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/Data/Real/Irrational.lean | irrational_iff_ne_rational | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ Irrational x ↔ ∀ (a b : ℤ), x ≠ ↑a / ↑b",
"tactic": "simp only [Irrational, Rat.forall, cast_mk, not_exists, Set.mem_range, cast_coe_int, cast_div,\n eq_comm]"
}
] | [
37,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eqOn_open_of_ae_eq | [
{
"state_after": "X : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\nm : MeasurableSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\nμ ν : Measure X\ninst✝ : IsOpenPosMeasure μ\ns U : Set X\nx : X\nf g : X → Y\nhU : IsOpen U\nhf : ContinuousOn f U\nhg : ContinuousOn g U\nh : ∀ᵐ (x : X) ∂μ, x ∈ U →... | [
104,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_eq_zero | [
{
"state_after": "case mp\nC : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasZeroMorphisms C\nX Y : C\nP : Subobject Y\nf : X ⟶ Y\nh : Factors P f\n⊢ factorThru P f h = 0 → f = 0\n\ncase mpr\nC : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category ... | [
158,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/Data/Complex/Basic.lean | Complex.rat_cast_im | [
{
"state_after": "no goals",
"state_before": "q : ℚ\n⊢ (↑q).im = 0",
"tactic": "rw [← ofReal_rat_cast, ofReal_im]"
}
] | [
873,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | UniformSpace.secondCountable_of_separable | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\ninst✝² : UniformSpace α\ninst✝¹ : IsCountablyGenerated (𝓤 α)\ninst✝ : SeparableSpace α\ns : Set α\nhsc : Set.Countable s\nhsd : Dense s\n⊢ SecondCountableTopology α",
"state_before": "α : Type u\nβ : Type v\ninst✝² : UniformSpace α\ninst✝¹ : IsCou... | [
775,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Data/List/Basic.lean | List.takeD_eq_take | [] | [
2364,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2362,
1
] |
Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.monic_generator_eq_minpoly | [
{
"state_after": "case pos\n𝕜 : Type u_1\nA : Type u_2\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\ninst✝ : Algebra 𝕜 A\na : A\np : 𝕜[X]\np_monic : Monic p\np_gen : Ideal.span {p} = annIdeal 𝕜 a\nh : p = 0\n⊢ annIdealGenerator 𝕜 a = p\n\ncase neg\n𝕜 : Type u_1\nA : Type u_2\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\nin... | [
181,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_nonneg | [] | [
479,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeEquivCodomain_symm_apply | [] | [
1385,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
] |
Mathlib/Data/List/FinRange.lean | Equiv.Perm.ofFn_comp_perm | [
{
"state_after": "n : ℕ\nα : Type u\nσ : Perm (Fin n)\nf : Fin n → α\n⊢ map f (map (↑σ) (finRange n)) ~ map f (finRange n)",
"state_before": "n : ℕ\nα : Type u\nσ : Perm (Fin n)\nf : Fin n → α\n⊢ ofFn (f ∘ ↑σ) ~ ofFn f",
"tactic": "rw [ofFn_eq_map, ofFn_eq_map, ← map_map]"
},
{
"state_after": "n... | [
89,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.sum | [] | [
361,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Order/LatticeIntervals.lean | Set.Iic.coe_bot | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_compContinuous_le | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.1066082\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : SeminormedAddCommGroup β\nf✝ g✝ : α →ᵇ β\nx : α\nC : ℝ\ninst✝ : TopologicalSpace γ\nf : α →ᵇ β\ng : C(γ, α)\n⊢ ↑1 * dist f 0 ≤ ‖f‖",
"tactic": "rw [NNReal.coe_one,... | [
1044,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.ring_inverse_ring_inverse | [] | [
49,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Order/WithBot.lean | WithTop.monotone_iff | [] | [
1124,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_top_of_mul_ne_top_right | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.92309\nβ : Type ?u.92312\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a * b ≠ ⊤\nha : a ≠ 0\n⊢ b * a ≠ ⊤",
"tactic": "rwa [mul_comm]"
}
] | [
595,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovaryOn_univ | [] | [
79,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_def | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ c a b : Ordinal\n⊢ a ♯ b = max (blsub a fun a' x => a' ♯ b) (blsub b fun b' x => a ♯ b')",
"tactic": "rw [nadd]"
}
] | [
213,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.symm_symm | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\nP : Type w₂\ninst✝¹⁴ : CommRing R\ninst✝¹³ : LieRing L\ninst✝¹² : LieAlgebra R L\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : AddCommGroup N\ninst✝⁹ : AddCommGroup P\ninst✝⁸ : Module R M\ninst✝⁷ : Module R N\ninst✝⁶ : Mod... | [
1080,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | Monotone.div_const | [
{
"state_after": "ι : Type ?u.113111\nα : Type u_2\nβ✝ : Type ?u.113117\ninst✝¹ : LinearOrderedSemifield α\na b c✝ d e : α\nm n : ℤ\nβ : Type u_1\ninst✝ : Preorder β\nf : β → α\nhf : Monotone f\nc : α\nhc : 0 ≤ c\nthis : DecidableRel fun x x_1 => x ≤ x_1\n⊢ Monotone fun x => f x / c",
"state_before": "ι : T... | [
582,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_toNNReal | [] | [
179,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.reduce_isReduced | [
{
"state_after": "u✝ x✝ : XgcdType\nu : XgcdType := x✝\nh : r u = 0\n⊢ IsReduced (finish u)",
"state_before": "u✝ x✝ : XgcdType\nu : XgcdType := x✝\nh : r u = 0\n⊢ IsReduced (reduce x✝)",
"tactic": "rw [reduce_a h]"
},
{
"state_after": "no goals",
"state_before": "u✝ x✝ : XgcdType\nu : XgcdT... | [
370,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Topology/Constructions.lean | isClosedMap_ofMul | [] | [
118,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.incl_apply | [] | [
1116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.div_self | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.48815\nG : Type ?u.48818\nα : Type u_1\nM : Type ?u.48824\nN : Type ?u.48827\ninst✝ : DivisionMonoid α\na b c : α\nh : IsUnit a\n⊢ a / a = 1",
"tactic": "rw [div_eq_mul_inv, h.mul_inv_cancel]"
}
] | [
314,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
11
] |
Mathlib/Analysis/MeanInequalities.lean | Real.Lp_add_le_of_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nf g : ι → ℝ\np q : ℝ\nhp : 1 ≤ p\nhf : ∀ (i : ι), i ∈ s → 0 ≤ f i\nhg : ∀ (i : ι), i ∈ s → 0 ≤ g i\n⊢ (∑ i in s, (f i + g i) ^ p) ^ (1 / p) ≤ (∑ i in s, f i ^ p) ^ (1 / p) + (∑ i in s, g i ^ p) ^ (1 / p)",
"tactic": "convert Lp_add_... | [
666,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.comap_equiv_eq_map_symm | [] | [
843,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_one | [
{
"state_after": "case a.h\nl : Type ?u.318419\nm : Type u_2\nn : Type u_1\no : Type ?u.318428\nm' : o → Type ?u.318433\nn' : o → Type ?u.318438\nR : Type ?u.318441\nS : Type ?u.318444\nα : Type v\nβ : Type w\nγ : Type ?u.318451\ninst✝² : NonAssocSemiring α\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nM : Matrix... | [
1115,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
11
] |
Mathlib/Deprecated/Ring.lean | IsRingHom.to_isSemiringHom | [] | [
136,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofSubmodule'_symm_apply | [] | [
2088,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2086,
1
] |
Mathlib/Order/BooleanAlgebra.lean | le_sdiff_iff | [] | [
329,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | Subalgebra.rank_bot | [
{
"state_after": "K : Type u\nV : Type v\nF : Type u_2\nE : Type u_1\ninst✝⁵ : CommRing F\ninst✝⁴ : Ring E\ninst✝³ : Algebra F E\ninst✝² : StrongRankCondition F\ninst✝¹ : NoZeroSMulDivisors F E\ninst✝ : Nontrivial E\nthis : Nontrivial F := Module.nontrivial F E\n⊢ Module.rank F { x // x ∈ span F {1} } = 1",
... | [
567,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.pointwise_smul_subset_iff | [] | [
127,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Std/Data/List/Lemmas.lean | List.map_add_range' | [
{
"state_after": "no goals",
"state_before": "a s n step : Nat\n⊢ map (fun x => a + x) (range' s (n + 1) step) = range' (a + s) (n + 1) step",
"tactic": "simp [range', map_add_range' _ (s + step) n step, Nat.add_assoc]"
}
] | [
1830,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1828,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.incl_range | [
{
"state_after": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\n⊢ (LieHom.range (incl K)).toSubmodule = K.toSubmodule",
"state_before": "R... | [
377,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Topology/Constructions.lean | discreteTopology_subtype_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.13446\nδ : Type ?u.13449\nε : Type ?u.13452\nζ : Type ?u.13455\ninst✝ : TopologicalSpace α\nS : Set α\n⊢ DiscreteTopology ↑S ↔ ∀ (x : α), x ∈ S → 𝓝[{x}ᶜ] x ⊓ 𝓟 S = ⊥",
"tactic": "simp_rw [discreteTopology_iff_nhds_ne, Se... | [
250,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/PFun.lean | PFun.mem_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.13942\nδ : Type ?u.13945\nε : Type ?u.13948\nι : Type ?u.13951\nf : α →. β\ns : Set α\nh : s ⊆ Dom f\na : α\nb : β\n⊢ b ∈ restrict f h a ↔ a ∈ s ∧ b ∈ f a",
"tactic": "simp [restrict]"
}
] | [
184,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.inter | [] | [
90,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.comp_one | [] | [
499,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.inf | [] | [
570,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Topology/Algebra/StarSubalgebra.lean | elementalStarAlgebra.starAlgHomClass_ext | [
{
"state_after": "R : Type u_3\nA : Type u_4\nB : Type u_1\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : StarRing R\ninst✝¹² : TopologicalSpace A\ninst✝¹¹ : Semiring A\ninst✝¹⁰ : StarRing A\ninst✝⁹ : TopologicalSemiring A\ninst✝⁸ : ContinuousStar A\ninst✝⁷ : Algebra R A\ninst✝⁶ : StarModule R A\ninst✝⁵ : TopologicalSpac... | [
237,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Topology/NhdsSet.lean | disjoint_principal_nhdsSet | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8192\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ Disjoint (𝓟 s) (𝓝ˢ t) ↔ Disjoint (closure s) t",
"tactic": "rw [disjoint_principal_left, ← subset_interior_iff_mem_nhdsSet, interior_... | [
65,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_le_of_compl_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.56679\nw x y z : α\ninst✝ : BooleanAlgebra α\nh : yᶜ ≤ x\n⊢ xᶜ ≤ y",
"tactic": "simpa only [compl_compl] using compl_le_compl h"
}
] | [
691,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Init/Algebra/Order.lean | gt_of_ge_of_gt | [] | [
139,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_apply_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nα : Type u_2\nG : SimpleGraph α\ninst✝¹ : MulZeroOneClass R\na b : α\ne : Sym2 α\ninst✝ : Nontrivial R\n⊢ incMatrix R G a e = 0 ↔ ¬e ∈ incidenceSet G a",
"tactic": "simp only [incMatrix_apply, Set.indicator_apply_eq_zero, Pi.one_apply, one_ne_z... | [
105,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | AddEquiv.map_dfinsupp_sumAddHom | [] | [
2360,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2357,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | mul_le_mul_of_mul_div_le | [
{
"state_after": "ι : Type ?u.106331\nα : Type u_1\nβ : Type ?u.106337\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : a * b / c ≤ d\nhc : 0 < c\n⊢ b * a ≤ d * c",
"state_before": "ι : Type ?u.106331\nα : Type u_1\nβ : Type ?u.106337\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\n... | [
558,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.symm_mulLeft | [] | [
115,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.finSuccEquiv_comp_C_eq_C | [
{
"state_after": "R✝ : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.975050\na a' a₁ a₂ : R✝\ne : ℕ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R✝\nn✝ : ℕ\nR : Type u\ninst✝ : CommSemiring R\nn : ℕ\nx : R\n⊢ ↑(RingHom.comp (↑(AlgEquiv.symm (finSuccEquiv R n))) (RingHom.comp Polynomial.C C)) x = ↑C x",
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351,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.span_singleton_sup_orthogonal_eq_top | [
{
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53
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | AffineSubspace.angle_coe | [] | [
70,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Ico | [
{
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1111,
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1021,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_iff_div_isBoundedUnder | [
{
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2004,
51
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1995,
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Mathlib/Data/Finsupp/Multiset.lean | Finsupp.prod_toMultiset | [
{
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107,
23
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100,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_alls | [
{
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898,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
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Std/Data/String/Lemmas.lean | String.foldlAux_of_valid | [
{
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687,
95
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680,
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Mathlib/Data/Int/Units.lean | Int.isUnit_eq_one_or | [] | [
37,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.smul | [] | [
994,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
11
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Mathlib/Data/Nat/Parity.lean | Nat.two_mul_div_two_add_one_of_odd | [
{
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"state_before": "m n : ℕ\nh : Odd n\n⊢ 2 * (n / 2) + 1 = n",
"tactic": "rw [← odd_iff.mp h, div_add_mod]"
}
] | [
231,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.smul_zero | [
{
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"tactic": "simpa [mem_smul] using hs"
... | [
2104,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2103,
1
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.a_mem_nhdsWithin_Ioi | [
{
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... | [
497,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
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Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.mul_rat | [
{
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"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith... | [
130,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.tendsto_atTop_iff | [] | [
318,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_empty' | [] | [
214,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.symm_dual_comp | [] | [
860,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Algebra/Associated.lean | Irreducible.ne_zero | [] | [
207,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Logic/Pairwise.lean | Set.Pairwise.eq | [] | [
77,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
src/lean/Init/Control/Lawful.lean | ExceptT.run_lift | [] | [
110,
136
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
110,
9
] |
Mathlib/Order/PFilter.lean | Order.PFilter.ext | [] | [
101,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.id_right | [] | [
62,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mem_span_image_iff_total | [
{
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696,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.right_mem_Icc | [] | [
126,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.compLinearMap_inj | [] | [
599,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Tactic/Congr!.lean | implies_congr' | [
{
"state_after": "case refl\nα : Sort u\nβ β' : Sort v\nh' : α → β = β'\n⊢ (α → β) = (α → β')",
"state_before": "α α' : Sort u\nβ β' : Sort v\nh : α = α'\nh' : α' → β = β'\n⊢ (α → β) = (α' → β')",
"tactic": "cases h"
},
{
"state_after": "case refl\nα : Sort u\nβ β' : Sort v\nh' : α → β = β'\n⊢ (... | [
648,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
9
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_sub | [] | [
637,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.conjLie_apply | [] | [
317,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.Term.listEncode_injective | [] | [
120,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Subsemigroup.coe_centralizer | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_iff_forall_nat_le | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1481,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.zero_shiftl | [] | [
452,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.int_cast_mod | [
{
"state_after": "a : ℤ\nb : ℕ\n⊢ a % ↑b ≡ a [ZMOD ↑b]",
"state_before": "a : ℤ\nb : ℕ\n⊢ ↑(a % ↑b) = ↑a",
"tactic": "rw [ZMod.int_cast_eq_int_cast_iff]"
},
{
"state_after": "no goals",
"state_before": "a : ℤ\nb : ℕ\n⊢ a % ↑b ≡ a [ZMOD ↑b]",
"tactic": "apply Int.mod_modEq"
}
] | [
554,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.mem_sym_iff | [
{
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163,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.isSFiniteKernel_sum_of_denumerable | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nι : Type u_1\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\ninst✝ : Denumerable ι\nκs : ι → { x // x ∈ kernel α β }\nhκs : ∀ (n : ι), IsSFiniteKernel (κs n)\ne : ℕ ≃ ι × ℕ := (Denumerable.eqv (ι × ℕ)).symm\n⊢ IsSFiniteKernel (kernel.su... | [
329,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ici_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : Preorder α\ninst✝ : OrderTopology α\na : α\nha : ∃ u, a < u\n⊢ 𝓝[Ici a] a = ⨅ (u : α) (_ : a < u), 𝓟 (Ico a u)",
"tactic": "simp only [nhdsWithin_Ici_eq'', biInf_inf ha, inf_principa... | [
1097,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.add_div | [
{
"state_after": "m n a✝ b✝ c✝ d a b c : ℕ\nhc0 : 0 < c\n⊢ (a + b) % c + a % c + b % c + c * ((a + b) / c) =\n (a + b) % c + a % c + b % c + c * (a / c + b / c + if c ≤ a % c + b % c then 1 else 0)",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhc0 : 0 < c\n⊢ (a + b) / c = a / c + b / c + if c ≤ a % c + b ... | [
458,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ratCast_re | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6514218\ninst✝ : IsROrC K\nq : ℚ\n⊢ ↑re ↑q = ↑q",
"tactic": "rw [← ofReal_ratCast, ofReal_re]"
}
] | [
682,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.antidiagonal_succ | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ¬(0, n + 1) ∈\n map (Function.Embedding.prodMap { toFun := Nat.succ, inj' := Nat.succ_injective } (Function.Embedding.refl ℕ))\n (antidiagonal n)",
"tactic": "simp"
},
{
"state_after": "case a\nn : ℕ\n⊢ (antidiagonal (n + 1)).val... | [
61,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_empty | [] | [
1311,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_of_subset | [] | [
404,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.preimage_Icc | [
{
"state_after": "case h\nF : Type ?u.69367\nα : Type u_1\nβ : Type ?u.69373\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn : ℕ\na b : α\nhb : 0 ≤ b\nx✝ : ℕ\n⊢ x✝ ∈ Nat.cast ⁻¹' Icc a b ↔ x✝ ∈ Icc ⌈a⌉₊ ⌊b⌋₊",
"state_before": "F : Type ?u.69367\nα : Type u_1\nβ : Type ?u.69373\ninst✝¹ ... | [
407,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.subset_mul_left | [] | [
796,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.Ioo_add_bij | [
{
"state_after": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x + d) (Ioi a ∩ Iio b) (Ioi (a + d) ∩ Iio (b + d))",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x ... | [
58,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.col_eq_prod | [
{
"state_after": "case a.mk\nμ : YoungDiagram\nj a b : ℕ\n⊢ (a, b) ∈ col μ j ↔ (a, b) ∈ Finset.range (colLen μ j) ×ˢ {j}",
"state_before": "μ : YoungDiagram\nj : ℕ\n⊢ col μ j = Finset.range (colLen μ j) ×ˢ {j}",
"tactic": "ext ⟨a, b⟩"
},
{
"state_after": "case a.mk\nμ : YoungDiagram\nj a b : ℕ\n... | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/GroupTheory/Commensurable.lean | Commensurable.commensurable_inv | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\ng : ConjAct G\n⊢ Commensurable (g • H) H ↔ Commensurable H (g⁻¹ • H)",
"tactic": "rw [commensurable_conj, inv_smul_smul]"
}
] | [
85,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.card_dvd_of_surjective | [
{
"state_after": "no goals",
"state_before": "G✝ : Type ?u.118962\ninst✝⁴ : Group G✝\nH✝ K L : Subgroup G✝\nG : Type u_1\nH : Type u_2\ninst✝³ : Group G\ninst✝² : Group H\ninst✝¹ : Fintype G\ninst✝ : Fintype H\nf : G →* H\nhf : Function.Surjective ↑f\n⊢ Fintype.card H ∣ Fintype.card G",
"tactic": "simp ... | [
323,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_subset_compl_diagonal_iff_disjoint | [] | [
506,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_all_finite | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.142957\nι✝ : Sort x\nι : Type u_1\nI : Set ι\nhI : Set.Finite I\nl : Filter α\np : ι → α → Prop\n⊢ (∀ᶠ (x : α) in l, ∀ (i : ι), i ∈ I → p i x) ↔ ∀ (i : ι), i ∈ I → ∀ᶠ (x : α) in l, p i x",
"tactic": "simpa only... | [
1166,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Algebra/Bounds.lean | ciSup_div | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nG : Type u_1\ninst✝³ : Group G\ninst✝² : ConditionallyCompleteLattice G\ninst✝¹ : CovariantClass G G (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : Nonempty ι\nf : ι → G\nhf : BddAbove (range f)\na : G\n⊢ (⨆ (i : ι), f i) / a = ⨆ (i : ι)... | [
158,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_dvd_iff | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b c : α\nh : a = 0 ∨ b = 0\n⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c\n\ncase neg\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b c : α\nh : ¬(a = 0 ∨ b = 0)\n⊢ lcm a b ∣ c ↔ a ∣ c ∧ b ∣ c",
... | [
712,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.vsub_orthogonalProjection_mem_direction | [] | [
374,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
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