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/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.lift.unique | [] | [
121,
71
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119,
11
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Mathlib/Algebra/Field/Basic.lean | div_neg_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.38193\nβ : Type ?u.38196\nK : Type u_1\ninst✝ : DivisionRing K\na✝ b c d a : K\nh : a ≠ 0\n⊢ a / -a = -1",
"tactic": "rw [div_neg_eq_neg_div, div_self h]"
}
] | [
145,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Order/Interval.lean | Interval.coe_dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27118\nγ : Type ?u.27121\nδ : Type ?u.27124\nι : Sort ?u.27127\nκ : ι → Sort ?u.27132\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\ns✝ t : Interval α\na b : α\ns : Interval α\n⊢ ↑(↑dual s) = ↑ofDual ⁻¹' ↑s",
"tactic": "cases s w... | [
510,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_int_mul_two_pi_add_pi | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ cos (↑n * (2 * π) + π) = -1",
"tactic": "simpa only [cos_zero] using (cos_periodic.int_mul n).add_antiperiod_eq cos_antiperiodic"
}
] | [
391,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.eq_sign_of_surjective_hom | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns : Perm α →* ℤˣ\nhs : Surjective ↑s\nf : Perm α\nx✝ : IsSwap f\nx y : α\nhxy : x ≠ y\nhxy' : f = swap x y\nh : ¬↑s (swap x y) = -1\nthis : ∀ (f : Perm α), IsSwap f → ↑s f = 1\n⊢ False",
"state_before": "α : Type u\nβ : Typ... | [
659,
31
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637,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_reverse | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ support (reverse p) = List.reverse (support p)",
"tactic": "induction p <;> simp [support_append, *]"
}
] | [
559,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
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Mathlib/Analysis/Complex/Basic.lean | Complex.ofRealClm_apply | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
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Mathlib/Algebra/Order/UpperLower.lean | IsLowerSet.div_right | [] | [
125,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
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Mathlib/Data/Fin/Basic.lean | Fin.succRecOn_succ | [
{
"state_after": "case mk\nn✝ m : ℕ\nC : (n : ℕ) → Fin n → Sort u_1\nH0 : (n : ℕ) → C (n + 1) 0\nHs : (n : ℕ) → (i : Fin n) → C n i → C (Nat.succ n) (succ i)\nn val✝ : ℕ\nisLt✝ : val✝ < n\n⊢ succRecOn (succ { val := val✝, isLt := isLt✝ }) H0 Hs =\n Hs n { val := val✝, isLt := isLt✝ } (succRecOn { val := val✝... | [
1676,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1675,
1
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integrable_neg | [] | [
293,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.bddAbove_coe | [] | [
481,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_zero | [] | [
119,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
11
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.fromLocalizedModule'_mk | [] | [
733,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.inv_range | [
{
"state_after": "F : Type ?u.7720\nα : Type u_2\nβ : Type ?u.7726\nγ : Type ?u.7729\ninst✝ : InvolutiveInv α\ns t : Set α\na : α\nι : Sort u_1\nf : ι → α\n⊢ Inv.inv '' range f = range fun i => (f i)⁻¹",
"state_before": "F : Type ?u.7720\nα : Type u_2\nβ : Type ?u.7726\nγ : Type ?u.7729\ninst✝ : InvolutiveI... | [
293,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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Mathlib/Data/Polynomial/Reverse.lean | Polynomial.eval₂_reflect_eq_zero_iff | [
{
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"state_before": "R : Type u_1\ninst✝² : Semiring... | [
242,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_right_inj | [] | [
944,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
9
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.add | [
{
"state_after": "no goals",
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196,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.ker_le_comap | [] | [
947,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
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Mathlib/Algebra/Order/Floor.lean | Int.ceil_natCast | [
{
"state_after": "no goals",
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"tactic": "rw [ceil_le, ← cast_ofNat, cast_le]"
}
] | [
1136,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Analysis/SpecificLimits/FloorPow.lean | tendsto_div_of_monotone_of_exists_subseq_tendsto_div | [
{
"state_after": "u : ℕ → ℝ\nl : ℝ\nhmono : Monotone u\nhlim :\n ∀ (a : ℝ),\n 1 < a →\n ∃ c,\n (∀ᶠ (n : ℕ) in atTop, ↑(c (n + 1)) ≤ a * ↑(c n)) ∧\n Tendsto c atTop atTop ∧ Tendsto (fun n => u (c n) / ↑(c n)) atTop (𝓝 l)\nlnonneg : 0 ≤ l\n⊢ Tendsto (fun n => u n / ↑n) atTop (𝓝 l)",
... | [
207,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.mem_supp_iff | [] | [
2159,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2157,
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Mathlib/Data/Rat/NNRat.lean | Rat.le_coe_toNNRat | [] | [
108,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.prodMap_comp | [] | [
347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.of_eq_tot | [] | [
437,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
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] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.iInf_ker_proj_le_iSup_range_stdBasis | [
{
"state_after": "R : Type u_3\nι : Type u_1\ninst✝³ : Semiring R\nφ : ι → Type u_2\ninst✝² : (i : ι) → AddCommMonoid (φ i)\ninst✝¹ : (i : ι) → Module R (φ i)\ninst✝ : DecidableEq ι\nI : Finset ι\nJ : Set ι\nhu : Set.univ ⊆ ↑I ∪ J\nb : (i : ι) → φ i\nhb : b ∈ ⨅ (i : ι) (_ : i ∈ J), ker (proj i)\n⊢ b ∈ ⨆ (i : ι)... | [
125,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.isUnit_iff | [
{
"state_after": "case mp\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedAddCommGroup Γ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nx : HahnSeries Γ R\n⊢ IsUnit x → IsUnit (coeff x (order x))\n\ncase mpr\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedAddCommGroup Γ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R... | [
1858,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1845,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_mul_apply | [
{
"state_after": "no goals",
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692,
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690,
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Mathlib/Order/WellFoundedSet.lean | Set.isPwo_insert | [
{
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"tactic": "simp only [← singleton_union, isPwo_union, isPwo_singleton, true_and_iff]"
}
] | [
461,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
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Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1 | [
{
"state_after": "E : Type u_1\nF : Type ?u.798589\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.mono_of_mem | [] | [
372,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Order/WithBot.lean | WithTop.some_lt_none | [] | [
1070,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.constr_eq | [] | [
642,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
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] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_comp_map | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.coe_copy | [] | [
611,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
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] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value₂_eventually₁ | [
{
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111,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_lineMap_left | [] | [
344,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
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Mathlib/Algebra/RingQuot.lean | RingQuot.eq_lift_comp_mkRingHom | [
{
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477,
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473,
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Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Comonad.algebra_epi_of_epi | [] | [
509,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_sup | [] | [
326,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_comp_hom_inv_comp | [
{
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17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_lift_preimage | [] | [
679,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
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Mathlib/Data/List/BigOperators/Basic.lean | map_list_prod | [] | [
695,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
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Std/Data/List/Lemmas.lean | List.modifyNth_eq_set_get? | [
{
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"tactic": "cases l <;> rfl"
},
{
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.liftPred_coe | [] | [
299,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_liftCover | [
{
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790,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | WellFounded.rank_eq | [
{
"state_after": "α : Type u\nr : α → α → Prop\na b : α\nhwf : WellFounded r\n⊢ (sup fun b => succ (Acc.rank (_ : Acc r ↑b))) = sup fun b => succ (rank hwf ↑b)",
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"tactic": "rw [r... | [
2568,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2565,
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Mathlib/Analysis/Convex/Between.lean | not_sbtw_self_right | [] | [
317,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.completeSpace | [
{
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477,
56
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471,
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Mathlib/Data/Fin/Tuple/Reflection.lean | FinVec.exists_iff | [
{
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"tactic": "simp only [Exists, Fin.exists_fin_z... | [
137,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Data/PFun.lean | PFun.prodLift_fst_comp_snd_comp | [
{
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] | [
696,
23
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692,
1
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Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuous.upperSemicontinuousOn | [] | [
709,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_sInf' | [
{
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1493,
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1492,
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Mathlib/Data/Nat/Cast/Basic.lean | eq_natCast' | [
{
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{
"st... | [
221,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
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Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.pullback_close | [
{
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137,
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129,
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Mathlib/Data/Multiset/Basic.lean | Multiset.erase_lt | [
{
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}
] | [
1075,
48
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1073,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_le_zero | [] | [
1015,
41
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1014,
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Mathlib/Order/Chain.lean | Flag.top_mem | [] | [
341,
21
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340,
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Std/Data/Array/Init/Lemmas.lean | Array.foldlM_eq_foldlM_data.aux | [
{
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40,
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31,
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Mathlib/Topology/Constructions.lean | prod_mem_nhds | [] | [
577,
31
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575,
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Mathlib/GroupTheory/OrderOfElement.lean | orderOf_pow | [] | [
716,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
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Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.cons | [] | [
49,
22
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48,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasStrictFDerivAt.continuousAt | [] | [
752,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
11
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epi | [] | [
877,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
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Mathlib/Algebra/Hom/Units.lean | Units.map_id | [
{
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103,
71
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103,
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Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_strictMono | [
{
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189,
80
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185,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_id | [] | [
448,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
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Mathlib/Analysis/Normed/Order/Lattice.lean | lipschitzWith_sup_right | [
{
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"state_before": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\nz x y : α\n⊢ dist (x ⊔ z) (y ⊔ z) ≤ ↑1 * dist x y",
"tactic": "rw [NNReal.coe_one, one_mul, dist_eq_norm, dist_eq_norm]"
},
... | [
201,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.IccExtend_right | [] | [
130,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/Data/Finset/Basic.lean | Finset.not_mem_empty | [
{
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"tactic": "simp only [mem_def, empty_val, not_mem_zero, not_false_iff]"
}
] | [
553,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSet_top | [] | [
476,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
24
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.HeapNode.WellFormed.realSize_eq | [
{
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"state_before": "α : Type u_1\nle : α → α → Bool\na a✝² : ... | [
438,
40
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433,
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Mathlib/Algebra/Order/Ring/Defs.lean | Antitone.mul_const | [] | [
286,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/List/Basic.lean | List.takeWhile_eq_self_iff | [
{
"state_after": "case nil\nι : Type ?u.399470\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : List α\n⊢ takeWhile p [] = [] ↔ ∀ (x : α), x ∈ [] → p x = true\n\ncase cons\nι : Type ?u.399470\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : Lis... | [
3639,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3636,
1
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.hasColimitsOfSize_shrink | [] | [
1199,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
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Mathlib/Data/Sigma/Basic.lean | Sigma.exists | [] | [
97,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/GroupTheory/Submonoid/Center.lean | Submonoid.mem_center_iff | [] | [
58,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.Memℒp.snorm_indicator_le | [
{
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401,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Antivary.sum_mul_eq_sum_comp_perm_mul_iff | [] | [
534,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.ext | [] | [
395,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.sub_def | [] | [
345,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_le_of_isEmpty_rightMoves | [] | [
692,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Set/Prod.lean | Set.Nonempty.snd | [] | [
317,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_map_eq_of_injective | [] | [
384,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kronecker_assoc | [] | [
368,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_fract_right | [] | [
188,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Topology/PathConnected.lean | JoinedIn.symm | [
{
"state_after": "case intro\nX : Type u_1\nY : Type ?u.621994\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.622009\nF : Set X\nh : JoinedIn F x y\nhx : x ∈ F\nhy : y ∈ F\n⊢ JoinedIn F y x",
"state_before": "X : Type u_1\nY : Type ?u.621994\ninst✝¹ : TopologicalSpace X\nin... | [
884,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.eq_iff | [] | [
103,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
11
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.biUnion_top | [
{
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326,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.trace_kronecker | [] | [
379,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_sub_int_mul_two_pi | [] | [
371,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_eq_left_inv | [] | [
155,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ tan (π / 2) = 0",
"tactic": "simp [tan_eq_sin_div_cos]"
}
] | [
936,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Data/Quot.lean | Quot.liftOn_mk | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.derivative_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑Polynomial.derivative (bernsteinPolynomial R n 0) = -↑n * bernsteinPolynomial R (n - 1) 0",
"tactic": "simp [bernsteinPolynomial, Polynomial.derivative_pow]"
}
] | [
149,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq | [
{
"state_after": "ctx : Context\nc d : ExprCnstr\nh✝ : (toNormPoly c == toPoly d) = true\nh : PolyCnstr.denote ctx (toNormPoly c) = PolyCnstr.denote ctx (toPoly d)\n⊢ denote ctx c = denote ctx d",
"state_before": "ctx : Context\nc d : ExprCnstr\nh : (toNormPoly c == toPoly d) = true\n⊢ denote ctx c = denote... | [
718,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
715,
1
] |
Mathlib/Topology/Maps.lean | Inducing.dense_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.6389\nδ : Type ?u.6392\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : Inducing f\ns : Set α\n⊢ Dense s ↔ ∀ (x : α), f x ∈ closure (f '' s... | [
180,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ici_basis_Ico | [] | [
1778,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1776,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_neg_coe_nonpos_of_nonneg_of_le_pi | [
{
"state_after": "θ : ℝ\nh0 : 0 ≤ θ\nhpi : θ ≤ π\n⊢ 0 ≤ sin ↑θ",
"state_before": "θ : ℝ\nh0 : 0 ≤ θ\nhpi : θ ≤ π\n⊢ sign (-↑θ) ≤ 0",
"tactic": "rw [sign, sign_nonpos_iff, sin_neg, Left.neg_nonpos_iff]"
},
{
"state_after": "no goals",
"state_before": "θ : ℝ\nh0 : 0 ≤ θ\nhpi : θ ≤ π\n⊢ 0 ≤ sin... | [
988,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.gcd_to_nat_aux | [
{
"state_after": "n : ℕ\na : PosNum\nb : Num\nab : pos a ≤ b\nh : natSize (pos a * b) ≤ Nat.succ n\n⊢ ↑(gcdAux n (b % pos a) (pos a)) = Nat.gcd ↑a ↑b",
"state_before": "n : ℕ\na : PosNum\nb : Num\nab : pos a ≤ b\nh : natSize (pos a * b) ≤ Nat.succ n\n⊢ ↑(gcdAux (Nat.succ n) (pos a) b) = Nat.gcd ↑(pos a) ↑b"... | [
1696,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1674,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.IsAdjMatrix.apply_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.6455\nA : Matrix V V α\ninst✝¹ : MulZeroOneClass α\ninst✝ : Nontrivial α\nh : IsAdjMatrix A\ni j : V\n⊢ ¬A i j = 0 ↔ A i j = 1",
"tactic": "rw [← apply_ne_one_iff h, Classical.not_not]"
}
] | [
78,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
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