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Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix'_comp | [
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Mathlib/Algebra/Order/Ring/Defs.lean | bit1_le_bit1 | [] | [
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Mathlib/Topology/Inseparable.lean | IsClosed.not_inseparable | [] | [
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.separatingRight_iff_flip_ker_eq_bot | [
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Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.wEquiv_map | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.isCycle_pow_pos_of_lt_prime_order | [
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Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementarySubstructure.coeSubtype | [] | [
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.coe_affineMap_mk | [] | [
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Mathlib/Control/ULift.lean | PLift.map_up | [] | [
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Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.Fix.dest_mk | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isAdjointPair_iff_eq_of_nondegenerate | [] | [
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Mathlib/Data/Set/Basic.lean | Set.ite_left | [
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Mathlib/Data/Real/Sqrt.lean | Real.sqrt_lt' | [
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_le_prod | [] | [
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Mathlib/Logic/Function/Basic.lean | Function.partialInv_of_injective | [
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_hom_rel | [
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Mathlib/RingTheory/Noetherian.lean | isNoetherian_span_of_finite | [] | [
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableWithinAt.norm | [] | [
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Mathlib/Topology/ContinuousOn.lean | ContinuousOn.if | [
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Mathlib/MeasureTheory/Measure/Stieltjes.lean | MeasureTheory.tendsto_measure_Ico_atTop | [
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_mem | [] | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_subgroupOf | [] | [
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Mathlib/Topology/Order.lean | mem_nhds_induced | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux | [
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_subset_coe | [] | [
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsNormal.cof_eq | [] | [
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Mathlib/Topology/Constructions.lean | continuous_subtype_val | [] | [
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Mathlib/FieldTheory/Separable.lean | Polynomial.X_pow_sub_one_separable_iff | [
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_X | [
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Mathlib/Topology/ShrinkingLemma.lean | exists_subset_iUnion_closed_subset | [] | [
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Mathlib/RingTheory/FiniteType.lean | Algebra.FiniteType.mvPolynomial | [
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.coe_fn_mk | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_of_subset_of_measure_ge | [] | [
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Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.domRestrict₂_apply | [] | [
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Mathlib/Analysis/Normed/Group/Basic.lean | dist_one_right | [
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Mathlib/Analysis/Convex/Between.lean | wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos | [
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.affineSpan_eq_sInf | [] | [
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Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.ZeroAtFilter.boundedAtFilter | [
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.isOpenPosMeasure_of_mulLeftInvariant_of_compact | [
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Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | BoxIntegral.Box.volume_apply | [
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Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_zero_left | [] | [
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_diagonal | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_indicator_subset | [
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Mathlib/Data/Analysis/Topology.lean | Ctop.ofEquiv_val | [
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Mathlib/Data/Set/Intervals/Infinite.lean | Set.Ioo.infinite | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
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Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.mul_leftInvEquiv_symm | [
{
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218,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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src/lean/Init/Control/Lawful.lean | StateT.run_seqLeft | [
{
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286,
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284,
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.coe_add | [] | [
541,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_one | [
{
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633,
57
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632,
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.nonempty_type_iff_nonempty | [] | [
373,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_source_iso_zero' | [] | [
396,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.coe_mkFinCons | [
{
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1310,
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1304,
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Mathlib/Data/Finset/Sups.lean | Finset.sups_left_comm | [] | [
208,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
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Mathlib/RingTheory/Localization/Basic.lean | Localization.toLocalizationMap_eq_monoidOf | [] | [
1017,
6
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1016,
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Mathlib/Topology/Maps.lean | Inducing.continuousAt_iff' | [
{
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141,
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139,
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Mathlib/Order/CompleteLattice.lean | iInf_comm | [] | [
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25
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableWithinAt.ccosh | [] | [
457,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
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Mathlib/Data/List/AList.lean | AList.union_assoc | [
{
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}
] | [
488,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
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Mathlib/GroupTheory/OrderOfElement.lean | orderOf_pow'' | [
{
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"state_before": "G : Type u\nA : Type v\nx ... | [
365,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
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Mathlib/Order/Filter/Lift.lean | Filter.lift'_cong | [] | [
292,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
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Mathlib/Order/Filter/Pi.lean | Filter.pi_inf_principal_univ_pi_neBot | [
{
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}
] | [
141,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_left' | [] | [
130,
47
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128,
1
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_toMulHom | [] | [
139,
6
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138,
1
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Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.append_assoc | [
{
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467,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
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Mathlib/Order/Filter/Archimedean.lean | Filter.Tendsto.atBot_mul_neg_const' | [
{
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"tactic": "simpa only [mul_neg, tendsto_neg_atBot_iff] using hf.atBot_... | [
205,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_omega | [
{
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}
] | [
2405,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2404,
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Mathlib/Data/Set/NAry.lean | Set.mem_image2_iff | [
{
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55,
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Mathlib/Order/Monotone/Monovary.lean | Antitone.antivary | [] | [
333,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
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Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.support_gen_of_gen | [
{
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520,
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508,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.Bounded.union | [] | [
2377,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2376,
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Mathlib/Analysis/Normed/Group/Basic.lean | Filter.Tendsto.norm' | [] | [
1188,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.denumerable_iff | [
{
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"state_before": "α✝ β α : Type u\nh : (#α) = ℵ₀\n⊢ Nonempty (Denumerable α)",
"tactic": "cases' Quotient.exact h with f"
},
{
"state_after": "no goals",
"state_before": "case intro\nα✝... | [
1622,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1619,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.C_mul_prod_X_sub_C_eq | [
{
"state_after": "R : Type ?u.90291\nS : Type u_1\nF : Type ?u.90297\nK : Type ?u.90300\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝¹ : Semiring R\ninst✝ : CommRing S\nw x y z : S\n⊢ ↑C w * (X - ↑C x) * (X - ↑C y) * (X - ↑C z) =\n ↑C w * X ^ 3 + ↑C w * -(↑C x + ↑C y + ↑C z) * X ^ 2 + ↑C w * (↑C x * ↑C y + ... | [
74,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.swap_mul_self_mul | [
{
"state_after": "no goals",
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}
] | [
543,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
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Std/Data/List/Init/Lemmas.lean | List.foldrM_cons | [
{
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171,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
168,
9
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Mathlib/Algebra/Order/Ring/Abs.lean | abs_mul_self | [
{
"state_after": "no goals",
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"tactic": "rw [abs_mul, abs_mul_abs_self]"
}
] | [
57,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_iInter_ge_nat_add | [] | [
2220,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2218,
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] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.irreducible_of_mirror | [
{
"state_after": "case not_unit\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : NoZeroDivisors R\nf : R[X]\nh1 : ¬IsUnit f\nh2 : ∀ (k : R[X]), f * mirror f = k * mirror k → k = f ∨ k = -f ∨ k = mirror f ∨ k = -mirror f\nh3 : ∀ (g : R[X]), g ∣ f → g ∣ mirror f → IsUnit g\n⊢ ¬IsUnit f\n\ncase isUnit_or_isUnit'\nR : T... | [
247,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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Mathlib/Init/Function.lean | Function.right_id | [] | [
50,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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Mathlib/Topology/Basic.lean | continuous_def | [] | [
1567,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1565,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.frequently_iff | [
{
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372,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
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Mathlib/Algebra/Order/Field/Basic.lean | div_lt_div' | [] | [
400,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_inter_Ici | [] | [
643,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.star_smul | [] | [
1141,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/Order/Lattice.lean | Monotone.map_inf_le | [] | [
1104,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.range_inl | [
{
"state_after": "case h\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.35589\nM₆ : Type ?u.35592\nS : Type ?u.35595\ninst✝¹³ : Semiring R\ninst✝¹² : Semiring S\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M₂\... | [
157,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.isVonNBounded_iff_seminorm_bounded | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type ?u.478584\n𝕝 : Type ?u.478587\n𝕝₂ : Type ?u.478590\nE : Type u_1\nF : Type ?u.478596\nG : Type ?u.478599\nι : Type u_3\nι' : Type ?u.478605\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\np : SeminormFamily �... | [
575,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
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Mathlib/Order/Filter/Pointwise.lean | Filter.map₂_mul | [] | [
294,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.hom_comp_eq_id | [] | [
482,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toEquiv_inj | [] | [
165,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_mul_le | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g✝ f g : Perm α\nx : α\n⊢ x ∈ support (f * g) → x ∈ support f ∪ support g",
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... | [
332,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isOpenMap_coe | [] | [
271,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | Finset.norm_prod_le' | [
{
"state_after": "case mk.mk\nα✝ : Type ?u.116719\nβ : Type ?u.116722\nγ : Type ?u.116725\nι : Type u_2\ninst✝¹ : SeminormedRing α✝\nα : Type u_1\ninst✝ : NormedCommRing α\nf : ι → α\nval✝ : Multiset ι\nl : List ι\nhl : Multiset.Nodup (Quot.mk Setoid.r l)\nhs : Finset.Nonempty { val := Quot.mk Setoid.r l, nodup... | [
340,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_inj' | [] | [
318,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrFilter.comp_antitone | [] | [
338,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.natSize_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.335729\nn : PosNum\n⊢ natSize n = Nat.size ↑n",
"tactic": "rw [← size_eq_natSize, size_to_nat]"
}
] | [
581,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Algebra/NeZero.lean | neZero_iff | [] | [
41,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.basisSingleton_apply | [
{
"state_after": "case refl\nK : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\nι : Type u_1\ninst✝ : Unique ι\nh : finrank K V = 1\nv : V\nhv : v ≠ 0\n⊢ ↑(basisSingleton ι h v hv) default = v",
"state_... | [
619,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.exists_enc_dec | [
{
"state_after": "Γ : Type u_1\ninst✝¹ : Inhabited Γ\ninst✝ : Fintype Γ\nthis : DecidableEq Γ := Classical.decEq Γ\n⊢ ∃ n enc dec, enc default = Vector.replicate n false ∧ ∀ (a : Γ), dec (enc a) = a",
"state_before": "Γ : Type u_1\ninst✝¹ : Inhabited Γ\ninst✝ : Fintype Γ\n⊢ ∃ n enc dec, enc default = Vector... | [
1633,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
1
] |
Mathlib/Topology/Order/Basic.lean | isClosed_Ici | [] | [
147,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
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