file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/QuadraticForm/Isometry.lean | QuadraticForm.Equivalent.symm | [] | [
114,
27
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113,
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Mathlib/Deprecated/Subring.lean | isSubring_iUnion_of_directed | [] | [
95,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Lattice.lean | inf_ind | [] | [
869,
23
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.congr_of_eventuallyEq | [] | [
899,
72
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Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.nullHomotopicMap'_f_of_not_rel_left | [
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Mathlib/Algebra/GroupPower/Order.lean | lt_of_pow_lt_pow | [] | [
607,
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Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Colimit.ι_map_apply' | [] | [
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Mathlib/Analysis/NormedSpace/BanachSteinhaus.lean | banach_steinhaus | [
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Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.dual_left | [] | [
232,
5
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Std/Data/Rat/Lemmas.lean | Rat.ofScientific_def | [
{
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Mathlib/Data/PNat/Interval.lean | PNat.Ico_eq_finset_subtype | [] | [
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Mathlib/Computability/RegularExpressions.lean | RegularExpression.rmatch_iff_matches' | [
{
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398,
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Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.s_as_blocks | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Lemmas.lean | Nat.mul_right_comm | [
{
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] | [
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Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.mkDerivation_X | [] | [
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22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/RingQuot.lean | RingQuot.ringQuot_ext | [
{
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Mathlib/Order/MinMax.lean | max_associative | [] | [
292,
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Mathlib/Order/JordanHolder.lean | JordanHolderLattice.second_iso_of_eq | [
{
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115,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | Basis.coe_toOrthonormalBasis | [
{
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edge_other_ne | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Hom/Basic.lean | OrderEmbedding.le_map_sup | [] | [
1193,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/ModEq.lean | Nat.modEq_iff_dvd | [
{
"state_after": "no goals",
"state_before": "m n a b c d : ℕ\n⊢ a ≡ b [MOD n] ↔ ↑n ∣ ↑b - ↑a",
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}
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Mathlib/Data/Prod/Basic.lean | Prod.forall' | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finsupp/Fin.lean | Finsupp.cons_ne_zero_of_right | [
{
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"tactic": "contrapose! h wi... | [
89,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Projection.lean | finrank_orthogonal_span_singleton | [
{
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1129,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tensorTensorTensorComm_symm | [
{
"state_after": "case h\nR : Type u_5\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1128882\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1128888\ninst✝¹² : Semiring R''\nM : Type u_1\nN : Type u_2\nP : Type u_3\nQ : Type u_4\nS : Type ?u.1128906\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoid P\... | [
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Mathlib/RingTheory/PolynomialAlgebra.lean | matPolyEquiv_coeff_apply | [
{
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Mathlib/RingTheory/NonZeroDivisors.lean | mul_cancel_left_coe_nonZeroDivisors | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Regularity/Equitabilise.lean | Finpartition.card_parts_equitabilise | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Skeletal.lean | CategoryTheory.ThinSkeleton.skeletal | [] | [
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80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | List.Nat.mem_antidiagonalTuple | [
{
"state_after": "case h0.zero\nk : ℕ\n⊢ Fin.elim0 ∈ antidiagonalTuple 0 Nat.zero ↔ ∑ i : Fin 0, Fin.elim0 i = Nat.zero\n\ncase h0.succ\nk n✝ : ℕ\n⊢ Fin.elim0 ∈ antidiagonalTuple 0 (Nat.succ n✝) ↔ ∑ i : Fin 0, Fin.elim0 i = Nat.succ n✝",
"state_before": "case h0\nk n : ℕ\n⊢ Fin.elim0 ∈ antidiagonalTuple 0 n... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/Algebra/Hom/Units.lean | Units.coe_map_inv | [] | [
91,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/RingTheory/NonZeroDivisors.lean | nonZeroDivisors.ne_zero | [] | [
87,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Std/Data/List/Lemmas.lean | List.enumFrom_map_fst | [] | [
1956,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1953,
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Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.posDef_pi_iff | [
{
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.lieSpan_eq | [] | [
639,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
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Mathlib/Data/Int/Units.lean | Int.eq_one_or_neg_one_of_mul_eq_neg_one' | [
{
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"tactic": "rcases isUnit_eq_one_or (IsUnit.mul_iff.mp (Int.isUnit_... | [
80,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.compactOpen_le_induced | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | smooth_barycentric_coord | [] | [
54,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_self | [
{
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"tactic": "simp [uIcc]"
}
] | [
896,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.sum_map_singleton | [
{
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.159176\nα : Type u_1\nβ : Type ?u.159182\nγ... | [
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46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.range_val | [] | [
1021,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
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Std/Data/Fin/Lemmas.lean | Fin.modn_val | [] | [
18,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
17,
9
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_inf_prod | [] | [
1707,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
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Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.right_inv | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Artinian.lean | IsArtinianRing.localization_artinian | [] | [
445,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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Mathlib/Order/BooleanAlgebra.lean | inf_sdiff_inf | [
{
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"tactic": "rw [inf_comm, inf_inf_sdiff]"
}
] | [
114,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mp_mem | [] | [
176,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | cycleType_finRotate | [
{
"state_after": "n : ℕ\n⊢ ↑[n + 2] = {n + 2}",
"state_before": "n : ℕ\n⊢ cycleType (finRotate (n + 2)) = {n + 2}",
"tactic": "rw [isCycle_finRotate.cycleType, support_finRotate, ← Fintype.card, Fintype.card_fin]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑[n + 2] = {n + 2}",... | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_inj | [] | [
176,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsMaximal.eq_of_le | [] | [
317,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/ModelTheory/Order.lean | FirstOrder.Language.realize_denselyOrdered | [] | [
277,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_rec' | [] | [
584,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.forget_obj_left | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Coalgebra.mono_of_mono | [] | [
394,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Algebra/Algebra/RestrictScalars.lean | RestrictScalars.ringEquiv_algebraMap | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Order/Filter/CountableInter.lean | EventuallyLE.countable_iUnion | [] | [
79,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_natAbs_valMinAbs | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\nthis : ↑(val a) - ↑n ≤ 0\n⊢ ↑(Int.natAbs (valMinAbs a)) = if val a ≤ n / 2 then a else -a",
"state_before": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ ↑(Int.natAbs (valMinAbs a)) = if val a ≤ n / 2 then a else -a",
"tactic": "have : (a.val : ℤ) - n ≤ 0... | [
1013,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ 2 • θ = 0 ↔ θ = 0 ∨ θ = ↑π",
"tactic": "convert two_nsmul_eq_iff <;> simp"
}
] | [
199,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.isOpenMap | [] | [
315,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
11
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.not_isPrime_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI✝ : Ideal α\na b : α\nI : Ideal α\n⊢ (I = ⊤ ∨ ∃ x x_1 h, ¬x ∈ I ∧ ¬x_1 ∈ I) ↔ I = ⊤ ∨ ∃ x _hx y _hy, x * y ∈ I",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI✝ : Ideal α\na b : α\nI : Ideal α\n⊢ ¬IsPrime I ↔ I = ⊤ ∨ ∃ x _hx y _h... | [
276,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.congr_arg | [] | [
158,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
11
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_symm_smul | [] | [
817,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_starAe | [] | [
1185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/AlgebraicGeometry/RingedSpace.lean | AlgebraicGeometry.RingedSpace.basicOpen_of_isUnit | [
{
"state_after": "case a\nX : RingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nf : ↑(X.presheaf.obj U.op)\nhf : IsUnit f\n⊢ basicOpen X f ≤ U\n\ncase a\nX : RingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nf : ↑(X.presheaf.obj U.op)\nhf : IsUnit f\n⊢ U ≤ basicOpen X f",
"state_before": "X : RingedSpace\nU : Opens... | [
254,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegrable_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.578469\n𝕜 : Type ?u.578472\nE : Type u_1\nF : Type ?u.578478\nA : Type ?u.578481\ninst✝¹ : NormedAddCommGroup E\nf : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\ninst✝ : NoAtoms μ\n⊢ IntervalIntegrable f μ a b ↔ IntegrableOn f [[a, b]]",
"tactic... | [
101,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_fin_cons | [
{
"state_after": "ι : Type u'\nι' : Type ?u.1242248\nR : Type ?u.1242251\nK : Type u_1\nM : Type ?u.1242257\nM' : Type ?u.1242260\nM'' : Type ?u.1242263\nV : Type u\nV' : Type ?u.1242268\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module K V\ninst✝ : Module K V'\nv✝ : ι... | [
1235,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_sub_cancel_of_le | [
{
"state_after": "case inl\nα : Type ?u.129526\nβ : Type ?u.129529\nγ : Type ?u.129532\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nh : b ≤ a\ne : a - b = 0\n⊢ b + (a - b) ≤ a\n\ncase inr.inl.intro\nα : Type ?u.129526\nβ : Type ?u.129529\nγ : Type ?u.129532\nr : α → α → Prop\ns : β → β ... | [
572,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
11
] |
Mathlib/Order/Partition/Equipartition.lean | Finpartition.indiscrete_isEquipartition | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nhs : s ≠ ∅\n⊢ Set.EquitableOn {s} Finset.card",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nhs : s ≠ ∅\n⊢ IsEquipartition (indiscrete hs)",
"tactic": "rw [IsEquipartit... | [
83,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_smul | [] | [
360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_const_smul | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.470041\nG : Type ?u.470044\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\n𝕜 : Type u_3\n𝕜' : Type ?u.470082\ninst✝⁵ : NormedRing 𝕜\ninst✝⁴ : Nor... | [
474,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_iUnion_ae | [] | [
263,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/List/Basic.lean | List.foldl_map' | [
{
"state_after": "case nil\nι : Type ?u.234160\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα β : Type u\ng : α → β\nf : α → α → α\nf' : β → β → β\nh : ∀ (x y : α), f' (g x) (g y) = g (f x y)\na : α\n⊢ foldl f' (g a) (map g []) = g (foldl f a [])\n\ncase cons\nι : Type ?u.234160\nα✝ : Typ... | [
2477,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2472,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_mul_cancel_right | [] | [
418,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_le_add_iff_right | [] | [
701,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableWithinAt.sin | [] | [
1006,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.face_points | [] | [
841,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.finite_spans_dense | [
{
"state_after": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type ?u.887976\ninst✝¹ : (i : ι) → NormedAddCommGroup (G i)\ninst✝ : (i : ι) → InnerProductSpace 𝕜 (G i)\nb : HilbertBasis ι 𝕜 E\n⊢ t... | [
541,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.mod_to_int | [
{
"state_after": "n : PosNum\nd : ZNum\n⊢ ↑(↑(Num.pos n) % natAbs ↑d) = ↑↑n % ↑d",
"state_before": "n : PosNum\nd : ZNum\n⊢ ↑(Num.pos n % abs d) = ↑(pos n) % ↑d",
"tactic": "rw [← Num.to_nat_to_int, cast_pos, Num.mod_to_nat, ← PosNum.to_nat_to_int, abs_to_nat]"
},
{
"state_after": "no goals",
... | [
1769,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1759,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.smul_sup | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.197400\nR : Type u_2\nR' : Type ?u.197406\nE : Type u_1\nF : Type ?u.197412\nG : Type ?u.197415\ninst✝³ : AddGroup E\ninst✝² : SMul R ℝ\ninst✝¹ : SMul R ℝ≥0\ninst✝ : IsScalarTower R ℝ≥0 ℝ\nr : R\np q : NonarchAddGroupSeminorm E\nx y : ℝ\n⊢ r • max x ... | [
732,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.eq_padicNorm | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\n⊢ ↑(↑padicNormE ↑q) = ↑(padicNorm p q)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\n⊢ ‖↑q‖ = ↑(padicNorm p q)",
"tactic": "dsimp [norm]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ... | [
836,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Order/Bounds/Basic.lean | BddAbove.bddBelow_image2_of_bddAbove | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Antitone (swap f b)\nh₁ : ∀ (a : α), Monotone (f a)\na : α\nha : a ∈ upperBounds s\nb : β\nhb : b... | [
1536,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1533,
1
] |
Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.coe_zero | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Topology/SubsetProperties.lean | nonempty_preirreducible_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.187622\nπ : ι → Type ?u.187627\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns✝ t✝ : Set α\ninst✝ : PreirreducibleSpace α\ns t : Set α\n⊢ IsOpen s → IsOpen t → Set.Nonempty s → Set.Nonempty t → Set.Nonempty (s ∩ t... | [
1848,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1845,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.zero_of_padicNorm_eq_zero | [
{
"state_after": "case a\np : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nh : padicNorm p q = 0\n⊢ ¬q = 0 → False",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nh : padicNorm p q = 0\n⊢ q = 0",
"tactic": "apply by_contradiction"
},
{
"state_after": "case a\np : ℕ\nhp : Fact (Nat.Prime p)\nq : ... | [
149,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.coe_neg | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_rec | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.94667\nδ : Type ?u.94670\nσ : Type ?u.94673\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : α → β\ng : α → ℕ × β → β\nhf : Primrec f\nhg : Primrec₂ g\nn : ℕ\n⊢ Nat.rec 0\n (... | [
578,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_mul_right_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.87422\nα : Type u_1\nβ : Type ?u.87428\n𝕜 : Type ?u.87431\nE : Type ?u.87434\ninst✝ : CancelCommMonoid α\ns : Set α\na : α\nhs : MulSalemSpencer ((fun x => x * a) '' s)\nb c d : α\nhb : b ∈ s\nhc : c ∈ s\nhd : d ∈ s\nh : b * c = d * d\n⊢ b * a * (c ... | [
211,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.isOpen_cylinder | [
{
"state_after": "E : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\nx : (n : ℕ) → E n\nn : ℕ\n⊢ IsOpen (Set.pi ↑(Finset.range n) fun i => {x i})",
"state_before": "E : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTo... | [
365,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | ne₂₃_of_not_collinear | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.309152\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ : P\nh : ¬Collinear k {p₁, p₂, p₂}\n⊢ False",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.309152\ni... | [
509,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_cells | [] | [
82,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/List.lean | List.continuous_removeNth | [] | [
163,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivWithinAt.clm_comp | [] | [
73,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsDetector.isSeparator | [] | [
441,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_empty | [] | [
94,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_le_div_iff_le_mul | [] | [
829,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Data/Vector3.lean | Vector3.cons_fs | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.const_mul | [] | [
279,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.noZeroDivisors_fin | [] | [
1097,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.not_sOppSide | [] | [
657,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
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