝ\nha : 0 < a\nh₁ : 0 ≤ a * t\nh₂ : a * t ≤ 1\n⊢ t ≤ 1 / a\n\ncase mpr.intro.left\na t : ℝ\nha : 0 < a\nh₁ : 0 ≤ t\nh₂ : t ≤ 1 / a\n⊢ 0 ≤ a * t\n\ncase mpr.intro.right\na t : ℝ\nha : ... | [
174,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | ContinuousMap.coe_mulLeft | [] | [
894,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.biUnion_image_right | [
{
"state_after": "α : Type u_3\nα' : Type ?u.57542\nβ : Type u_2\nβ' : Type ?u.57548\nγ : Type u_1\nγ' : Type ?u.57554\nδ : Type ?u.57557\nδ' : Type ?u.57560\nε : Type ?u.57563\nε' : Type ?u.57566\nζ : Type ?u.57569\nζ' : Type ?u.57572\nν : Type ?u.57575\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵... | [
300,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.smul | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
1506,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.support_subtypeDomain | [
{
"state_after": "no goals",
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1033,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/Topology/Constructions.lean | interior_prod_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.60232\nδ : Type ?u.60235\nε : Type ?u.60238\nζ : Type ?u.60241\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
760,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.nonneg | [] | [
248,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Bool/Count.lean | List.Chain'.length_div_two_le_count_bool | [
{
"state_after": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\n⊢ length l - (2 - 1) ≤ 2 * count b l",
"state_before": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\n⊢ length l / 2 ≤ count b l",
"tactic": "rw [Nat.div_le_iff_le_mul_add_pred two_pos, ← tsub_le_iff_right]... | [
132,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3108160\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\nh : inner x y = 0\n⊢ 2 = 0 ∨ ↑re (inner x y) = 0",
"state_befo... | [
1478,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1474,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_map | [] | [
1433,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1432,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_diff | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.96997\nι : Type ?u.97000\nM : Type ?u.97003\nN : Type ?u.97006\nG : Type u_2\ninst✝ : Group G\ns t : Set α\nf✝ g : α → G\na : α\nh : s ⊆ t\nf : α → G\n⊢ Disjoint (t \\ s) s",
"state_before": "α : Type u_1\nβ : Type ?u.96997\nι : Type ?u.97000\nM : Type ?u.... | [
564,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Order/Disjoint.lean | isCompl_ofDual_iff | [] | [
618,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.fiber_nonempty_iff_mem_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.71261\ninst✝ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt : Finset β\na : α\nb c : β\nf : α → β\ns : Finset α\ny : β\n⊢ Finset.Nonempty (filter (fun x => f x = y) s) ↔ y ∈ image f s",
"tactic": "simp [Finset.Nonempt... | [
381,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.Nodup.nontrivial_iff | [
{
"state_after": "α : Type u_1\ns : Cycle α\nh : Nodup s\n⊢ Nontrivial s ↔ ¬length s ≤ 1",
"state_before": "α : Type u_1\ns : Cycle α\nh : Nodup s\n⊢ Nontrivial s ↔ ¬Subsingleton s",
"tactic": "rw [length_subsingleton_iff]"
},
{
"state_after": "case h\nα : Type u_1\na✝ : List α\nh : Nodup (Quoti... | [
683,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_le_div_right | [] | [
1646,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1645,
21
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_iff_exists_eq_mul | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.630634\nE : Type ?u.630637\nF : Type ?u.630640\nG : Type ?u.630643\nE' : Type ?u.630646\nF' : Type ?u.630649\nG' : Type ?u.630652\nE'' : Type ?u.630655\nF'' : Type ?u.630658\nG'' : Type ?u.630661\nR : Type ?u.630664\nR' : Type ?u.630667\n𝕜 : Type u_2\n𝕜' : ... | [
1947,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1939,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsAdjointPair.comp | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.317511\nR₂ : Type ?u.317514\nR₃ : Type ?u.317517\nM : Type u_4\nM₁ : Type u_2\nM₂ : Type u_3\nMₗ₁ : Type ?u.317529\nMₗ₁' : Type ?u.317532\nMₗ₂ : Type ?u.317535\nMₗ₂' : Type ?u.317538\nK : Type ?u.317541\nK₁ : Type ?u.317544\nK₂ : Type ... | [
460,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_empty | [] | [
141,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mapRange.addMonoidHom_comp | [
{
"state_after": "case refine'_1\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : (i : ι) → AddZeroClass (β i)\ninst✝¹ : (i : ι) → AddZeroClass (β₁ i)\ninst✝ : (i : ι) → AddZeroClass (β₂ i)\nf : (i : ι) → β₁ i →+ β₂ i\nf₂ : (i : ι) → β i →+ β₁ i\n⊢ ∀ (i ... | [
2178,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.hausdorffDist_optimal_le_HD | [
{
"state_after": "X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : GromovHausdorff.Cb X Y\nh : f ∈ GromovHausdorff.candidatesB X Y\nr : ℝ\nhr : HD (GromovHausdorff.optimalGHDist X Y) < r\n⊢ haus... | [
525,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithBot.coe_iSup | [] | [
148,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | iter_deriv_inv' | [] | [
152,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_abs_right | [] | [
721,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineMap.vectorSpan_image_eq_submodule_map | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV₁ : Type u_4\nP₁ : Type u_1\nV₂ : Type u_2\nP₂ : Type u_5\nV₃ : Type ?u.522649\nP₃ : Type ?u.522652\ninst✝⁹ : Ring k\ninst✝⁸ : AddCommGroup V₁\ninst✝⁷ : Module k V₁\ninst✝⁶ : AffineSpace V₁ P₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module k V₂\ninst✝... | [
1496,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1494,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.comp_continuous_iff | [] | [
1072,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.toFun_eq_coe | [
{
"state_after": "no goals",
"state_before": "K : Type ?u.30649\nF : Type ?u.30652\nR : Type u_1\ninst✝⁴ : DivisionRing K\nΓ₀ : Type u_2\nΓ'₀ : Type ?u.30664\nΓ''₀ : Type ?u.30667\ninst✝³ : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\ninst✝ : LinearOrde... | [
138,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_span_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝³ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝² : CommRing S\ninst✝¹ : Algebra R S\nP : Type ?u.88589\ninst✝ : CommRing P\nx : R\n⊢ coeSubmodule S (Ideal.span {x}) = Submodule.span R {↑(algebraMap R S) x}",
"tactic": "rw [coeSubmodul... | [
88,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.IsPrimitive.ne_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\nhp : IsPrimitive 0\n⊢ False",
"state_before": "R : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\np : R[X]\nhp : IsPrimitive p\n⊢ p ≠ 0",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_bef... | [
66,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_nsmul | [] | [
589,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | Nat.four_pow_le_two_mul_add_one_mul_central_binom | [
{
"state_after": "R : Type ?u.164552\nn : ℕ\n⊢ 4 ^ n = (2 ^ 2) ^ n",
"state_before": "R : Type ?u.164552\nn : ℕ\n⊢ 4 ^ n = (1 + 1) ^ (2 * n)",
"tactic": "simp only [pow_mul, one_add_one_eq_two]"
},
{
"state_after": "no goals",
"state_before": "R : Type ?u.164552\nn : ℕ\n⊢ 4 ^ n = (2 ^ 2) ^ n... | [
134,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.res_succ | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_mul_transpose_diag | [
{
"state_after": "R : Type u_2\nα : Type u_1\nG : SimpleGraph α\ninst✝³ : Fintype α\ninst✝² : NonAssocSemiring R\na b : α\ne : Sym2 α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableRel G.Adj\n⊢ (incMatrix R G ⬝ (incMatrix R G)ᵀ) a a = ∑ e : Sym2 α, incMatrix R G a e",
"state_before": "R : Type u_2\nα : Type u_1\... | [
132,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_of_intervalIntegral_norm_bounded | [
{
"state_after": "ι : Type u_2\nE : Type u_1\nμ : Measure ℝ\nl : Filter ι\ninst✝² : NeBot l\ninst✝¹ : IsCountablyGenerated l\ninst✝ : NormedAddCommGroup E\na✝ b : ι → ℝ\nf : ℝ → E\nI a : ℝ\nhfi : ∀ (i : ι), IntegrableOn f (Ioc a (b i))\nhb : Tendsto b l atTop\nh : ∀ᶠ (i : ι) in l, (∫ (x : ℝ) in a..b i, ‖f x‖ ∂μ... | [
579,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_lowerSemicontinuousAt | [
{
"state_after": "α : Type u_3\ninst✝⁷ : TopologicalSpace α\nβ : Type ?u.42638\ninst✝⁶ : Preorder β\nf✝ g✝ : α → β\nx : α\ns t : Set α\ny z : β\nγ : Type u_1\ninst✝⁵ : LinearOrder γ\ninst✝⁴ : TopologicalSpace γ\ninst✝³ : OrderTopology γ\nδ : Type u_2\ninst✝² : LinearOrder δ\ninst✝¹ : TopologicalSpace δ\ninst✝ :... | [
331,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mulLeftRight_le | [] | [
1154,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
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Mathlib/Order/UpperLower/Hom.lean | LowerSet.coe_iicsInfHom | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.homIso_hom | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.nonneg | [] | [
104,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
11
] |
Mathlib/Topology/Basic.lean | IsClosed.frontier_subset | [] | [
719,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Data/Nat/PartENat.lean | PartENat.add_eq_top_iff | [
{
"state_after": "case refine_2.refine_2\na b : PartENat\n⊢ ∀ (n n_1 : ℕ), ¬↑n_1 + ↑n = ⊤",
"state_before": "a b : PartENat\n⊢ a + b = ⊤ ↔ a = ⊤ ∨ b = ⊤",
"tactic": "refine PartENat.casesOn a ?_ ?_\n<;> refine PartENat.casesOn b ?_ ?_\n<;> simp"
},
{
"state_after": "no goals",
"state_before"... | [
529,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.X_pow_dvd_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommSemiring R\nf : R[X]\nn : ℕ\nx✝ : X ^ n ∣ f\nd : ℕ\nhd : d < n\ng : R[X]\nhgf : f = X ^ n * g\n⊢ coeff f d = 0",
"tactic": "simp only [hgf, coeff_X_pow_mul', ite_eq_right_iff, not_l... | [
58,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_quotient_mk' | [] | [
980,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.disjoint_iff | [
{
"state_after": "no goals",
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"tactic": "classical\n rw [disjoint_iff, disjoint_iff, Finsupp.bot_eq_zero, ← Finsupp.support_eq_empty,\n Finsupp.suppo... | [
245,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
8
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.fg_bot | [
{
"state_after": "no goals",
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"tactic": "rw [Finset.coe_empty, closure_empty]"
}
] | [
67,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.dvd_choose_pow_iff | [
{
"state_after": "no goals",
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}
] | [
261,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_chain_2 | [] | [
108,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ Neg.neg '' Icc a b = Icc (-b) (-a)",
"tactic": "simp"
}
] | [
303,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/Basic.lean | eq_of_forall_gt_iff | [] | [
561,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | IsHilbertSum.mkInternal | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\n𝕜 : Type u_2\ninst✝⁵ : IsROrC 𝕜\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type ?u.514897\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G... | [
321,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerTMul_apply | [] | [
454,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.minimalPeriod_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.22741\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhn : 0 < n\nhx : IsPeriodicPt f n x\n⊢ Nat.find (_ : x ∈ periodicPts f) ≤ n",
"state_before": "α : Type u_1\nβ : Type ?u.22741\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhn : 0 < n\nhx : IsPeriodicPt f n x\n⊢ mi... | [
326,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Analysis/BoxIntegral/DivergenceTheorem.lean | BoxIntegral.hasIntegral_GP_pderiv | [
{
"state_after": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nn : ℕ\ninst✝ : CompleteSpace E\nI : Box (Fin (n + 1))\ni✝ : Fin (n + 1)\nf : (Fin (n + 1) → ℝ) → E\nf' : (Fin (n + 1) → ℝ) → (Fin (n + 1) → ℝ) →L[ℝ] E\ns : Set (Fin (n + 1) → ℝ)\nhs : Set.Countable s\nHs : ∀ (x : Fin (n + 1) ... | [
261,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_sum | [] | [
944,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
11
] |
Mathlib/Data/Finmap.lean | AList.toFinmap_entries | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderiv_ccosh | [] | [
483,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.coe_mul_zeta_apply | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nx : ℕ\n⊢ ∑ x in divisorsAntidiagonal x, ↑f x.fst * ↑↑ζ x.snd = ∑ i in divisors x, ↑f i",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nx : ℕ\n⊢ ↑(f * ↑ζ) x = ∑ i in divisors x, ↑f i",
"tactic": "... | [
486,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/NumberTheory/Primorial.lean | primorial_add | [
{
"state_after": "case hab\nm n : ℕ\n⊢ 0 ≤ m + 1\n\ncase hbc\nm n : ℕ\n⊢ m + 1 ≤ m + n + 1\n\nm n : ℕ\n⊢ Disjoint (filter Nat.Prime (Ico 0 (m + 1))) (filter Nat.Prime (Ico (m + 1) (m + n + 1)))",
"state_before": "m n : ℕ\n⊢ (m + n)# = m# * ∏ p in filter Nat.Prime (Ico (m + 1) (m + n + 1)), p",
"tactic":... | [
59,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk | [] | [
626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Topology/Instances/Discrete.lean | LinearOrder.bot_topologicalSpace_eq_generateFrom | [
{
"state_after": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : PredOrder α\ninst✝ : SuccOrder α\na : α\n⊢ IsOpen {a}",
"state_before": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : PredOrder α\ninst✝ : SuccOrder α\n⊢ ⊥ = generateFrom {s | ∃ a, s ... | [
104,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.lt_of_nadd_lt_nadd_right | [] | [
407,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/List/Chain.lean | List.chain'_cons' | [] | [
282,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_neg | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | ContinuousOn.arsinh | [] | [
229,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_lt_add_iff_right | [] | [
711,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
11
] |
Std/Data/List/Init/Lemmas.lean | List.or_nil | [] | [
38,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
38,
9
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalClosure_idempotent | [] | [
2516,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2515,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.inf_apply | [] | [
686,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
src/lean/Init/SimpLemmas.lean | true_iff | [] | [
94,
121
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
94,
9
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgHom.range_comp_le_range | [] | [
630,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sup_inf_inf_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.58905\nw x y z : α\ninst✝ : BooleanAlgebra α\n⊢ x ⊓ y ⊔ x ⊓ yᶜ = x",
"tactic": "rw [← sdiff_eq, sup_inf_sdiff _ _]"
}
] | [
713,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Algebra/Group/Ext.lean | DivInvMonoid.ext | [
{
"state_after": "M : Type u_1\nm₁ m₂ : DivInvMonoid M\nh_mul : Mul.mul = Mul.mul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\n⊢ m₁ = m₂",
"state_before": "M : Type u_1\nm₁ m₂ : DivInvMonoid M\nh_mul : Mul.mul = Mul.mul\nh_inv : Inv.inv = Inv.inv\n⊢ m₁ = m₂",
"tactic": "have h_mon := Monoid.... | [
142,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/GroupTheory/Submonoid/Centralizer.lean | Submonoid.center_le_centralizer | [] | [
71,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.coprod_comp_inr | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.66901\nB : Type ?u.66904\nG : Type ?u.66907\nH : Type ?u.66910\nM : Type u_3\nN : Type u_1\nP : Type u_2\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : CommMonoid P\nf : M →* P\ng : N →* P\nx : N\n⊢ ↑(comp (coprod f g) (inr M N)) x = ↑g x",... | [
650,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Algebra/AlgebraicCard.lean | Algebraic.cardinal_mk_le_max | [
{
"state_after": "R A : Type u\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : IsDomain A\ninst✝¹ : Algebra R A\ninst✝ : NoZeroSMulDivisors R A\n⊢ lift (#{ x // IsAlgebraic R x }) ≤ max (lift (#R)) ℵ₀",
"state_before": "R A : Type u\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : IsDomain A\ninst✝¹ ... | [
103,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/CategoryTheory/Preadditive/InjectiveResolution.lean | CategoryTheory.InjectiveResolution.ι_f_succ | [
{
"state_after": "case i\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroObject C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasEqualizers C\ninst✝ : HasImages C\nZ : C\nI : InjectiveResolution Z\nn : ℕ\n⊢ HomologicalComplex.X ((CochainComplex.single₀ C).obj Z) (n + 1) ≅ 0",
"state_before": "C : Type u\ninst✝... | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_pow | [] | [
701,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_range_eq_span_range_vsub_left_ne | [
{
"state_after": "k : Type u_2\nV : Type u_1\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\ni₀ : ι\n⊢ Submodule.span k ((fun x x_1 => x -ᵥ x_1) (p i₀) '' (p '' (univ \\ {i₀}))) =\n Submodule.span k (range fun i => p i₀ -ᵥ p ↑i)"... | [
1128,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.top_prod_top | [] | [
1683,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1682,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curry0_uncurry0 | [] | [
1660,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1658,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.neg_mem | [] | [
192,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.inv | [] | [
446,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
11
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.subset_mul_right | [] | [
904,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Differentiable.cexp | [] | [
155,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/Convex/Function.lean | neg_strictConvexOn_iff | [
{
"state_after": "case mp\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.653643\nα : Type ?u.653646\nβ : Type u_3\nι : Type ?u.653652\ninst✝⁵ : OrderedSemiring 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid F\ninst✝² : OrderedAddCommGroup β\ninst✝¹ : SMul 𝕜 E\ninst✝ : Module 𝕜 β\ns : Set E\nf g : E → β\n⊢ St... | [
866,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.tail_pure | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/MetricSpace/CauSeqFilter.lean | CauSeq.tendsto_limit | [
{
"state_after": "β : Type v\ninst✝¹ : NormedRing β\nhn : IsAbsoluteValue norm\nf : CauSeq β norm\ninst✝ : IsComplete β norm\ns : Set β\nos : IsOpen s\nlfs : lim f ∈ s\n⊢ ↑f ⁻¹' s ∈ atTop",
"state_before": "β : Type v\ninst✝¹ : NormedRing β\nhn : IsAbsoluteValue norm\nf : CauSeq β norm\ninst✝ : IsComplete β... | [
43,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.convexOn | [] | [
372,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.forall_sigma_iff | [] | [
84,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.measure_inter_union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm : OuterMeasure α\ns s₁ s₂ : Set α\nh : s₁ ∩ s₂ ⊆ ∅\nh₁ : IsCaratheodory m s₁\nt : Set α\n⊢ ↑m (t ∩ (s₁ ∪ s₂)) = ↑m (t ∩ s₁) + ↑m (t ∩ s₂)",
"tactic": "rw [h₁, Set.inter_assoc, Set.union_inter_cancel_left, inter_diff_assoc, union_diff_cancel_lef... | [
976,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
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