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/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_power_aleph0 | [
{
"state_after": "no goals",
"state_before": "⊢ 𝔠 ^ ℵ₀ = 𝔠",
"tactic": "rw [← two_power_aleph0, ← power_mul, mul_eq_left le_rfl le_rfl aleph0_ne_zero]"
}
] | [
197,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_top | [] | [
508,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.preimage_spanningSetsIndex_singleton | [] | [
3502,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3500,
1
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.coe_tsum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → ℝ≥0\nhf : ¬Summable f\n⊢ ↑(∑' (a : α), f a) = ∑' (a : α), ↑(f a)",
"tactic": "simp [tsum_def, hf, mt summable_coe.1 hf]"
}
] | [
186,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuous.add | [] | [
963,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_eq_extend | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.12666\nγ : Type ?u.12669\nδ : Type ?u.12672\nι : Type ?u.12675\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nhs : MeasurableSet s\n⊢ MeasurableSet s",
"state_before": "α : Type u_1\nβ : Type ?u.12666\nγ : Type ?u.12669\nδ : Type ?u.12... | [
183,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_left | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints | [
{
"state_after": "case intro.intro.intro.intro\nk : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\np1 p2 : P\nhp2 : p2 ∈ spanPoints k s\np1a : P\nhp1a : p1a ∈ s\nv1 : V\nhv1 : v1 ∈ vectorSpan k s\nhv1p : p1 = v1 +ᵥ p1a\n⊢ ... | [
151,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.card_boundaries_pos | [] | [
882,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
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Mathlib/Topology/SubsetProperties.lean | LocallyFinite.finite_of_compact | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι✝ : Type ?u.89316\nπ : ι✝ → Type ?u.89321\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\nι : Type u_1\ninst✝ : CompactSpace α\nf : ι → Set α\nhf : LocallyFinite f\nhne : ∀ (i : ι), Set.Nonempty (f i)\n⊢ Set.Finit... | [
826,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bindOnSupport_eq_zero_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.110688\np : Pmf α\nf : (a : α) → a ∈ support p → Pmf β\nb : β\n⊢ (∀ (i : α), ¬↑p i = 0 → (if h : ↑p i = 0 then 0 else ↑(f i (_ : ¬↑p i = 0)) b) = 0) ↔\n ∀ (a : α) (ha : ↑p a ≠ 0), ↑(f a ha) b = 0",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : ... | [
261,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_top | [] | [
1349,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_bind | [] | [
1677,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1674,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | cauchy_pure | [] | [
90,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Models.setParent | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\narr : Array (UFNode α)\nn : ℕ\nm : UFModel n\nhm : Models arr m\ni j : Fin n\nH : rank m ↑i < rank m ↑j\nhi : ↑i < Array.size arr\nx : UFNode α\nhp : x.parent = ↑j\nhrk : x.rank = arr[i].rank\nk : Fin n\nh : ↑k ≠ ↑i\n⊢ ↑(parent (UFModel.setParent m... | [
152,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofAdd_eq_one | [] | [
240,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.castLE_comp_castLE | [] | [
478,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.atom_pf' | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na a' : R\np : a = a'\n⊢ a = a' ^ Nat.rawCast 1 * Nat.rawCast 1 + 0",
"tactic": "simp [*]"
}
] | [
867,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | DifferentiableAt.inv | [] | [
155,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.to_append_iff | [
{
"state_after": "α : Type u\nL L₁ L₂ L₃ L₄ L₁₂ : List (α × Bool)\neq : L₁ ++ L₂ = L₁₂\n⊢ Red L L₁₂ → ∃ L₃ L₄, L = L₃ ++ L₄ ∧ Red L₃ L₁ ∧ Red L₄ L₂",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\n⊢ Red L (L₁ ++ L₂) → ∃ L₃ L₄, L = L₃ ++ L₄ ∧ Red L₃ L₁ ∧ Red L₄ L₂",
"tactic": "generalize e... | [
310,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_nonneg | [] | [
698,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/NumberTheory/FermatPsp.lean | FermatPsp.AB_id_helper | [
{
"state_after": "b p : ℕ\nx✝ : 2 ≤ b\nhp : Odd p\nq₁ : b - 1 ∣ b ^ p - 1\n⊢ (b ^ p - 1) / (b - 1) * ((b ^ p + 1) / (b + 1)) = (b ^ (2 * p) - 1) / (b ^ 2 - 1)",
"state_before": "b p : ℕ\nx✝ : 2 ≤ b\nhp : Odd p\n⊢ (b ^ p - 1) / (b - 1) * ((b ^ p + 1) / (b + 1)) = (b ^ (2 * p) - 1) / (b ^ 2 - 1)",
"tactic... | [
165,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
9
] |
Mathlib/Analysis/Convex/Topology.lean | bounded_stdSimplex | [] | [
61,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_succEmbedding | [] | [
884,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Topology/MetricSpace/Closeds.lean | EMetric.NonemptyCompacts.ToCloseds.uniformEmbedding | [] | [
261,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.comp_apply | [] | [
751,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.symm_comp_self | [] | [
275,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_subset | [] | [
122,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Sign.lean | SignType.neg_eq_neg_one | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | hasSum_two_pi_I_cauchyPowerSeries_integral | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nc : ℂ\nR : ℝ\nw : ℂ\nhf : CircleIntegrable f c R\nhw : ↑Complex.abs w < R\nhR : 0 < R\n⊢ HasSum (fun n => ∮ (z : ℂ) in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z)\n (∮ (z : ℂ) in C(c... | [
608,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset.ext_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.469108\nγ : Type ?u.469111\ninst✝ : DecidableEq α\nl l' : List α\na✝ : α\na b : List α\n⊢ toFinset a = toFinset b ↔ ∀ (x : α), x ∈ a ↔ x ∈ b",
"tactic": "simp only [Finset.ext_iff, mem_toFinset]"
}
] | [
3285,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3284,
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] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_eq_zero_iff_of_nonneg | [
{
"state_after": "x y : ℝ\nhx : 0 ≤ x\n⊢ (if x = 0 then if y = 0 then 1 else 0 else exp (log x * y)) = 0 ↔ x = 0 ∧ y ≠ 0",
"state_before": "x y : ℝ\nhx : 0 ≤ x\n⊢ x ^ y = 0 ↔ x = 0 ∧ y ≠ 0",
"tactic": "simp only [rpow_def_of_nonneg hx]"
},
{
"state_after": "no goals",
"state_before": "x y : ... | [
70,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns✝ : Finmap β\ns : AList β\n⊢ lookup a (insert a b ⟦s⟧) = some b",
"tactic": "simp only [insert_toFinmap, lookup_toFinmap, AList.lookup_insert]"
}
] | [
502,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.const_mul_eq_map | [] | [
575,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Group.lean | ciSup_mul_le | [] | [
50,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_prod | [] | [
1445,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.list_sum_mem | [] | [
161,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
11
] |
Mathlib/Computability/Partrec.lean | Partrec.rfindOpt | [] | [
580,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_toAddSubmonoid | [] | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.log | [] | [
148,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.exists_pair_of_one_lt_card | [] | [
585,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.sInf_add' | [
{
"state_after": "n : ℕ\np : ℕ → Prop\nh : 0 < sInf {m | p m}\nh₁ : n ≤ sInf {m | p (m - n)}\n⊢ sInf {m | p m} + n = sInf {m | p (m - n)}\n\ncase h₁\nn : ℕ\np : ℕ → Prop\nh : 0 < sInf {m | p m}\n⊢ n ≤ sInf {m | p (m - n)}",
"state_before": "n : ℕ\np : ℕ → Prop\nh : 0 < sInf {m | p m}\n⊢ sInf {m | p m} + n =... | [
173,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Set/Image.lean | Function.Semiconj.set_image | [] | [
290,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.ker_le_comap | [] | [
2101,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2100,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.exists_eq_cons | [] | [
75,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffAt_top | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1326,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.measurable_bind | [] | [
285,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/LinearAlgebra/Dual.lean | TensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse | [
{
"state_after": "R : Type u_2\nM : Type u_3\nN : Type u_5\nι : Type u_1\nκ : Type u_4\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : DecidableEq κ\ninst✝⁶ : Fintype ι\ninst✝⁵ : Fintype κ\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\nb : Basis ι R M\nc : Bas... | [
1614,
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1606,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_map | [] | [
1410,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofBijective_apply | [] | [
2224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2222,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.coe_mul_self_eq | [
{
"state_after": "case h\nα : Type ?u.3401\nG : Type ?u.3404\nM : Type u_1\nR : Type ?u.3410\nA : Type ?u.3413\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\ns✝ t u : Set M\ns : Submonoid M\nx : M\n⊢ x ∈ ↑s * ↑s ↔ x ∈ ↑s",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Set/Function.lean | Set.RightInvOn.congr_left | [] | [
1118,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_zero_eval_zero | [
{
"state_after": "no goals",
"state_before": "S : Type u\ninst✝ : Semiring S\n⊢ eval 0 (pochhammer S 0) = 1",
"tactic": "simp"
}
] | [
91,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | StrictMonoOn.continuousWithinAt_right_of_surjOn | [] | [
133,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Topology/Inseparable.lean | inseparable_iff_closure_eq | [
{
"state_after": "no goals",
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308,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.beq_comm | [
{
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"state_before": "α : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\n⊢ (a == b) = true ↔ (b == a) = true",
"tactic": "simp [@eq_comm α]"
}
] | [
92,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.pointReflection_involutive | [] | [
582,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
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Mathlib/Analysis/Convex/Extreme.lean | IsExtreme.refl | [] | [
73,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
11
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_inj | [] | [
97,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimit_of_dense | [] | [
54,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.zsmul | [] | [
642,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.drop | [] | [
1020,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1019,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.comap_mono | [] | [
1296,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Subgroup.coe_norm | [] | [
2661,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2660,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_eq_iSup' | [
{
"state_after": "no goals",
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"tactic": "rw [iSup, Subtype.... | [
630,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | powersHom_apply | [] | [
849,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_one | [
{
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2145,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2144,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mrange_inr | [
{
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"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.150835\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.150856\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\n⊢ mrange (inr M N) = prod ⊥ ⊤",
"tactic": "simp... | [
1293,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_csInf | [] | [
257,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.MemLeftTransversals.mk''_toEquiv | [] | [
351,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isAsymm | [] | [
351,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_add_left | [
{
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"tactic": "simp"
},
{
... | [
2757,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2745,
1
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Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.val_eq | [] | [
861,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_sum_index | [
{
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377,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/CategoryTheory/Limits/EssentiallySmall.lean | CategoryTheory.Limits.hasLimitsOfShape_of_essentiallySmall | [] | [
34,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.const_smul | [] | [
142,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
8
] |
Mathlib/Analysis/Subadditive.lean | Subadditive.eventually_div_lt_of_div_lt | [
{
"state_after": "u : ℕ → ℝ\nh : Subadditive u\nL : ℝ\nn : ℕ\nhn : n ≠ 0\nhL : u n / ↑n < L\nr : ℕ\nx✝ : r < n\n⊢ ∀ᶠ (a : ℕ) in atTop, u (n * a + r) / ↑(n * a + r) < L",
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"tac... | [
84,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_disjoint_Ico | [
{
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212,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective | [
{
"state_after": "R : Type u_1\nM : Type u_2\nM' : Type u_3\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M'\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nhf : Function.Surjective ↑(dualMap (Submodule.subtype (range f)))\nrr_surj : Function.Surjective ↑(rangeRestrict f)\n⊢ ra... | [
1328,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.snd_iso_of_left_embedding_range_subset | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\nhf : Embedding ((forget TopCat).map f)\ng : Y ⟶ S\nH : Set.range ((forget TopCat).map g) ⊆ Set.range ((forget TopCat).map f)\nesto : ↑(pullback f g) ≃ₜ ↑Y :=\n Homeomorph.trans\n (Homeomorph.ofEmbedding ((for... | [
370,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.preimage_add_right | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.67540\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y✝ z : E\ns : Set E\nhs : StarConvex 𝕜 (z + x) s\ny : E\nhy : y ∈ (fun x => z + x) ⁻¹' s\na b : 𝕜\nha : 0 ≤ a\nhb : 0 ... | [
257,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Monoid.fg_of_surjective | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.44817\ninst✝³ : Monoid M\ninst✝² : AddMonoid N\nM' : Type u_1\ninst✝¹ : Monoid M'\ninst✝ : FG M\nf : M →* M'\nhf : Function.Surjective ↑f\n⊢ FG M'",
"tactic": "classical\n obtain ⟨s, hs⟩ := Monoid.fg_def.mp ‹_›\n use s.image f\n ... | [
182,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioo_pred_right_eq_insert | [
{
"state_after": "no goals",
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"tactic": "simp_rw [← Ioi_inter_Iio, Ioi_pred_eq_insert, insert_inter_of_mem (mem_Iio.2 h)]"
}
] | [
859,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_iff_exists_subset_range | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝ : Nonempty α\ns : Set α\nh : Set.Countable s\ninhabited_h : Inhabited α\n⊢ ∃ f, s ⊆ range f",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝ : Nonempty α\ns : Set α\nh : Set.Countable s\n⊢ ∃ f, s ⊆ range f",
... | [
101,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Invertible.lean | nonzero_of_invertible | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : MulZeroOneClass α\na : α\ninst✝¹ : Nontrivial α\ninst✝ : Invertible a\nha : a = 0\n⊢ 0 = ⅟a * a",
"tactic": "simp [ha]"
}
] | [
350,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Logic/Nontrivial.lean | not_nontrivial_iff_subsingleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2730\n⊢ ¬Nontrivial α ↔ Subsingleton α",
"tactic": "simp only [nontrivial_iff, subsingleton_iff, not_exists, Ne.def, not_not]"
}
] | [
119,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_eq_neg_pi_div_two_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal θ = -π / 2 ↔ θ = ↑(-π / 2)",
"tactic": "rw [← toReal_inj, toReal_neg_pi_div_two]"
}
] | [
629,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.union_ae_eq_univ_of_ae_eq_univ_right | [
{
"state_after": "case h.e'_5\nα : Type u_1\nβ : Type ?u.115131\nγ : Type ?u.115134\nδ : Type ?u.115137\nι : Type ?u.115140\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh : t =ᵐ[μ] univ\n⊢ univ = s ∪ univ",
"state_before": "α : Type u_1\nβ : Type ?u.115131\nγ : Type ?u.115134\nδ : Typ... | [
518,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Data/List/Sigma.lean | List.lookupAll_eq_dlookup | [
{
"state_after": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl : List (Sigma β)\nh : NodupKeys l\n⊢ lookupAll a l = Option.toList (head? (lookupAll a l))",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl : List... | [
325,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | Basis.parallelepiped_reindex | [] | [
219,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.disjoint_conj | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h✝ h : Perm α\nx✝ : α\n⊢ ↑(h * f * h⁻¹) x✝ = x✝ ∨ ↑(h * g * h⁻¹) x✝ = x✝ ↔ ↑f (↑h⁻¹ x✝) = ↑h⁻¹ x✝ ∨ ↑g (↑h⁻¹ x✝) = ↑h⁻¹ x✝",
"tactic": "simp only [mul_apply, eq_inv_iff_eq]"
}
] | [
122,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_zero_right_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.266271\nE : Type ?u.266274\nF : Type ?u.266277\nG : Type ?u.266280\nE' : Type ?u.266283\nF' : Type u_3\nG' : Type ?u.266289\nE'' : Type u_2\nF'' : Type ?u.266295\nG'' : Type ?u.266298\nR : Type ?u.266301\nR' : Type ?u.266304\n𝕜 : Type ... | [
1224,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Coalgebra.id_f | [] | [
334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_lt_one | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.136627\nβ : Type ?u.136630\nM : Type u_2\nN : Type ?u.136636\nG : Type ?u.136639\nk : Type ?u.136642\nR : Type ?u.136645\ninst✝ : OrderedCancelCommMonoid M\nf g : ι → M\ns t : Finset ι\nh : ∀ (i : ι), i ∈ s → f i < 1\nhs : Finset.Nonemp... | [
515,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_mul_lt_left | [] | [
228,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.coe_inj | [] | [
117,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
11
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_toMatrix | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommSemiring R\nl : Type ?u.1419247\nm : Type u_4\nn : Type u_5\ninst✝⁶ : Fintype n\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq n\nM₁ : Type u_2\nM₂ : Type u_3\ninst✝³ : AddCommMonoid M₁\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M₁\ninst... | [
566,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_strictMono | [] | [
1403,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_unit | [] | [
1933,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1932,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | IsCompact.mul_closedBall | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx✝ y : E\nhs : IsCompact s\nhδ : 0 ≤ δ\nx : E\n⊢ s * closedBall x δ = x • cthickening δ s",
"tactic": "rw [← smul_closedBall_one, mul_smul_comm, hs.mul_closedBall_one hδ]"
}
] | [
286,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Subsets and Splits
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