file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.sub_const | [] | [
114,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_closedBall_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.33624\nι : Type ?u.33627\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nh : 0 ≤ ε\n⊢ x ∈ closedBall x ε",
"tactic": "rwa [mem_closedBall, dist_self]"
}
] | [
510,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_contract | [] | [
169,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_eq | [
{
"state_after": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nx✝ : FractionRing K[X]\nx : K[X] × { x // x ∈ K[X]⁰ }\n⊢ IsLocalization.mk' (RatFunc K) x.fst x.snd =\n IsLocalization.mk' (RatFunc K) (↑(RingHom.id K[X]) x.fst)\n { val := ↑(RingHom.id K[X]) ↑x.snd, property := (_ : ↑x.snd ∈ Submono... | [
1051,
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1043,
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.eqLocus_same | [] | [
2897,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2896,
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.coe_top | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPullback.iso_inv_snd | [
{
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141,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Topology/Algebra/MulAction.lean | ContinuousOn.smul | [] | [
118,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Control/Basic.lean | pure_id'_seq | [] | [
61,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_diagonal | [
{
"state_after": "case a.mk.h.mk\nl : Type ?u.136326\nm : Type u_1\nn : Type ?u.136332\no : Type u_2\np : Type ?u.136338\nq : Type ?u.136341\nm' : o → Type ?u.136346\nn' : o → Type ?u.136351\np' : o → Type ?u.136356\nR : Type ?u.136359\nS : Type ?u.136362\nα : Type u_3\nβ : Type ?u.136368\ninst✝³ : DecidableEq ... | [
410,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_le_of_ae_le_trim | [] | [
4401,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4399,
1
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Mathlib/NumberTheory/Bernoulli.lean | bernoulli'_eq_bernoulli | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.631794\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn : ℕ\n⊢ bernoulli' n = (-1) ^ n * bernoulli n",
"tactic": "simp [bernoulli, ← mul_assoc, ← sq, ← pow_mul, mul_comm n 2, pow_mul]"
}
] | [
209,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_reverse | [
{
"state_after": "α : Type u_1\nβ : Type ?u.774227\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl : List α\nh : Nodup l\n⊢ formPerm l * formPerm (reverse l) = 1",
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325,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
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src/lean/Init/SimpLemmas.lean | heq_eq_eq | [] | [
143,
113
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
143,
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_fderiv | [
{
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171,
54
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168,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_le_infDist_of_subset | [] | [
516,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfRightIso_π_app_none | [
{
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"tactic": "simp"
}
] | [
1705,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.deriv_cos | [] | [
96,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_lt_coe | [] | [
120,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.linMulLinSelfPosDef | [] | [
959,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
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Mathlib/Algebra/BigOperators/Order.lean | Finset.card_biUnion_le_card_mul | [] | [
232,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/Analysis/SpecificLimits/Basic.lean | dist_le_of_le_geometric_of_tendsto | [
{
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403,
39
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397,
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Mathlib/Order/SymmDiff.lean | bihimp_bihimp_sup | [] | [
322,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
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Mathlib/Data/List/Zip.lean | List.zip_nil_right | [] | [
65,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
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Mathlib/Order/Monotone/Basic.lean | monotone_snd | [] | [
1153,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_nonneg_of_nonneg_of_le_pi_div_two | [
{
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"state_before": "x : ℝ\nh0x : 0 ≤ x\nhxp✝ : x ≤ π / 2\nh✝ : 0 < x\nhxp : x = π / 2\n⊢ 0 ≤ tan x",
"tactic": "simp [hxp, tan_eq_sin_div_cos]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nh0x : 0 ≤ x\nhxp : x ≤ π / 2\nhx0 : 0 = x\nx✝ : x < π / 2 ∨ x = π ... | [
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40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | RingEquiv.mapMatrix_trans | [] | [
1577,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1575,
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Mathlib/Order/Interval.lean | Interval.coe_inf | [
{
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"state_before": "case none\nα : Type u_1\nβ : Type ?u.38930\nγ : Type ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.lower_le_lower | [] | [
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38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_lintegral_nn_filter_of_le_const | [
{
"state_after": "case refine_1\nΩ : Type u_2\ninst✝⁴ : MeasurableSpace Ω\ninst✝³ : TopologicalSpace Ω\ninst✝² : OpensMeasurableSpace Ω\nι : Type u_1\nL : Filter ι\ninst✝¹ : IsCountablyGenerated L\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nfs : ι → Ω →ᵇ ℝ≥0\nc : ℝ≥0\nfs_le_const : ∀ᶠ (i : ι) in L, ∀ᵐ (ω : Ω) ∂μ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mul_mem_left | [] | [
68,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.funLeft_surjective_of_injective | [
{
"state_after": "R : Type u_4\nR₁ : Type ?u.2320959\nR₂ : Type ?u.2320962\nR₃ : Type ?u.2320965\nR₄ : Type ?u.2320968\nS : Type ?u.2320971\nK : Type ?u.2320974\nK₂ : Type ?u.2320977\nM : Type u_3\nM' : Type ?u.2320983\nM₁ : Type ?u.2320986\nM₂ : Type ?u.2320989\nM₃ : Type ?u.2320992\nM₄ : Type ?u.2320995\nN : ... | [
2629,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2619,
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] |
Mathlib/Computability/Primrec.lean | Primrec.nat_double_succ | [] | [
860,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
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] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_subsemigroup_closure | [] | [
649,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
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Mathlib/Data/Set/Finite.lean | Set.Finite.of_diff | [] | [
772,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
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Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_last_apply | [
{
"state_after": "case intro\nm n : ℕ\ni : Fin n\nh : ↑Fin.castSucc i ≠ Fin.last n\n⊢ ↑(finSuccEquiv' (Fin.last n)) (↑Fin.castSucc i) = some (Fin.castLT (↑Fin.castSucc i) (_ : ↑(↑Fin.castSucc i) < n))",
"state_before": "m n : ℕ\ni : Fin (n + 1)\nh : i ≠ Fin.last n\n⊢ ↑(finSuccEquiv' (Fin.last n)) i = some (... | [
233,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
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Mathlib/Order/JordanHolder.lean | CompositionSeries.chain'_toList | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\ni : ℕ\nhi : i < List.length (toList s) - 1\n⊢ IsMaximal (List.get (toList s) { val := i, isLt := (_ : i < List.length (toList s)) })\n (List.get (toList s) { val := i + 1, isLt := (_ : Nat.succ i < List.... | [
254,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/Data/Finset/Image.lean | Finset.image_eq_empty | [] | [
528,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
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] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.leadingCoeff_of_a_ne_zero' | [] | [
209,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/Algebra/Ring/Divisibility.lean | dvd_sub_self_right | [] | [
158,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lie_inf | [
{
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199,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffAt.sin | [] | [
1040,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
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Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.tprod_mul_tprod | [
{
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"state_before": "R : Type u_1\n... | [
167,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/Logic/Nontrivial.lean | Pi.nontrivial_at | [
{
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"state_before": "α : Type ?u.4851\nβ : Type ?u.4854... | [
188,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
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Mathlib/Init/CcLemmas.lean | and_eq_of_eq | [] | [
34,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GCDMonoid/Basic.lean | normUnit_mul_normUnit | [
{
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... | [
169,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Mathlib/Data/Finset/Image.lean | Finset.subtype_eq_empty | [
{
"state_after": "no goals",
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"tactic": "simp [ext_iff, Subtype.forall, Subtype.coe_mk]"
}
] | [
670,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Topology/Sequences.lean | tendsto_subseq_of_frequently_bounded | [] | [
426,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_comap'_iff | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.311794\nι : Sort x\nm : α → β\nf : Fil... | [
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51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2958,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.lcm_eq_inf | [] | [
879,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.invRev_invRev | [] | [
567,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_right_inj | [] | [
395,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_ringHom_trans | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11546\nι : Type ?u.11549\nM : Type u_2\nN : Type ?u.11555\ninst✝¹ : One M\ninst✝ : One N\ns✝ t : Set α\nf g : α → M\na : α\ns : Set α\n⊢ Disjoint (mulSupport fun x => 1) s",
"tactic": "simp only [mulSupport_one, empty_disjoint]"
}... | [
222,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.supported_iUnion | [
{
"state_after": "α : Type u_2\nM : Type u_3\nN : Type ?u.93459\nP : Type ?u.93462\nR : Type u_4\nS : Type ?u.93468\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nδ : Type u_1\... | [
297,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.image_comap_zeroLocus_eq_zeroLocus_comap | [
{
"state_after": "R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nS' : Type ?u.338029\ninst✝ : CommRing S'\nf : R →+* S\nhf : Surjective ↑f\nI : Ideal S\n⊢ ∀ (x : PrimeSpectrum R), (∃ x_1, I ≤ x_1.asIdeal ∧ ↑(comap f) x_1 = x) ↔ Ideal.comap f I ≤ x.asIdeal",
"state_before": "R : Type u\nS ... | [
736,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Order/Bounds/Basic.lean | Set.Nonempty.bddAbove_lowerBounds | [] | [
266,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_normal | [] | [
395,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Bundle.zeroSection_snd | [] | [
390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.Parallel.refl | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\n⊢ s = map (↑(constVAdd k P 0)) s",
"tactic": "simp"
}
] | [
1735,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1734,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.complete' | [
{
"state_after": "case intro\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] ↑padicNormE\nε : ℚ\nhε : ε > 0\nN : ℕ\nhN : ∀ (i : ℕ), i ≥ N → ↑padicNormE (↑f i - ↑(limSeq f i)) < ε / 2\n⊢ ∃ N, ∀ (i : ℕ), i ≥ N → ↑padicNormE (Padic.lim f - ↑f i) < ε",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf ... | [
748,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | isCyclic_of_card_pow_eq_one_le | [
{
"state_after": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhn : ∀ (n : ℕ), 0 < n → card (filter (fun a => a ^ n = 1) univ) ≤ n\n⊢ 0 < φ (Fintype.card α)",
"state_before": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhn : ∀ (n : ℕ), 0... | [
404,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/List/Basic.lean | List.takeWhile_takeWhile | [
{
"state_after": "case nil\nι : Type ?u.417345\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np✝ : α → Bool\nl : List α\np q : α → Bool\n⊢ takeWhile p (takeWhile q []) = takeWhile (fun a => decide (p a = true ∧ q a = true)) []\n\ncase cons\nι : Type ?u.417345\nα : Type u\nβ : Type v\nγ : Type ... | [
3666,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3662,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_iUnion | [] | [
326,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_sub_swap | [] | [
296,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
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Mathlib/Topology/Connected.lean | preimage_connectedComponent_connected | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.107968\nπ : ι → Type ?u.107973\ninst✝¹ : TopologicalSpace α\ns t✝ u v : Set α\ninst✝ : TopologicalSpace β\nf : α → β\nconnected_fibers : ∀ (t : β), IsConnected (f ⁻¹' {t})\nhcl : ∀ (T : Set β), IsClosed T ↔ IsClosed (f ⁻¹' T)\nt : β\nhf : Surjective f\n⊢ IsC... | [
1084,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Int.cast_list_prod | [] | [
2232,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2231,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.lxor_bit | [
{
"state_after": "no goals",
"state_before": "a : Bool\nm : ℤ\nb : Bool\nn : ℤ\n⊢ lxor' (bit a m) (bit b n) = bit (xor a b) (lxor' m n)",
"tactic": "rw [← bitwise_xor, bitwise_bit]"
}
] | [
325,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22649\nσ : Type ?u.22652\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\n⊢ ∀ (n : ℕ), encode (decode n) = encode (Option.map id (decode n))",
"tactic": "simp"
}
] | [
259,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
11
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.dist_le_distortion_mul | [
{
"state_after": "ι : Type u_1\nI✝ J : Box ι\nx y : ι → ℝ\ninst✝ : Fintype ι\nI : Box ι\ni : ι\nA : lower I i - upper I i < 0\n⊢ dist I.lower I.upper ≤ ↑(distortion I) * (upper I i - lower I i)",
"state_before": "ι : Type u_1\nI✝ J : Box ι\nx y : ι → ℝ\ninst✝ : Fintype ι\nI : Box ι\ni : ι\n⊢ dist I.lower I.... | [
528,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
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Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.prime_C_iff | [
{
"state_after": "R : Type u\nS : Type ?u.467790\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nr : R\nhr : Prime r\nh : ↑C r = 0\n⊢ 0 = ↑C 0",
"state_before": "R : Type u\nS : Type ?u.467790\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝... | [
811,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Topology/Order/Basic.lean | interior_Ici | [] | [
2277,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2276,
1
] |
Mathlib/Topology/Algebra/FilterBasis.lean | ModuleFilterBasis.smul_right | [] | [
366,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.eventuallyEq_one | [] | [
360,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_one | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.4278\nm : Type ?u.4281\nn : Type u_2\no : Type ?u.4287\nR : Type u_1\nm_fin : Fintype m\ninst✝⁴ : Fintype n\ninst✝³ : Fintype o\ninst✝² : CommRing R\ninst✝¹ : StrongRankCondition R\ninst✝ : DecidableEq n\n⊢ rank 1 = Fintype.card n",
"tactic": "rw... | [
56,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | two_dvd_bit1 | [] | [
134,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.num_zero | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | LipschitzOnWith.extend_finite_dimension | [
{
"state_after": "𝕜 : Type u\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nF : Type w\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁹ : AddCommGroup F'\ninst✝⁸ : Module 𝕜 F'\ninst✝⁷ : TopologicalSpace F'\ninst✝⁶ ... | [
223,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.cocone_inl | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_iInf_le | [] | [
200,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_of_finite_subfamily_closed | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.27539\nπ : ι → Type ?u.27544\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nh :\n ∀ {ι : Type u} (Z : ι → Set α),\n (∀ (i : ι), IsClosed (Z i)) → (s ∩ ⋂ (i : ι), Z i) = ∅ → ∃ t, (s ∩ ⋂ (i : ι) (_ : i ∈ t), Z i) = ∅\nι✝ : Type u\nU... | [
348,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.mulSingle_strictMono | [] | [
715,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Data/Finset/Pi.lean | Finset.pi_disjoint_of_disjoint | [] | [
138,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Module/Projective.lean | Module.Projective.of_lifting_property' | [] | [
188,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.rightInverse_iff_comp | [] | [
340,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/List/Lattice.lean | List.inter_reverse | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁ l₂ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nxs ys : List α\n⊢ List.inter xs (reverse ys) = List.inter xs ys",
"tactic": "simp only [List.inter, mem_reverse]"
}
] | [
198,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/Covering.lean | IsCoveringMapOn.continuousAt | [] | [
100,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.measurable_uncurry_of_continuous_of_measurable | [
{
"state_after": "case intro\nα✝ : Type ?u.556281\nβ✝ : Type ?u.556284\nγ : Type ?u.556287\nι✝ : Type ?u.556290\ninst✝⁸ : Countable ι✝\nα : Type u_1\nβ : Type u_2\nι : Type u_3\ninst✝⁷ : TopologicalSpace ι\ninst✝⁶ : MetrizableSpace ι\ninst✝⁵ : MeasurableSpace ι\ninst✝⁴ : SecondCountableTopology ι\ninst✝³ : Open... | [
2008,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.exists_mem_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.438021\nγ : Type ?u.438024\np : α → Prop\n⊢ (∃ x, x ∈ ∅ ∧ p x) ↔ False",
"tactic": "simp only [not_mem_empty, false_and_iff, exists_false]"
}
] | [
3068,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3067,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.Subset.trans | [] | [
396,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Combinatorics/Additive/Energy.lean | Finset.multiplicativeEnergy_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Mul α\ns s₁ s₂ t t₁ t₂ : Finset α\n⊢ multiplicativeEnergy s t = 0 ↔ s = ∅ ∨ t = ∅",
"tactic": "simp [← (Nat.zero_le _).not_gt_iff_eq, not_and_or, imp_iff_or_not, or_comm]"
}
] | [
122,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_zero | [] | [
98,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Order/Basic.lean | Ne.lt_or_lt | [] | [
480,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/GroupTheory/Abelianization.lean | commutator_def | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_coeIdeal | [] | [
259,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | quotient_norm_add_le | [
{
"state_after": "case intro.intro.intro\nM : Type u_1\nN : Type ?u.346908\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nx y : M\n⊢ ‖↑x + ↑y‖ ≤ ‖↑x‖ + ‖↑y‖",
"state_before": "M : Type u_1\nN : Type ?u.346908\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAdd... | [
217,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.disjoint_ker' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.1371370\nR₂ : Type u_3\nR₃ : Type ?u.1371376\nR₄ : Type ?u.1371379\nS : Type ?u.1371382\nK : Type ?u.1371385\nK₂ : Type ?u.1371388\nM : Type u_2\nM' : Type ?u.1371394\nM₁ : Type ?u.1371397\nM₂ : Type u_4\nM₃ : Type ?u.1371403\nM₄ : Typ... | [
1495,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.exists_nonzero_mem_of_ne_bot | [
{
"state_after": "case intro\nR : Type u_1\ninst✝¹ : CommRing R\nS : Type ?u.73967\ninst✝ : CommRing S\nf : R →+* S\nI J : Ideal S\nP : Ideal R[X]\nPb : P ≠ ⊥\nhP : ∀ (x : R), ↑C x ∈ P → x = 0\nm : { x // x ∈ P }\nhm : m ≠ 0\n⊢ ∃ p, p ∈ P ∧ Polynomial.map (Quotient.mk (comap C P)) p ≠ 0",
"state_before": "R... | [
129,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.nat_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.96089\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : Semiring α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (↑n * c)",
"tactic": "simpa only [nsmul_eq_mul] using h.nsmul n"
}
] | [
206,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sigmaToiUnion_injective | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.300743\nι : Sort ?u.300746\nι' : Sort ?u.300749\nι₂ : Sort ?u.300752\nκ : ι → Sort ?u.300757\nκ₁ : ι → Sort ?u.300762\nκ₂ : ι → Sort ?u.300767\nκ' : ι' → Sort ?u.300772\nt : α → Set β\nh : ∀ (i j : α), i ≠ j → Disjoint (t i) (t j)\na₁ : α\nb₁ : β\nh₁ : b... | [
2183,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2175,
1
] |
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