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Mathlib/LinearAlgebra/PiTensorProduct.lean
PiTensorProduct.lift_reindex
[]
[ 498, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 496, 1 ]
Mathlib/Topology/LocalHomeomorph.lean
LocalHomeomorph.symm_mapsTo
[]
[ 175, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 174, 11 ]
Mathlib/Analysis/NormedSpace/Units.lean
NormedRing.inverse_add_norm_diff_second_order
[ { "state_after": "case h.e'_7.h\nR : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : Rˣ\nx✝ : R\n⊢ inverse (↑x + x✝) - ↑x⁻¹ + ↑x⁻¹ * x✝ * ↑x⁻¹ = inverse (↑x + x✝) - (∑ i in range 2, (-↑x⁻¹ * x✝) ^ i) * ↑x⁻¹", "state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : Rˣ...
[ 213, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 209, 1 ]
Mathlib/Data/Polynomial/Expand.lean
Polynomial.map_expand_pow_char
[ { "state_after": "case zero\nR : Type u\ninst✝² : CommSemiring R\nS : Type v\ninst✝¹ : CommSemiring S\np q : ℕ\ninst✝ : CharP R p\nhp : Fact (Nat.Prime p)\nf : R[X]\n⊢ map (frobenius R p ^ Nat.zero) (↑(expand R (p ^ Nat.zero)) f) = f ^ p ^ Nat.zero\n\ncase succ\nR : Type u\ninst✝² : CommSemiring R\nS : Type v\n...
[ 262, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 256, 1 ]
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean
affineIndependent_iff_not_collinear_set
[ { "state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.277216\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ : P\n⊢ ¬Collinear k (Set.range ![p₁, p₂, p₃]) ↔ ¬Collinear k {p₁, p₂, p₃}", "state_before": "k : Type u_1\nV : Type u_2\nP ...
[ 464, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 461, 1 ]
Mathlib/Data/Nat/ModEq.lean
Nat.ModEq.mul_right'
[ { "state_after": "m n a b c✝ d c : ℕ\nh : a ≡ b [MOD n]\n⊢ c * a ≡ c * b [MOD c * n]", "state_before": "m n a b c✝ d c : ℕ\nh : a ≡ b [MOD n]\n⊢ a * c ≡ b * c [MOD n * c]", "tactic": "rw [mul_comm a, mul_comm b, mul_comm n]" }, { "state_after": "no goals", "state_before": "m n a b c✝ d c : ℕ...
[ 122, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 121, 11 ]
Mathlib/Data/List/Infix.lean
List.mem_of_mem_suffix
[]
[ 510, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 509, 1 ]
Mathlib/CategoryTheory/Idempotents/Karoubi.lean
CategoryTheory.Idempotents.Karoubi.comp_f
[ { "state_after": "no goals", "state_before": "C : Type u_1\ninst✝ : Category C\nP Q R : Karoubi C\nf : P ⟶ Q\ng : Q ⟶ R\n⊢ (f ≫ g).f = f.f ≫ g.f", "tactic": "rfl" } ]
[ 124, 93 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 124, 1 ]
Mathlib/Topology/Category/Compactum.lean
Compactum.basic_inter
[ { "state_after": "case h\nX : Compactum\nA B : Set X.A\nG : Ultrafilter X.A\n⊢ G ∈ Compactum.basic (A ∩ B) ↔ G ∈ Compactum.basic A ∩ Compactum.basic B", "state_before": "X : Compactum\nA B : Set X.A\n⊢ Compactum.basic (A ∩ B) = Compactum.basic A ∩ Compactum.basic B", "tactic": "ext G" }, { "stat...
[ 217, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 210, 9 ]
Mathlib/Topology/UniformSpace/Completion.lean
UniformSpace.Completion.coe_injective
[]
[ 459, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 458, 1 ]
Mathlib/GroupTheory/Abelianization.lean
abelianizationCongr_of
[]
[ 227, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 225, 1 ]
Mathlib/Data/Set/Image.lean
Subtype.range_val
[]
[ 1400, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1399, 1 ]
Mathlib/Algebra/GroupWithZero/Units/Basic.lean
Ring.inverse_zero
[ { "state_after": "α : Type ?u.9084\nM₀ : Type u_1\nG₀ : Type ?u.9090\nM₀' : Type ?u.9093\nG₀' : Type ?u.9096\nF : Type ?u.9099\nF' : Type ?u.9102\ninst✝ : MonoidWithZero M₀\n✝ : Nontrivial M₀\n⊢ inverse 0 = 0", "state_before": "α : Type ?u.9084\nM₀ : Type u_1\nG₀ : Type ?u.9090\nM₀' : Type ?u.9093\nG₀' : Ty...
[ 152, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 150, 1 ]
Mathlib/Topology/Bases.lean
TopologicalSpace.isOpen_sUnion_countable
[ { "state_after": "no goals", "state_before": "α : Type u\nt : TopologicalSpace α\ninst✝ : SecondCountableTopology α\nS : Set (Set α)\nH : ∀ (s : Set α), s ∈ S → IsOpen s\nT : Set ↑S\ncT : Set.Countable T\nhT : (⋃ (i : ↑S) (_ : i ∈ T), ↑i) = ⋃ (i : ↑S), ↑i\n⊢ ⋃₀ (Subtype.val '' T) = ⋃₀ S", "tactic": "rwa...
[ 738, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 734, 1 ]
Mathlib/RingTheory/FractionalIdeal.lean
FractionalIdeal.coe_spanSingleton
[ { "state_after": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1296088\ninst✝³ : CommRing R₁\nK : Type ?u.1296094\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx : P\n⊢ ↑{ val := span ...
[ 1302, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1300, 1 ]
Mathlib/Topology/MetricSpace/Antilipschitz.lean
AntilipschitzWith.of_subsingleton
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.14379\ninst✝³ : PseudoEMetricSpace α\ninst✝² : PseudoEMetricSpace β\ninst✝¹ : PseudoEMetricSpace γ\nK✝ : ℝ≥0\nf : α → β\ninst✝ : Subsingleton α\nK : ℝ≥0\nx y : α\n⊢ edist x y ≤ ↑K * edist (f x) (f y)", "tactic": "simp ...
[ 209, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 208, 1 ]
Mathlib/Data/Complex/Exponential.lean
Real.sin_zero
[ { "state_after": "no goals", "state_before": "x y : ℝ\n⊢ sin 0 = 0", "tactic": "simp [sin]" } ]
[ 1177, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1177, 1 ]
Mathlib/Algebra/Order/ToIntervalMod.lean
toIocDiv_neg
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocDiv hp a (-b) = -(toIcoDiv hp (-a) b + 1)", "tactic": "rw [← neg_neg b, toIcoDiv_neg, neg_neg, neg_neg, neg_add', neg_neg, add_sub_c...
[ 397, 86 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 396, 1 ]
Mathlib/Algebra/Star/Subalgebra.lean
StarSubalgebra.adjoin_induction'
[ { "state_after": "F : Type ?u.594069\nR : Type u_2\nA : Type u_1\nB : Type ?u.594078\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRing B\ninst✝ : StarModule R B\ns :...
[ 542, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 530, 1 ]
Mathlib/Data/Complex/Exponential.lean
Real.exp_le_exp
[]
[ 1525, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1524, 1 ]
Mathlib/Combinatorics/SimpleGraph/Coloring.lean
SimpleGraph.Colorable.mono
[ { "state_after": "no goals", "state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nn m : ℕ\nh : n ≤ m\nhc : Colorable G n\n⊢ Fintype.card (Fin n) ≤ Fintype.card (Fin m)", "tactic": "simp [h]" } ]
[ 203, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 202, 1 ]
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean
MvPolynomial.coeff_weightedHomogeneousComponent
[]
[ 341, 71 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 338, 1 ]
Mathlib/Data/Polynomial/Monic.lean
Polynomial.Monic.natDegree_mul_comm
[ { "state_after": "case pos\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q✝ r : R[X]\nhp : Monic p\nq : R[X]\nh : q = 0\n⊢ natDegree (p * q) = natDegree (q * p)\n\ncase neg\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q✝ r : R[X]\nhp : Monic p\nq : ...
[ 197, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 193, 1 ]
Mathlib/Algebra/Module/Basic.lean
Int.smul_one_eq_coe
[ { "state_after": "no goals", "state_before": "α : Type ?u.325888\nR✝ : Type ?u.325891\nk : Type ?u.325894\nS : Type ?u.325897\nM : Type ?u.325900\nM₂ : Type ?u.325903\nM₃ : Type ?u.325906\nι : Type ?u.325909\nR : Type u_1\ninst✝ : Ring R\nm : ℤ\n⊢ m • 1 = ↑m", "tactic": "rw [zsmul_eq_mul, mul_one]" } ...
[ 767, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 766, 1 ]
Mathlib/Data/Finset/Image.lean
Finset.forall_mem_map
[ { "state_after": "case intro.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.6251\nf✝ : α ↪ β\ns✝ : Finset α\nf : α ↪ β\ns : Finset α\np : (a : β) → a ∈ map f s → Prop\nh : ∀ (x : α) (H : x ∈ s), p (↑f x) (_ : ↑f x ∈ map f s)\ny : α\nhy : y ∈ s\nhx : ↑f y ∈ map f s\n⊢ p (↑f y) hx", "state_before": "α : Type ...
[ 96, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 91, 1 ]
Mathlib/RingTheory/Ideal/Operations.lean
Ideal.comap_inf
[]
[ 1471, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1470, 1 ]
Mathlib/Topology/Algebra/Module/CharacterSpace.lean
WeakDual.CharacterSpace.coe_toNonUnitalAlgHom
[]
[ 108, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 107, 1 ]
Std/Data/RBMap/Alter.lean
Std.RBNode.Path.zoom_zoomed₂
[ { "state_after": "α✝ : Type u_1\ncut : α✝ → Ordering\nt : RBNode α✝\npath : Path α✝\nt'✝ : RBNode α✝\npath'✝ : Path α✝\ne : zoom cut t path = (t'✝, path'✝)\nhp : Zoomed cut path\npath' : Path α✝\nt' : RBNode α✝\nc✝ : RBColor\nl✝ : RBNode α✝\nv✝ : α✝\nr✝ : RBNode α✝\n⊢ zoom cut (node c✝ l✝ v✝ r✝) path = (t', pat...
[ 235, 33 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 227, 1 ]
Mathlib/Algebra/Order/ToIntervalMod.lean
toIcoMod_sub_self
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoMod hp a b - b = -toIcoDiv hp a b • p", "tactic": "rw [toIcoMod, sub_sub_cancel_left, neg_smul]" } ]
[ 136, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 135, 1 ]
Mathlib/Topology/SubsetProperties.lean
ClosedEmbedding.compactSpace
[ { "state_after": "α : Type u\nβ : Type v\nι : Type ?u.96598\nπ : ι → Type ?u.96603\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nh : CompactSpace β\nf : α → β\nhf : ClosedEmbedding f\n⊢ IsCompact (range f)", "state_before": "α : Type u\nβ : Type v\nι : Type ?u.96598\nπ : ι → Type ?u...
[ 940, 87 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 938, 11 ]
Mathlib/Data/Set/Intervals/Infinite.lean
Set.Iio_infinite
[]
[ 81, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 80, 1 ]
Mathlib/Analysis/Convex/Quasiconvex.lean
Monotone.quasiconcaveOn
[]
[ 213, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 212, 1 ]
Mathlib/Algebra/Order/Monoid/WithTop.lean
WithBot.coe_eq_one
[]
[ 491, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 490, 1 ]
Mathlib/MeasureTheory/MeasurableSpace.lean
exists_measurable_piecewise
[ { "state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.93731\nδ : Type ?u.93734\nδ' : Type ?u.93737\nι✝ : Sort uι\ns t✝ u : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nmγ : MeasurableSpace γ\nι : Type u_1\ninst✝¹ : Countable ι\ninst✝ : Nonempty ι\nt : ι → Set α\nt_meas : ∀ (n : ι), MeasurableSet (t...
[ 816, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 797, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.mem_singleton_self
[ { "state_after": "α : Type u_1\nβ : Type ?u.25331\nγ : Type ?u.25334\na : α\n⊢ a ∈ a ::ₘ 0", "state_before": "α : Type u_1\nβ : Type ?u.25331\nγ : Type ?u.25334\na : α\n⊢ a ∈ {a}", "tactic": "rw [← cons_zero]" }, { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.25331\n...
[ 344, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 342, 1 ]
Mathlib/LinearAlgebra/Projection.lean
Submodule.coe_prodEquivOfIsCompl'
[]
[ 118, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 117, 1 ]
Mathlib/Data/Finsupp/Basic.lean
Finsupp.mapRange.addMonoidHom_comp
[ { "state_after": "no goals", "state_before": "α : Type u_4\nβ : Type ?u.49269\nγ : Type ?u.49272\nι : Type ?u.49275\nM : Type u_3\nM' : Type ?u.49281\nN : Type u_1\nP : Type u_2\nG : Type ?u.49290\nH : Type ?u.49293\nR : Type ?u.49296\nS : Type ?u.49299\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMonoid N\ni...
[ 228, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 224, 1 ]
Mathlib/Topology/Connected.lean
Inducing.isPreconnected_image
[ { "state_after": "α : Type u\nβ : Type v\nι : Type ?u.24377\nπ : ι → Type ?u.24382\ninst✝¹ : TopologicalSpace α\ns✝ t u v : Set α\ninst✝ : TopologicalSpace β\ns : Set α\nf : α → β\nhf : Inducing f\nh : IsPreconnected (f '' s)\n⊢ IsPreconnected s", "state_before": "α : Type u\nβ : Type v\nι : Type ?u.24377\n...
[ 375, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 366, 1 ]
Mathlib/Topology/Constructions.lean
nhds_toAdd
[]
[ 139, 81 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 139, 1 ]
Mathlib/Analysis/SpecificLimits/Normed.lean
tsum_geometric_of_abs_lt_1
[]
[ 314, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 313, 1 ]
Mathlib/Topology/Instances/RealVectorSpace.lean
map_real_smul
[]
[ 30, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 26, 1 ]
Mathlib/Order/Minimal.lean
maximals_singleton
[ { "state_after": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\nb✝ b : α\n⊢ r b b → r b b", "state_before": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na b : α\n⊢ ∀ ⦃b : α⦄, b ∈ {a} → r a b → r b a", "tactic": "rintro b (rfl : b = a)" }, { "state_after": "no goals", "state_befor...
[ 68, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 63, 1 ]
Mathlib/Analysis/Convex/Segment.lean
segment_eq_uIcc
[]
[ 530, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 529, 1 ]
Mathlib/Data/PNat/Xgcd.lean
PNat.XgcdType.finish_isSpecial
[ { "state_after": "u : XgcdType\nhs : u.wp + u.zp + u.wp * u.zp = u.x * u.y\n⊢ u.wp + (u.y * qp u + u.zp) + u.wp * (u.y * qp u + u.zp) = ((u.wp + 1) * qp u + u.x) * u.y", "state_before": "u : XgcdType\nhs : IsSpecial u\n⊢ IsSpecial (finish u)", "tactic": "dsimp [IsSpecial, finish] at hs⊢" }, { "s...
[ 286, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 283, 1 ]
Mathlib/Data/Set/Countable.lean
Set.Countable.biUnion_iff
[ { "state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nt : (a : α) → a ∈ s → Set β\nhs : Set.Countable s\nthis : Countable ↑s\n⊢ Set.Countable (⋃ (a : α) (h : a ∈ s), t a h) ↔ ∀ (a : α) (ha : a ∈ s), Set.Countable (t a ha)", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort...
[ 201, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Mathlib/Data/Finset/Card.lean
Finset.card_le_one_iff_subset_singleton
[ { "state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.54709\ns t : Finset α\nf : α → β\nn : ℕ\ninst✝ : Nonempty α\nH : card s ≤ 1\n⊢ ∃ x, s ⊆ {x}\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.54709\ns t : Finset α\nf : α → β\nn : ℕ\ninst✝ : Nonempty α\n⊢ (∃ x, s ⊆ {x}) → card s ≤ 1", "state_before": "α...
[ 551, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 544, 1 ]
Mathlib/Geometry/Manifold/ChartedSpace.lean
OpenEmbedding.singletonChartedSpace_chartAt_eq
[]
[ 1037, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1035, 1 ]
Mathlib/Analysis/ODE/PicardLindelof.lean
PicardLindelof.continuous_proj
[]
[ 157, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 156, 1 ]
Mathlib/Data/Nat/PartENat.lean
PartENat.add_lt_add_right
[ { "state_after": "case intro\ny z : PartENat\nhz : z ≠ ⊤\nm : ℕ\nh : ↑m < y\n⊢ ↑m + z < y + z", "state_before": "x y z : PartENat\nh : x < y\nhz : z ≠ ⊤\n⊢ x + z < y + z", "tactic": "rcases ne_top_iff.mp (ne_top_of_lt h) with ⟨m, rfl⟩" }, { "state_after": "case intro.intro\ny : PartENat\nm : ℕ\n...
[ 469, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 460, 11 ]
Mathlib/Combinatorics/SimpleGraph/Hasse.lean
SimpleGraph.hasse_preconnected_of_succ
[ { "state_after": "α : Type u_1\nβ : Type ?u.5179\ninst✝² : LinearOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\na b : α\n⊢ ReflTransGen (hasse α).Adj a b", "state_before": "α : Type u_1\nβ : Type ?u.5179\ninst✝² : LinearOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\na b : α\n⊢ Reac...
[ 91, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 86, 1 ]
Std/Data/List/Lemmas.lean
List.pairwise_append
[ { "state_after": "no goals", "state_before": "α : Type u_1\nR : α → α → Prop\nl₁ l₂ : List α\n⊢ Pairwise R (l₁ ++ l₂) ↔ Pairwise R l₁ ∧ Pairwise R l₂ ∧ ∀ (a : α), a ∈ l₁ → ∀ (b : α), b ∈ l₂ → R a b", "tactic": "induction l₁ <;> simp [*, or_imp, forall_and, and_assoc, and_left_comm]" } ]
[ 1289, 74 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 1287, 1 ]
Mathlib/Analysis/Calculus/ContDiffDef.lean
contDiffWithinAt_iff_forall_nat_le
[]
[ 436, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 434, 1 ]
Mathlib/LinearAlgebra/Prod.lean
LinearEquiv.fst_comp_prodComm
[ { "state_after": "no goals", "state_before": "N : Type u_1\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.401591\nM₆ : Type ?u.401594\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst...
[ 755, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 753, 1 ]
Mathlib/Algebra/Homology/Augment.lean
CochainComplex.augment_d_succ_succ
[]
[ 283, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 281, 1 ]
Mathlib/Computability/TMToPartrec.lean
Turing.PartrecToTM2.tr_ret_cons₂
[]
[ 1140, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1139, 1 ]
Mathlib/Algebra/Quaternion.lean
QuaternionAlgebra.neg_imK
[]
[ 252, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 252, 9 ]
Mathlib/Algebra/Homology/HomologicalComplex.lean
CochainComplex.mk_d_1_0
[ { "state_after": "ι : Type ?u.323151\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nX₀ X₁ X₂ : V\nd₀ : X₀ ⟶ X₁\nd₁ : X₁ ⟶ X₂\ns : d₀ ≫ d₁ = 0\nsucc :\n (t : (X₀ : V) ×' (X₁ : V) ×' (X₂ : V) ×' (d₀ : X₀ ⟶ X₁) ×' (d₁ : X₁ ⟶ X₂) ×' d₀ ≫ d₁ = 0) →\n (X₃ : V) ×' (d₂ : t.snd.snd.fst ⟶ X₃) ×' t.snd....
[ 1010, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1008, 1 ]
Mathlib/Algebra/MonoidAlgebra/Grading.lean
AddMonoidAlgebra.mem_grade_iff'
[ { "state_after": "M : Type u_2\nι : Type ?u.7453\nR : Type u_1\ninst✝¹ : DecidableEq M\ninst✝ : CommSemiring R\nm : M\na : AddMonoidAlgebra R M\n⊢ (∃ b, a = Finsupp.single m b) ↔ a ∈ LinearMap.range (Finsupp.lsingle m)", "state_before": "M : Type u_2\nι : Type ?u.7453\nR : Type u_1\ninst✝¹ : DecidableEq M\n...
[ 80, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 74, 1 ]
Mathlib/Data/List/BigOperators/Basic.lean
List.prod_take_mul_prod_drop
[ { "state_after": "no goals", "state_before": "ι : Type ?u.51930\nα : Type ?u.51933\nM : Type u_1\nN : Type ?u.51939\nP : Type ?u.51942\nM₀ : Type ?u.51945\nG : Type ?u.51948\nR : Type ?u.51951\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl l₁ l₂ : List M\na : M\ni : ℕ\n⊢ prod (take i []) * prod ...
[ 170, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 165, 1 ]
Mathlib/MeasureTheory/Function/LpSeminorm.lean
MeasureTheory.Memℒp.of_le
[]
[ 537, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 535, 1 ]
Mathlib/SetTheory/Cardinal/Divisibility.lean
Cardinal.dvd_of_le_of_aleph0_le
[]
[ 75, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 74, 1 ]
Mathlib/Computability/Primrec.lean
Primrec.of_graph
[ { "state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.161236\nγ : Type ?u.161239\nδ : Type ?u.161242\nσ : Type ?u.161245\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : α → ℕ\nh₂ : PrimrecRel fun a b => f a = b\ng : α → ℕ\npg : ...
[ 812, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 808, 1 ]
Mathlib/Order/SymmDiff.lean
sdiff_symmDiff_eq_sup
[ { "state_after": "no goals", "state_before": "ι : Type ?u.32704\nα : Type u_1\nβ : Type ?u.32710\nπ : ι → Type ?u.32715\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ (a \\ b) ∆ b = a ⊔ b", "tactic": "rw [symmDiff_comm, symmDiff_sdiff_eq_sup, sup_comm]" } ]
[ 189, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 188, 1 ]
Mathlib/Init/CcLemmas.lean
imp_eq_of_eq_false_right
[]
[ 61, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 60, 1 ]
Mathlib/Data/Finsupp/Defs.lean
Finsupp.unique_ext
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.26168\nγ : Type ?u.26171\nι : Type ?u.26174\nM : Type u_2\nM' : Type ?u.26180\nN : Type ?u.26183\nP : Type ?u.26186\nG : Type ?u.26189\nH : Type ?u.26192\nR : Type ?u.26195\nS : Type ?u.26198\ninst✝¹ : Zero M\ninst✝ : Unique α\nf g : α ...
[ 275, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 274, 1 ]
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
MeasureTheory.integrableOn_Ioi_comp_mul_right_iff
[ { "state_after": "no goals", "state_before": "E : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℝ → E\nc a : ℝ\nha : 0 < a\n⊢ IntegrableOn (fun x => f (x * a)) (Ioi c) ↔ IntegrableOn f (Ioi (c * a))", "tactic": "simpa only [mul_comm, MulZeroClass.mul_zero] using integrableOn_Ioi_comp_mul_left_iff f c ha" ...
[ 950, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 948, 1 ]
Mathlib/Algebra/EuclideanDomain/Basic.lean
EuclideanDomain.dvd_lcm_left
[ { "state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\nhxy : gcd x y = 0\n⊢ x ∣ 0", "state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\nhxy : gcd x y = 0\n⊢ x ∣ lcm x y", "tactic": "rw [lcm, hxy, div_zero]" }, { "state_after...
[ 258, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 251, 1 ]
Mathlib/Probability/ProbabilityMassFunction/Basic.lean
Pmf.apply_eq_zero_iff
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.6289\nγ : Type ?u.6292\np : Pmf α\na : α\n⊢ ↑p a = 0 ↔ ¬a ∈ support p", "tactic": "rw [mem_support_iff, Classical.not_not]" } ]
[ 106, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 105, 1 ]
Mathlib/Data/Real/GoldenRatio.lean
gold_irrational
[ { "state_after": "this : Irrational (sqrt ↑5)\n⊢ Irrational φ", "state_before": "⊢ Irrational φ", "tactic": "have := Nat.Prime.irrational_sqrt (show Nat.Prime 5 by norm_num)" }, { "state_after": "this✝ : Irrational (sqrt ↑5)\nthis : Irrational (↑1 + sqrt ↑5)\n⊢ Irrational φ", "state_before":...
[ 147, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 141, 1 ]
Mathlib/ModelTheory/Semantics.lean
FirstOrder.Language.Relations.realize_antisymmetric
[]
[ 1017, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1014, 1 ]
Mathlib/Combinatorics/SetFamily/Intersecting.lean
Set.Intersecting.mono
[]
[ 50, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 49, 1 ]
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean
BoxIntegral.TaggedPrepartition.iUnion_toPrepartition
[]
[ 77, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 77, 1 ]
Mathlib/Topology/MetricSpace/PiNat.lean
PiNat.firstDiff_le_longestPrefix
[ { "state_after": "E : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\ns : Set ((n : ℕ) → E n)\nhs : IsClosed s\nx y : (n : ℕ) → E n\nhx : ¬x ∈ s\nhy : y ∈ s\n⊢ firstDiff x y + 1 ≤ shortestPrefixDiff x s\n\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace ...
[ 542, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 538, 1 ]
Mathlib/Data/Dfinsupp/Basic.lean
Dfinsupp.comapDomain_single
[ { "state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type u_1\ninst✝¹ : DecidableEq κ\ninst✝ : (i : ι) → Zero (β i)\nh : κ → ι\nhh : Function.Injective h\nk : κ\nx : β (h k)\ni : κ\n⊢ ↑(comapDomain h hh (single (h k) x)) i = ↑(single k x)...
[ 1350, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1344, 1 ]
Std/Data/Option/Init/Lemmas.lean
Option.getD_some
[]
[ 17, 55 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 17, 9 ]
Mathlib/RingTheory/PowerSeries/Basic.lean
PowerSeries.inv_mul_cancel
[]
[ 2164, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2163, 11 ]
Mathlib/Algebra/Star/StarAlgHom.lean
StarAlgEquiv.symm_bijective
[]
[ 842, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 841, 1 ]
Mathlib/GroupTheory/Perm/Sign.lean
Equiv.Perm.sign_symm
[]
[ 575, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 574, 1 ]
Mathlib/Probability/Kernel/Basic.lean
ProbabilityTheory.kernel.integral_deterministic
[ { "state_after": "no goals", "state_before": "α : Type u_2\nβ : Type u_3\nι : Type ?u.401033\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nf : β → E\ng : α → β\na : α\nhg : Measur...
[ 405, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 402, 1 ]
Mathlib/Data/Vector/Basic.lean
Vector.ne_cons_iff
[ { "state_after": "no goals", "state_before": "n : ℕ\nα : Type u_1\na : α\nv : Vector α (Nat.succ n)\nv' : Vector α n\n⊢ v ≠ a ::ᵥ v' ↔ head v ≠ a ∨ tail v ≠ v'", "tactic": "rw [Ne.def, eq_cons_iff a v v', not_and_or]" } ]
[ 71, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 70, 1 ]
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean
CategoryTheory.ConcreteCategory.epi_iff_surjective_of_preservesPushout
[]
[ 186, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 184, 1 ]
Mathlib/Computability/Halting.lean
ComputablePred.halting_problem_not_re
[]
[ 269, 86 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 268, 1 ]
Mathlib/MeasureTheory/Group/FundamentalDomain.lean
MeasureTheory.sdiff_fundamentalFrontier
[]
[ 611, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 610, 1 ]
Mathlib/Order/Basic.lean
lt_iff_le_and_ne
[]
[ 378, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 377, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
Complex.cos_two_pi
[ { "state_after": "no goals", "state_before": "⊢ cos (2 * ↑π) = 1", "tactic": "simp [two_mul, cos_add]" } ]
[ 1134, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1134, 1 ]
Mathlib/Topology/Algebra/Module/WeakDual.lean
WeakBilin.embedding
[]
[ 136, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 134, 1 ]
Mathlib/Order/Heyting/Basic.lean
Codisjoint.himp_inf_cancel_left
[ { "state_after": "no goals", "state_before": "ι : Type ?u.74711\nα : Type u_1\nβ : Type ?u.74717\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\nh : Codisjoint a b\n⊢ b ⇨ a ⊓ b = a", "tactic": "rw [himp_inf_distrib, himp_self, inf_top_eq, h.himp_eq_right]" } ]
[ 450, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 449, 1 ]
Mathlib/Data/Num/Lemmas.lean
Num.of_to_nat
[]
[ 508, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 507, 1 ]
Mathlib/Algebra/Hom/Equiv/Basic.lean
MulEquiv.comp_symm_eq
[]
[ 432, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 430, 1 ]
Mathlib/Data/Polynomial/Degree/Definitions.lean
Polynomial.nextCoeff_X_sub_C
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\na b c✝ d : R\nn m : ℕ\ninst✝² : Ring R\ninst✝¹ : Nontrivial R\ninst✝ : Ring S\nc : S\n⊢ nextCoeff (X - ↑C c) = -c", "tactic": "rw [sub_eq_add_neg, ← map_neg C c, nextCoeff_X_add_C]" } ]
[ 1478, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1477, 1 ]
Mathlib/Data/Finset/MulAntidiagonal.lean
Finset.isPwo_support_mulAntidiagonal
[]
[ 113, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 112, 1 ]
Mathlib/Data/ZMod/Basic.lean
ZMod.int_cast_eq_int_cast_iff'
[]
[ 463, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 462, 1 ]
Mathlib/Order/FixedPoints.lean
OrderHom.map_lfp
[]
[ 82, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 80, 1 ]
Mathlib/Data/Finsupp/Basic.lean
Finsupp.sumElim_apply
[]
[ 1319, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1317, 1 ]
Mathlib/Data/Set/Intervals/Basic.lean
Set.right_mem_Ico
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.5009\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ b ∈ Ico a b ↔ False", "tactic": "simp [lt_irrefl]" } ]
[ 213, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 213, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean
CategoryTheory.Limits.MultispanIndex.multispan_obj_right
[]
[ 276, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 275, 1 ]
Mathlib/Algebra/Algebra/Unitization.lean
Unitization.inr_zero
[]
[ 286, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 285, 1 ]
Mathlib/CategoryTheory/Monad/Algebra.lean
CategoryTheory.Comonad.Coalgebra.id_f
[]
[ 411, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 410, 1 ]
Mathlib/Order/GaloisConnection.lean
GaloisConnection.l_unique
[]
[ 218, 96 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 216, 1 ]
Mathlib/GroupTheory/Finiteness.lean
Subgroup.rank_closure_finite_le_nat_card
[ { "state_after": "M : Type ?u.118917\nN : Type ?u.118920\ninst✝⁴ : Monoid M\ninst✝³ : AddMonoid N\nG : Type u_1\nH : Type ?u.118932\ninst✝² : Group G\ninst✝¹ : AddGroup H\ns : Set G\ninst✝ : Finite ↑s\nthis : Fintype ↑s\n⊢ Group.rank { x // x ∈ closure s } ≤ Nat.card ↑s", "state_before": "M : Type ?u.118917...
[ 460, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 456, 1 ]