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Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.toString | [] | [
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingCoeff_nonzero_iff_nonzero | [] | [
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34
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.differentiable_arsinh | [] | [
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41
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Mathlib/LinearAlgebra/Dimension.lean | cardinal_le_rank_of_linearIndependent | [
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.eq_mk_of_comm | [
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Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousAt_const | [] | [
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.card_typein_out_lt | [
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Mathlib/Topology/Connected.lean | isPreconnected_iff_subset_of_disjoint | [
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.one_sub_le_one | [
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.one_re | [] | [
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_lt_coe | [] | [
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Mathlib/Algebra/Invertible.lean | div_mul_cancel_of_invertible | [] | [
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Mathlib/Topology/Order/Basic.lean | Iic_mem_nhds | [] | [
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.seq_tendstoUniformlyOn | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_iInf | [
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Mathlib/Logic/Pairwise.lean | Set.Pairwise.imp_on | [] | [
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Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_biInf_principal' | [] | [
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39
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.bot | [
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Mathlib/Order/SymmDiff.lean | sup_himp_bihimp | [
{
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Mathlib/Algebra/Algebra/RestrictScalars.lean | RestrictScalars.smul_def | [] | [
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Mathlib/Algebra/Order/Ring/Lemmas.lean | Right.one_lt_mul_of_lt_of_le_of_pos | [] | [
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Mathlib/Algebra/GroupWithZero/Defs.lean | zero_eq_mul | [
{
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_eq_zero | [
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Mathlib/Analysis/Calculus/MeanValue.lean | norm_image_sub_le_of_norm_deriv_le_segment_01' | [
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Mathlib/Algebra/BigOperators/NatAntidiagonal.lean | Finset.Nat.prod_antidiagonal_subst | [
{
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.of_injective | [
{
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Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.nonuniformWitness_spec | [
{
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.smul_induction | [
{
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.equiv_toLinearEquiv | [] | [
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Mathlib/Data/Complex/Basic.lean | Complex.mem_reProdIm | [] | [
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Mathlib/Topology/Sheaves/LocalPredicate.lean | TopCat.stalkToFiber_germ | [
{
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.map_smul'' | [] | [
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Mathlib/Order/Category/PreordCat.lean | PreordCat.coe_of | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Game/PGame.lean | PGame.Fuzzy.not_equiv | [] | [
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Mathlib/Algebra/Order/Field/Basic.lean | div_lt_div_right_of_neg | [] | [
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.norm_approxOn_y₀_le | [
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Mathlib/Topology/Semicontinuous.lean | Continuous.comp_upperSemicontinuousOn | [] | [
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.symm | [] | [
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | mem_selfAdjointMatricesSubmodule | [
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Mathlib/Algebra/Order/Floor.lean | Nat.ceil_add_one | [
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Mathlib/Order/Lattice.lean | Monotone.map_sup | [
{
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Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix'_compRight | [
{
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Mathlib/NumberTheory/Divisors.lean | Nat.mem_divisors_self | [] | [
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30
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Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.map_rangeS | [
{
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Mathlib/Analysis/BoxIntegral/Integrability.lean | MeasureTheory.SimpleFunc.box_integral_eq_integral | [] | [
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42
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Mathlib/Analysis/Normed/Group/Quotient.lean | AddSubgroup.norm_normedMk | [
{
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_one | [] | [
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.rnDeriv_withDensity | [
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Mathlib/Data/Int/Interval.lean | Int.card_fintype_Ico_of_le | [
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43
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Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagramIso_app_right | [] | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.map_rightInverse | [] | [
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Mathlib/Analysis/Convex/Gauge.lean | gauge_unit_ball | [
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457,
68
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Mathlib/Data/Complex/Exponential.lean | Complex.cos_sq' | [
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Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.mem_sdiff | [] | [
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Mathlib/Order/Partition/Finpartition.lean | Finpartition.card_bot | [] | [
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20
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Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAtFilter.add_const | [] | [
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Mathlib/Order/BooleanAlgebra.lean | compl_eq_bot | [] | [
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Mathlib/Data/Rat/Cast.lean | Rat.preimage_cast_Ioo | [
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_zero | [] | [
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Mathlib/Topology/Basic.lean | map_nhds | [] | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_singleton | [
{
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.nneg_mul_add_sq_of_abs_le_one | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Iio | [] | [
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finite.infsep | [
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_prod | [
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.support_coeff_finSuccEquiv | [
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Mathlib/Topology/Algebra/Monoid.lean | tendsto_mul | [] | [
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.inl_union_inr | [
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Mathlib/Data/Multiset/Bind.lean | Multiset.cons_product | [
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261,
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Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.LaxMonoidalFunctor.prod'_ε | [
{
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411,
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409,
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Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.isLocal_of_isMaximal_radical | [] | [
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Mathlib/Data/Set/Finite.lean | Set.finite_image_iff | [] | [
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.map | [
{
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.funCongrLeft_apply | [] | [
2658,
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Mathlib/Order/Lattice.lean | semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder | [
{
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630,
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Mathlib/Topology/Basic.lean | IsOpen.mem_nhds | [] | [
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44
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915,
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Mathlib/Data/Finset/Image.lean | Finset.image_filter | [
{
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Mathlib/Topology/Instances/RatLemmas.lean | Rat.interior_compact_eq_empty | [] | [
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_add_left | [
{
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_copy | [] | [
122,
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.adjoint_adjoint | [
{
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Mathlib/Data/Fintype/Card.lean | not_injective_infinite_finite | [] | [
1142,
45
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1141,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.InfinitePos.not_infinitesimal | [] | [
490,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
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Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_four | [
{
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127,
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_one | [] | [
427,
21
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426,
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_comp_subtype_disjoint | [
{
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390,
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Mathlib/Data/Matrix/Basic.lean | Matrix.col_add | [
{
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2657,
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2655,
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Mathlib/Order/Iterate.lean | Monotone.seq_lt_seq_of_le_of_lt | [] | [
78,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_strictMono_of_surjective | [] | [
511,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
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] |
Std/Data/Int/DivMod.lean | Int.emod_neg | [
{
"state_after": "no goals",
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"tactic": "rw [emod_def, emod_def, Int.ediv_neg, Int.neg_mul_neg]"
}
] | [
344,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
343,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | le_mul_of_le_mul_of_nonneg_left | [] | [
430,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_iff_right | [] | [
246,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Mathlib/Topology/UniformSpace/Basic.lean | closure_eq_uniformity | [
{
"state_after": "case h.mk\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.85860\ninst✝ : UniformSpace α\ns : Set (α × α)\nx y : α\n⊢ (x, y) ∈ closure s ↔ (x, y) ∈ ⋂ (V : Set (α × α)) (_ : V ∈ {V | V ∈ 𝓤 α ∧ SymmetricRel V}), V ○ s ○ V",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type... | [
943,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Data/Part.lean | Part.bind_eq_bind | [] | [
618,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/RingTheory/Henselian.lean | HenselianLocalRing.TFAE | [
{
"state_after": "case _3_2\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : LocalRing R\n⊢ (∀ {K : Type u} [inst : Field K] (φ : R →+* K),\n Surjective ↑φ →\n ∀ (f : R[X]),\n Monic f → ∀ (a₀ : K), eval₂ φ a₀ f = 0 → eval₂ φ a₀ (↑derivative f) ≠ 0 → ∃ a, IsRoot f a ∧ ↑φ a = a₀) →\n ∀ (f : R[X])... | [
159,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.mul_nat | [] | [
382,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_le_pi_nnnorm' | [] | [
2517,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2516,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.not_mem_singleton | [] | [
690,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iInf_mul_right' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.118140\nβ : Type ?u.118143\nγ : Type ?u.118146\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nι : Sort u_1\nf : ι → ℝ≥0∞\na : ℝ≥0∞\nh : a = ⊤ → (⨅ (i : ι), f i) = 0 → ∃ i, f i = 0\nh0 : a = 0 → Nonempty ι\n⊢ (⨅ (i : ι), f i * a) =... | [
507,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.zero_mul | [
{
"state_after": "case c\nR : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nr : R\ns : { x // x ∈ S }\n⊢ 0 * (r /ₒ s) = 0",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nx : OreLocalization R S\n⊢ 0 * x = 0",
"tactic": "induction' x using OreL... | [
695,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
11
] |
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