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Mathlib/MeasureTheory/Measure/OpenPos.lean
Continuous.ae_eq_iff_eq
[]
[ 125, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 123, 1 ]
Mathlib/Topology/Sets/Opens.lean
TopologicalSpace.Opens.isBasis_iff_nbhd
[ { "state_after": "case mp\nι : Type ?u.30155\nα : Type u_1\nβ : Type ?u.30161\nγ : Type ?u.30164\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nB : Set (Opens α)\nh : IsBasis B\n⊢ ∀ {U : Opens α} {x : α}, x ∈ U → ∃ U', U' ∈ B ∧ x ∈ U' ∧ U' ≤ U\n\ncase mpr\nι : Type ?u.301...
[ 309, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 294, 1 ]
Mathlib/Logic/Basic.lean
not_ne_iff
[]
[ 254, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 254, 1 ]
Mathlib/CategoryTheory/Subobject/Basic.lean
CategoryTheory.Subobject.pullback_id
[ { "state_after": "case h\nC : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nf : MonoOver X\n⊢ (pullback (𝟙 X)).obj (Quotient.mk'' f) = Quotient.mk'' f", "state_before": "C : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝...
[ 562, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 560, 1 ]
Mathlib/Analysis/Calculus/BumpFunctionInner.lean
ContDiffBump.zero_of_le_dist
[ { "state_after": "no goals", "state_before": "E : Type u_1\nX : Type ?u.90452\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup X\ninst✝¹ : NormedSpace ℝ X\ninst✝ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\nhx : f.rOut ≤ dist x c\n⊢ ↑f x = 0", "tact...
[ 419, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 418, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean
lineMap_lt_lineMap_iff_of_lt
[ { "state_after": "k : Type u_1\nE : Type u_2\nPE : Type ?u.56390\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup E\ninst✝¹ : Module k E\ninst✝ : OrderedSMul k E\na a' b b' : E\nr r' : k\nh : r < r'\n⊢ (1 - r) • a + r • b < (1 - r') • a + r' • b ↔ a < b", "state_before": "k : Type u_1\nE : Type u_2\nPE...
[ 88, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 85, 1 ]
Mathlib/Algebra/Module/Submodule/Lattice.lean
Submodule.mem_bot
[]
[ 75, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 74, 1 ]
Mathlib/Topology/UniformSpace/CompactConvergence.lean
ContinuousMap.compactConvNhd_subset_inter
[]
[ 134, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 130, 1 ]
Mathlib/Data/Set/Basic.lean
Set.mem_ite_univ_right
[]
[ 2198, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2196, 1 ]
Mathlib/Analysis/Complex/UnitDisc/Basic.lean
Complex.UnitDisc.coe_zero
[]
[ 109, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 108, 1 ]
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean
Continuous.locallyIntegrable
[]
[ 253, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 251, 1 ]
Mathlib/Data/Polynomial/Eval.lean
Polynomial.eval_int_cast_map
[ { "state_after": "no goals", "state_before": "R✝ : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R✝\nm n : ℕ\ninst✝³ : Semiring R✝\np✝ q r : R✝[X]\ninst✝² : Semiring S✝\nf✝ : R✝ →+* S✝\nR : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\np : R[X]\ni : ℤ\n⊢ eval (↑i) (map f p) = ↑f...
[ 991, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 984, 1 ]
Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean
AEMeasurable.re
[]
[ 51, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 50, 1 ]
Mathlib/RingTheory/FiniteType.lean
MonoidAlgebra.fg_of_finiteType
[]
[ 617, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 615, 1 ]
Mathlib/Topology/SubsetProperties.lean
continuous_boolIndicator_iff_clopen
[ { "state_after": "case mp\nα : Type u\nβ : Type v\nι : Type ?u.178896\nπ : ι → Type ?u.178901\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\nX : Type u_1\ninst✝ : TopologicalSpace X\nU : Set X\n⊢ Continuous (boolIndicator U) → IsClopen U\n\ncase mpr\nα : Type u\nβ : Type v\nι : Type ?u....
[ 1670, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1662, 1 ]
Mathlib/GroupTheory/Subgroup/Basic.lean
MonoidHom.subgroupOf_range_eq_of_le
[ { "state_after": "case h\nG : Type ?u.484195\nG' : Type ?u.484198\ninst✝⁶ : Group G\ninst✝⁵ : Group G'\nA : Type ?u.484207\ninst✝⁴ : AddGroup A\nN : Type ?u.484213\nP : Type ?u.484216\ninst✝³ : Group N\ninst✝² : Group P\nK✝ : Subgroup G\nG₁ : Type u_1\nG₂ : Type u_2\ninst✝¹ : Group G₁\ninst✝ : Group G₂\nK : Sub...
[ 2697, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2692, 1 ]
Mathlib/LinearAlgebra/Trace.lean
LinearMap.trace_eq_contract'
[]
[ 184, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 182, 1 ]
Mathlib/Order/Monotone/Monovary.lean
Antivary.dual_right
[]
[ 220, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 219, 1 ]
Mathlib/Data/Fin/Basic.lean
Fin.nontrivial_iff_two_le
[ { "state_after": "no goals", "state_before": "n m : ℕ\n⊢ Nontrivial (Fin n) ↔ 2 ≤ n", "tactic": "rcases n with (_ | _ | n) <;>\nsimp [←Nat.one_eq_succ_zero, Fin.nontrivial, not_nontrivial, Nat.succ_le_iff]" } ]
[ 651, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 649, 1 ]
Mathlib/Data/Fin/Basic.lean
Fin.val_bit1
[ { "state_after": "case zero\nn m : ℕ\ninst✝ : NeZero zero\nk : Fin zero\n⊢ ↑(bit1 k) = bit1 ↑k % zero\n\ncase succ\nn m n✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\nk : Fin (Nat.succ n✝)\n⊢ ↑(bit1 k) = bit1 ↑k % Nat.succ n✝", "state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\nk : Fin n\n⊢ ↑(bit1 k) = bit1 ↑k % n", ...
[ 733, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 725, 1 ]
Mathlib/Probability/Kernel/Basic.lean
ProbabilityTheory.kernel.piecewise_apply
[]
[ 618, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 617, 1 ]
Std/Data/List/Lemmas.lean
List.erase_append_right
[ { "state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : ¬a ∈ l₁\n⊢ ∀ (b : α), b ∈ l₁ → ¬decide (a = b) = true", "state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : ¬a ∈ l₁\n⊢ List.erase (l₁ ++ l₂) a = l₁ ++ List.erase l₂ a", "tactic": "rw [e...
[ 1072, 63 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 1069, 1 ]
Mathlib/NumberTheory/Padics/RingHoms.lean
PadicInt.isUnit_den
[ { "state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖↑r‖ ≤ 1\n⊢ ‖↑r.den‖ = 1", "state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖↑r‖ ≤ 1\n⊢ IsUnit ↑r.den", "tactic": "rw [isUnit_iff]" }, { "state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖...
[ 103, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 84, 1 ]
Mathlib/MeasureTheory/Measure/NullMeasurable.lean
MeasureTheory.measurableSet_of_null
[]
[ 464, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 463, 1 ]
Mathlib/Analysis/Seminorm.lean
Seminorm.continuous_of_continuousAt_zero
[ { "state_after": "R : Type ?u.1410115\nR' : Type ?u.1410118\n𝕜 : Type ?u.1410121\n𝕜₂ : Type ?u.1410124\n𝕜₃ : Type ?u.1410127\n𝕝 : Type u_2\nE : Type u_1\nE₂ : Type ?u.1410136\nE₃ : Type ?u.1410139\nF : Type ?u.1410142\nG : Type ?u.1410145\nι : Type ?u.1410148\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : S...
[ 1147, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1143, 11 ]
Mathlib/Algebra/Lie/Basic.lean
LieModuleHom.coe_toLinearMap
[]
[ 726, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 725, 1 ]
Mathlib/Order/SemiconjSup.lean
Function.semiconj_of_isLUB
[ { "state_after": "α : Type u_1\nβ : Type ?u.7502\nγ : Type ?u.7505\nG : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' => ↑(↑f₁ g')⁻¹ (↑(↑f₂ g') x)) (h x)\ng : G\ny : α\n⊢ IsLUB (range fun g' => ↑(↑f₁ g')⁻¹ (↑(↑f₂ g') (↑(↑f₂ g) y))) (↑(↑f₁ ...
[ 110, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 104, 1 ]
Mathlib/Topology/ContinuousFunction/CocompactMap.lean
CocompactMap.tendsto_of_forall_preimage
[ { "state_after": "no goals", "state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.9571\nδ : Type ?u.9574\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nh : ∀ (s : Set β), IsCompact s → IsCompact (f ⁻¹' s)\ns : Set β\nhs : s ...
[ 179, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 175, 1 ]
Mathlib/Algebra/GeomSum.lean
Odd.geom_sum_pos
[ { "state_after": "case zero\nα : Type u\nβ : Type ?u.244183\nx : α\ninst✝ : LinearOrderedRing α\nh : Odd Nat.zero\n⊢ 0 < ∑ i in range Nat.zero, x ^ i\n\ncase succ.zero\nα : Type u\nβ : Type ?u.244183\nx : α\ninst✝ : LinearOrderedRing α\nh : Odd (Nat.succ Nat.zero)\n⊢ 0 < ∑ i in range (Nat.succ Nat.zero), x ^ i\...
[ 529, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 519, 1 ]
Mathlib/Topology/ContinuousOn.lean
nhdsWithin_univ
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.4196\nγ : Type ?u.4199\nδ : Type ?u.4202\ninst✝ : TopologicalSpace α\na : α\n⊢ 𝓝[univ] a = 𝓝 a", "tactic": "rw [nhdsWithin, principal_univ, inf_top_eq]" } ]
[ 81, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 80, 1 ]
Mathlib/RingTheory/Ideal/Basic.lean
Ideal.span_eq
[]
[ 158, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 157, 1 ]
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean
ENNReal.mul_rpow_of_ne_top
[ { "state_after": "no goals", "state_before": "x y : ℝ≥0∞\nhx : x ≠ ⊤\nhy : y ≠ ⊤\nz : ℝ\n⊢ (x * y) ^ z = x ^ z * y ^ z", "tactic": "simp [*, mul_rpow_eq_ite]" } ]
[ 505, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 504, 1 ]
Mathlib/Analysis/Convex/Basic.lean
convex_Ioo
[]
[ 295, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 294, 1 ]
Mathlib/Data/Set/Lattice.lean
Set.biInter_union
[]
[ 940, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 938, 1 ]
Mathlib/LinearAlgebra/Matrix/Adjugate.lean
Matrix.adjugate_apply
[ { "state_after": "no goals", "state_before": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\ni j : n\n⊢ adjugate A i j = det (updateRow A j (Pi.single i 1))", "tactic": "rw [adjugate_def, o...
[ 219, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 217, 1 ]
Mathlib/Topology/MetricSpace/Antilipschitz.lean
AntilipschitzWith.le_mul_ediam_image
[]
[ 124, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 123, 1 ]
Mathlib/Algebra/Module/LinearMap.lean
LinearMap.map_add
[]
[ 327, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 326, 11 ]
Mathlib/Analysis/SpecificLimits/Normed.lean
isLittleO_coe_const_pow_of_one_lt
[ { "state_after": "no goals", "state_before": "α : Type ?u.97427\nβ : Type ?u.97430\nι : Type ?u.97433\nR : Type u_1\ninst✝ : NormedRing R\nr : ℝ\nhr : 1 < r\n⊢ Nat.cast =o[atTop] fun n => r ^ n", "tactic": "simpa only [pow_one] using @isLittleO_pow_const_const_pow_of_one_lt R _ 1 _ hr" } ]
[ 212, 81 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 210, 1 ]
Mathlib/Logic/Equiv/Defs.lean
Equiv.toFun_as_coe
[]
[ 188, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 188, 9 ]
Mathlib/Deprecated/Subfield.lean
Preimage.isSubfield
[ { "state_after": "F : Type u_2\ninst✝¹ : Field F\nS : Set F\nK : Type u_1\ninst✝ : Field K\nf : F →+* K\ns : Set K\nhs : IsSubfield s\nsrc✝ : IsSubring (↑f ⁻¹' s) := RingHom.isSubring_preimage f hs.toIsSubring\na : F\nha : ↑f a ∈ s\n⊢ (↑f a)⁻¹ ∈ s", "state_before": "F : Type u_2\ninst✝¹ : Field F\nS : Set F...
[ 68, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 63, 1 ]
Mathlib/Algebra/GCDMonoid/Basic.lean
normalize_idem
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\nx : α\n⊢ ↑normalize (↑normalize x) = ↑normalize x", "tactic": "simp" } ]
[ 172, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 172, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.cons_swap
[]
[ 167, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 166, 1 ]
Mathlib/Topology/MetricSpace/Completion.lean
UniformSpace.Completion.continuous_dist
[]
[ 51, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 49, 11 ]
Mathlib/GroupTheory/Congruence.lean
Con.zpow
[ { "state_after": "no goals", "state_before": "M : Type u_1\nN : Type ?u.99934\nP : Type ?u.99937\ninst✝² : Group M\ninst✝¹ : Group N\ninst✝ : Group P\nc : Con M\nn : ℕ\nw x : M\nh : ↑c w x\n⊢ ↑c (w ^ Int.ofNat n) (x ^ Int.ofNat n)", "tactic": "simpa only [zpow_ofNat, Int.ofNat_eq_coe] using c.pow n h" ...
[ 1240, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1238, 11 ]
Mathlib/Geometry/Euclidean/Basic.lean
EuclideanGeometry.orthogonalProjectionFn_mem
[ { "state_after": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\np : P\n⊢ ↑s ∩ ↑(mk' p (direction s)ᗮ) ⊆ ↑s"...
[ 267, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 264, 1 ]
Mathlib/Data/Finset/Lattice.lean
Finset.inf_eq_sInf_image
[]
[ 760, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 758, 1 ]
Mathlib/Order/RelIso/Basic.lean
RelIso.eq_iff_eq
[]
[ 815, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 814, 1 ]
Mathlib/Data/Matrix/Block.lean
Matrix.fromBlocks_submatrix_sum_swap_left
[ { "state_after": "case a.h\nl : Type u_2\nm : Type u_4\nn : Type u_1\no : Type u_5\np : Type u_6\nq : Type ?u.18703\nm' : o → Type ?u.18708\nn' : o → Type ?u.18713\np' : o → Type ?u.18718\nR : Type ?u.18721\nS : Type ?u.18724\nα : Type u_3\nβ : Type ?u.18730\nA : Matrix n l α\nB : Matrix n m α\nC : Matrix o l α...
[ 168, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 164, 1 ]
Mathlib/Control/Functor.lean
Functor.Comp.map_mk
[]
[ 197, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 196, 1 ]
Mathlib/Topology/MetricSpace/Basic.lean
dist_triangle_left
[ { "state_after": "α : Type u\nβ : Type v\nX : Type ?u.9703\nι : Type ?u.9706\ninst✝ : PseudoMetricSpace α\nx y z : α\n⊢ dist x y ≤ dist x z + dist z y", "state_before": "α : Type u\nβ : Type v\nX : Type ?u.9703\nι : Type ?u.9706\ninst✝ : PseudoMetricSpace α\nx y z : α\n⊢ dist x y ≤ dist z x + dist z y", ...
[ 204, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 203, 1 ]
Mathlib/Algebra/GradedMonoid.lean
GradedMonoid.list_prod_map_eq_dProd
[ { "state_after": "ι : Type u_2\nα : Type u_1\nA : ι → Type u_3\ninst✝¹ : AddMonoid ι\ninst✝ : GMonoid A\nl : List α\nf : α → GradedMonoid A\n⊢ List.prod (List.map f l) = List.prod (List.map (fun a => { fst := (f a).fst, snd := (f a).snd }) l)", "state_before": "ι : Type u_2\nα : Type u_1\nA : ι → Type u_3\n...
[ 418, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 415, 1 ]
Mathlib/Analysis/NormedSpace/ConformalLinearMap.lean
IsConformalMap.comp
[ { "state_after": "case intro.intro.intro\nR : Type u_1\nM : Type u_4\nN : Type u_2\nG : Type u_3\nM' : Type ?u.216873\ninst✝⁸ : NormedField R\ninst✝⁷ : SeminormedAddCommGroup M\ninst✝⁶ : SeminormedAddCommGroup N\ninst✝⁵ : SeminormedAddCommGroup G\ninst✝⁴ : NormedSpace R M\ninst✝³ : NormedSpace R N\ninst✝² : Nor...
[ 92, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 87, 1 ]
Mathlib/Data/Set/Sups.lean
Set.Nonempty.of_infs_left
[]
[ 279, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 278, 1 ]
Mathlib/LinearAlgebra/Determinant.lean
LinearEquiv.det_mul_det_symm
[ { "state_after": "no goals", "state_before": "R : Type ?u.1583222\ninst✝⁸ : CommRing R\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nM' : Type ?u.1583813\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M'\nι : Type ?u.1584355\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\ne : Basis ι R M\nA : Type...
[ 419, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 417, 1 ]
Mathlib/Data/Real/Sqrt.lean
NNReal.mul_self_sqrt
[ { "state_after": "no goals", "state_before": "x✝ y x : ℝ≥0\n⊢ ↑sqrt x * ↑sqrt x = x", "tactic": "rw [← sq, sq_sqrt]" } ]
[ 96, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 96, 1 ]
Mathlib/Data/List/Sigma.lean
List.kreplace_self
[ { "state_after": "case refine'_1\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : NodupKeys l\nh : { fst := a, snd := b } ∈ l\n⊢ ∀ (a_1 : Sigma β),\n a_1 ∈ l → (if a = a_1.fst then some { fst := a, snd := b } else none) = Option.guard (fu...
[ 367, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 354, 1 ]
Mathlib/Topology/MetricSpace/HausdorffDistance.lean
Metric.infDist_le_hausdorffDist_of_mem
[]
[ 797, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 795, 1 ]
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
MeasureTheory.integrableOn_Iic_of_intervalIntegral_norm_tendsto
[]
[ 564, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 560, 1 ]
Mathlib/Algebra/GroupPower/Basic.lean
pow_bit0
[]
[ 199, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Mathlib/Data/Nat/Digits.lean
Nat.ofDigits_eq_sum_mapIdx
[ { "state_after": "n b : ℕ\nL : List ℕ\n⊢ List.foldr (fun x y => ↑x + b * y) 0 L = List.sum (List.zipWith (fun i a => a * b ^ i) (List.range (List.length L)) L)", "state_before": "n b : ℕ\nL : List ℕ\n⊢ ofDigits b L = List.sum (List.mapIdx (fun i a => a * b ^ i) L)", "tactic": "rw [List.mapIdx_eq_enum_ma...
[ 187, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 180, 1 ]
Mathlib/Analysis/Complex/Basic.lean
Complex.nnnorm_real
[]
[ 186, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 185, 1 ]
Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean
CategoryTheory.Idempotents.app_p_comp
[]
[ 49, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 48, 1 ]
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean
CategoryTheory.Limits.PreservesPushout.inl_iso_inv
[ { "state_after": "no goals", "state_before": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nG : C ⥤ D\nW X Y Z : C\nh : X ⟶ Z\nk : Y ⟶ Z\nf : W ⟶ X\ng : W ⟶ Y\ncomm : f ≫ h = g ≫ k\ninst✝² : PreservesColimit (span f g) G\ninst✝¹ : HasPushout f g\ninst✝ : HasPushout (G.map f) (G.map g)\...
[ 243, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 241, 1 ]
Mathlib/Order/LiminfLimsup.lean
Filter.isBounded_top
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.3399\nγ : Type ?u.3402\nι : Type ?u.3405\nr : α → α → Prop\nf g : Filter α\n⊢ IsBounded r ⊤ ↔ ∃ t, ∀ (x : α), r x t", "tactic": "simp [IsBounded, eq_univ_iff_forall]" } ]
[ 83, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 83, 1 ]
Mathlib/Control/Traversable/Lemmas.lean
Traversable.traverse_id
[ { "state_after": "case h\nt : Type u → Type u\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nα β γ : Type u\ng : α → F β\nh : β → G γ\nf : β → γ\nx : t β\nx✝ : t α\n⊢ trave...
[ 116, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 114, 1 ]
Mathlib/Order/Filter/Cofinite.lean
Filter.comap_cofinite_le
[]
[ 114, 93 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 112, 1 ]
Mathlib/Algebra/Lie/Classical.lean
LieAlgebra.Orthogonal.pso_inv
[ { "state_after": "case a.h\nn : Type ?u.36435\np : Type u_1\nq : Type u_2\nl : Type ?u.36444\nR : Type u₂\ninst✝⁶ : DecidableEq n\ninst✝⁵ : DecidableEq p\ninst✝⁴ : DecidableEq q\ninst✝³ : DecidableEq l\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\nx y : p ⊕ q\n⊢ (Pso p q R...
[ 195, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 184, 1 ]
Std/Data/List/Basic.lean
List.takeList_eq_takeListTR
[ { "state_after": "case h.h.h\nα : Type u_1\nxs : List α\nns : List Nat\n⊢ takeList xs ns = takeListTR xs ns", "state_before": "⊢ @takeList = @takeListTR", "tactic": "funext α xs ns" }, { "state_after": "case h.h.h\nα : Type u_1\nxs : List α\nns : List Nat\n⊢ takeList xs ns = takeListTR.go ns xs ...
[ 1489, 24 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 1483, 10 ]
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean
AffineSubspace.coe_affineSpan_singleton
[ { "state_after": "case h\nk : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ p x : P\n⊢ x ∈ ↑(affineSpan k {p}) ↔ x ∈ {p}", "state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\nins...
[ 711, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 707, 1 ]
Mathlib/Data/Finset/Image.lean
Finset.Nonempty.image
[]
[ 391, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 389, 11 ]
Mathlib/LinearAlgebra/LinearIndependent.lean
LinearIndependent.subset_span_extend
[]
[ 1321, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1318, 1 ]
Mathlib/GroupTheory/Sylow.lean
Sylow.ext
[ { "state_after": "case mk\np : ℕ\nG : Type u_1\ninst✝ : Group G\nQ : Sylow p G\ntoSubgroup✝ : Subgroup G\nisPGroup'✝ : IsPGroup p { x // x ∈ toSubgroup✝ }\nis_maximal'✝ : ∀ {Q : Subgroup G}, IsPGroup p { x // x ∈ Q } → toSubgroup✝ ≤ Q → Q = toSubgroup✝\nh : ↑{ toSubgroup := toSubgroup✝, isPGroup' := isPGroup'✝,...
[ 78, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 78, 1 ]
Mathlib/Data/Real/Sqrt.lean
Real.le_sqrt'
[]
[ 309, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 308, 1 ]
Mathlib/Algebra/CharP/Two.lean
CharTwo.sub_eq_add
[ { "state_after": "no goals", "state_before": "R : Type u_1\nι : Type ?u.7549\ninst✝¹ : Ring R\ninst✝ : CharP R 2\nx y : R\n⊢ x - y = x + y", "tactic": "rw [sub_eq_add_neg, neg_eq]" } ]
[ 76, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 76, 1 ]
Mathlib/RingTheory/Ideal/LocalRing.lean
map_mem_nonunits_iff
[]
[ 230, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 228, 1 ]
Mathlib/Topology/Order/Basic.lean
isClosed_le
[]
[ 131, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 129, 1 ]
Mathlib/MeasureTheory/Measure/VectorMeasure.lean
MeasureTheory.VectorMeasure.restrict_le_zero_subset
[]
[ 1032, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1030, 1 ]
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean
continuousWithinAt_left_of_monotoneOn_of_closure_image_mem_nhdsWithin
[]
[ 173, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 169, 1 ]
Mathlib/Algebra/Ring/Defs.lean
mul_neg_one
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝¹ : MulOneClass α\ninst✝ : HasDistribNeg α\na : α\n⊢ a * -1 = -a", "tactic": "simp" } ]
[ 326, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 326, 1 ]
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean
Matrix.charpoly_sub_diagonal_degree_lt
[ { "state_after": "R : Type u\ninst✝³ : CommRing R\nn G : Type v\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nα β : Type v\ninst✝ : DecidableEq α\nM : Matrix n n R\n⊢ degree\n (∑ x in Finset.erase univ (Equiv.refl n), ↑↑(↑Equiv.Perm.sign x) * ∏ i : n, charmatrix M (↑x i) i +\n ↑↑(↑Equiv.Perm.sign (...
[ 82, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 64, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.mem_insert_self
[]
[ 1065, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1064, 1 ]
Mathlib/Analysis/Calculus/MeanValue.lean
norm_image_sub_le_of_norm_deriv_le_segment_01
[ { "state_after": "no goals", "state_before": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.44608\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → E\na b C : ℝ\nhf : DifferentiableOn ℝ f (Icc 0 1)\nbound : ∀ (x : ℝ), x ∈ Ico 0 1 → ‖derivWithin f (Icc 0 1)...
[ 394, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 390, 1 ]
Mathlib/Algebra/Order/Floor.lean
Int.fract_eq_self
[ { "state_after": "no goals", "state_before": "F : Type ?u.165723\nα : Type u_1\nβ : Type ?u.165729\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ a - a = ↑0", "tactic": "simp" } ]
[ 947, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 946, 1 ]
Mathlib/LinearAlgebra/BilinearForm.lean
BilinForm.IsAdjointPair.mul
[ { "state_after": "no goals", "state_before": "R : Type u_1\nM : Type u_2\ninst✝²⁴ : Semiring R\ninst✝²³ : AddCommMonoid M\ninst✝²² : Module R M\nR₁ : Type ?u.1104318\nM₁ : Type ?u.1104321\ninst✝²¹ : Ring R₁\ninst✝²⁰ : AddCommGroup M₁\ninst✝¹⁹ : Module R₁ M₁\nR₂ : Type ?u.1104930\nM₂ : Type ?u.1104933\ninst✝...
[ 1081, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1079, 1 ]
Mathlib/Topology/Algebra/ConstMulAction.lean
continuousOn_const_smul_iff
[]
[ 217, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 215, 1 ]
Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean
Matrix.exists_mulVec_eq_zero_iff'
[ { "state_after": "R : Type ?u.259223\nM✝ : Type ?u.259226\ninst✝⁹ : CommRing R\ninst✝⁸ : AddCommGroup M✝\ninst✝⁷ : Module R M✝\nn : Type u_3\ninst✝⁶ : Fintype n\nA : Type u_1\nK : Type u_2\ninst✝⁵ : DecidableEq n\ninst✝⁴ : CommRing A\ninst✝³ : Nontrivial A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFrac...
[ 170, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 138, 1 ]
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
MeasureTheory.integrableOn_Ioc_of_interval_integral_norm_bounded_left
[]
[ 608, 81 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 605, 1 ]
Mathlib/Algebra/Associated.lean
Associates.dvd_eq_le
[]
[ 861, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 860, 1 ]
Mathlib/Logic/Equiv/Basic.lean
Equiv.swapCore_comm
[ { "state_after": "α : Sort u_1\ninst✝ : DecidableEq α\nr a b : α\n⊢ (if r = a then b else if r = b then a else r) = if r = b then a else if r = a then b else r", "state_before": "α : Sort u_1\ninst✝ : DecidableEq α\nr a b : α\n⊢ swapCore a b r = swapCore b a r", "tactic": "unfold swapCore" }, { ...
[ 1539, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1535, 1 ]
Mathlib/Data/Set/Intervals/OrdConnected.lean
IsAntichain.ordConnected
[ { "state_after": "α : Type u_1\ninst✝ : PartialOrder α\ns : Set α\nhs : IsAntichain (fun x x_1 => x ≤ x_1) s\nx : α\nhx : x ∈ s\nz : α\nhy : x ∈ s\nhz : z ∈ Icc x x\n⊢ z ∈ s", "state_before": "α : Type u_1\ninst✝ : PartialOrder α\ns : Set α\nhs : IsAntichain (fun x x_1 => x ≤ x_1) s\nx : α\nhx : x ∈ s\ny : ...
[ 238, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 234, 11 ]
Mathlib/Data/Nat/Pairing.lean
Nat.pair_eq_pair
[]
[ 94, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 93, 1 ]
Mathlib/Topology/ContinuousOn.lean
ContinuousOn.fst
[]
[ 1274, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1272, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.comap_le_comap_iff
[]
[ 2270, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2268, 1 ]
Mathlib/Algebra/Order/Kleene.lean
kstar_mono
[]
[ 246, 98 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 244, 1 ]
Mathlib/Data/IsROrC/Basic.lean
IsROrC.abs_im_le_norm
[ { "state_after": "K : Type u_1\nE : Type ?u.6631852\ninst✝ : IsROrC K\nz : K\n⊢ ↑im z * ↑im z ≤ ↑normSq z", "state_before": "K : Type u_1\nE : Type ?u.6631852\ninst✝ : IsROrC K\nz : K\n⊢ abs (↑im z) ≤ ‖z‖", "tactic": "rw [mul_self_le_mul_self_iff (abs_nonneg _) (norm_nonneg _), abs_mul_abs_self, mul_sel...
[ 721, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 719, 1 ]
Mathlib/Data/Finset/LocallyFinite.lean
Finset.Iio_subset_Iic_self
[ { "state_after": "no goals", "state_before": "ι : Type ?u.66687\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\na : α\n⊢ Iio a ⊆ Iic a", "tactic": "simpa [← coe_subset] using Set.Iio_subset_Iic_self" } ]
[ 490, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 489, 1 ]
Mathlib/Deprecated/Submonoid.lean
powers.self_mem
[]
[ 146, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 145, 1 ]
Mathlib/Computability/Primrec.lean
Primrec.encode_iff
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.25349\nσ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α → σ\nh : Primrec fun a => encode (f a)\nn : ℕ\n⊢ encode (Option.map (fun a => encode (f a)) (decode n)) = encode (Option.map f (decode n))...
[ 276, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 275, 1 ]
Std/Data/Int/DivMod.lean
Int.ediv_zero
[ { "state_after": "no goals", "state_before": "a✝ : Nat\n⊢ ofNat (a✝ / 0) = 0", "tactic": "simp" } ]
[ 48, 18 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 46, 25 ]
Mathlib/Data/Nat/Prime.lean
Nat.coprime_or_dvd_of_prime
[ { "state_after": "p : ℕ\npp : Prime p\ni : ℕ\n⊢ coprime p i ∨ ¬coprime p i", "state_before": "p : ℕ\npp : Prime p\ni : ℕ\n⊢ coprime p i ∨ p ∣ i", "tactic": "rw [pp.dvd_iff_not_coprime]" }, { "state_after": "no goals", "state_before": "p : ℕ\npp : Prime p\ni : ℕ\n⊢ coprime p i ∨ ¬coprime p i"...
[ 684, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 683, 1 ]