file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_subset_of_subset | [] | [
942,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.coe_gcd | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.eq | [] | [
99,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
18
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.hom_mk | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.symm_dual_id | [] | [
1539,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.v2_coeff | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type ?u.284123\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\np' : ℕ\nR' : Type u_1\nx y : WittVector p' R'\ni : Fin 2\n⊢ (Matrix.vecCons x ![y] i).coeff = Matrix.vecCons x.coeff ![y.coeff] i",
"tactic": "fin_cases i <;> simp"
}
] | [
354,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_right_injective | [] | [
939,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.padicNorm_p_of_prime | [] | [
97,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.enum.sound | [] | [
1384,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.domRestrict₁₂_apply | [] | [
207,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_dist_inl | [] | [
143,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
9
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ker_eq_maximalIdeal | [] | [
504,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.toFun_eq_coe | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_max_right | [] | [
204,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
204,
11
] |
Std/Data/Int/Lemmas.lean | Int.sub_add_cancel | [] | [
486,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
485,
19
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.sub | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.1528\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhm : IsPeriodicPt f m x\nhn : IsPeriodicPt f n x\nh : n ≤ m\n⊢ IsPeriodicPt f (m - n) x\n\ncase inr\nα : Type u_1\nβ : Type ?u.1528\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhm : IsPeriodicPt f m x\nhn : I... | [
122,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderivWithin_clm_apply | [] | [
155,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.normalizedFactors_irreducible | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\na : α\nha : Irreducible a\np : α\na_assoc : a ~ᵤ p\nhp : normalizedFactors a = {p}\n⊢ normalizedFactors a = {↑normalize a}",
"st... | [
611,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_natCast | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.160206\nα : Type u_1\nβ : Type ?u.160212\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\nn : ℕ\n⊢ fract ↑n = 0",
"tactic": "simp [fract]"
}
] | [
911,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.bit1_apply_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nι : Type ?u.5425\ninst✝¹ : Semiring R\ninst✝ : CharP R 2\nx : R\n⊢ bit1 x = 1",
"tactic": "simp"
}
] | [
57,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.trans' | [] | [
90,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coe_eq_univ_iff | [] | [
842,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_coe_nat | [] | [
113,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Std/Data/Option/Lemmas.lean | Option.join_join | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx : Option (Option (Option α))\n⊢ join (join x) = join (Option.map join x)",
"tactic": "cases x <;> simp"
}
] | [
163,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
162,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.repr_fract_apply | [
{
"state_after": "no goals",
"state_before": "E : Type u_3\nι : Type u_2\nK : Type u_1\ninst✝⁴ : NormedLinearOrderedField K\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace K E\nb : Basis ι K E\ninst✝¹ : FloorRing K\ninst✝ : Fintype ι\nm : E\ni : ι\n⊢ ↑(↑b.repr (fract b m)) i = Int.fract (↑(↑b.repr m) i... | [
122,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nnnorm_eq_of_L2 | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.283751\n𝕜' : Type ?u.283754\nι : Type u_2\nα : ι → Type ?u.283762\nβ✝ : ι → Type ?u.283767\ninst✝² : Fintype ι\ninst✝¹ : Fact (1 ≤ p)\nβ : ι → Type u_1\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx : PiLp 2 β\n⊢ ‖x‖ = Real.sqrt (∑ x_1 : ι, ‖x x_1‖ ^ 2)",
"state... | [
593,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.le_of_eqLocus_ge | [] | [
296,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_C_left | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | IsUnit.smul_left_cancel | [] | [
381,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.derivFamily_fp | [
{
"state_after": "case H₁\nι : Type u\nf : ι → Ordinal → Ordinal\ni : ι\nH : IsNormal (f i)\n⊢ f i (derivFamily f 0) = derivFamily f 0\n\ncase H₂\nι : Type u\nf : ι → Ordinal → Ordinal\ni : ι\nH : IsNormal (f i)\no : Ordinal\na✝ : f i (derivFamily f o) = derivFamily f o\n⊢ f i (derivFamily f (succ o)) = derivFa... | [
196,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.sqrt | [
{
"state_after": "H : ∀ (n : ℕ), Nat.sqrt n = Nat.rec 0 (fun x y => if Nat.succ x < Nat.succ y * Nat.succ y then y else Nat.succ y) n\n⊢ Primrec' fun v => Nat.sqrt (Vector.head v)\n\ncase H\n\n⊢ ∀ (n : ℕ), Nat.sqrt n = Nat.rec 0 (fun x y => if Nat.succ x < Nat.succ y * Nat.succ y then y else Nat.succ y) n",
... | [
1507,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
] |
Mathlib/Data/Sigma/Order.lean | Sigma.lt_def | [
{
"state_after": "case mp\nι : Type u_2\nα : ι → Type u_1\ninst✝ : (i : ι) → LT (α i)\na b : (i : ι) × α i\n⊢ a < b → ∃ h, h ▸ a.snd < b.snd\n\ncase mpr\nι : Type u_2\nα : ι → Type u_1\ninst✝ : (i : ι) → LT (α i)\na b : (i : ι) × α i\n⊢ (∃ h, h ▸ a.snd < b.snd) → a < b",
"state_before": "ι : Type u_2\nα : ι... | [
98,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_assoc | [] | [
513,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
11
] |
Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean | Polynomial.exists_approx_polynomial | [
{
"state_after": "Fq : Type u_1\ninst✝¹ : Fintype Fq\ninst✝ : Field Fq\nb : Fq[X]\nhb : b ≠ 0\nε : ℝ\nhε : 0 < ε\nA : Fin (Nat.succ (Fintype.card Fq ^ ⌈-log ε / log ↑(Fintype.card Fq)⌉₊)) → Fq[X]\nhbε : 0 < ↑cardPowDegree b • ε\n⊢ ∃ i₀ i₁, i₀ ≠ i₁ ∧ ↑(↑cardPowDegree (A i₁ % b - A i₀ % b)) < ↑cardPowDegree b • ε... | [
154,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.card_interedges_le_mul | [] | [
399,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_le_middle_of_le_half_left | [] | [
296,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
9
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_integral_add | [] | [
394,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Order/PropInstances.lean | Prop.codisjoint_iff | [] | [
107,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.rightDistributor_assoc | [
{
"state_after": "case w.w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX Y : C\nf : J → C\nj✝ : J\n⊢ ((rightDistributor X f ⊗ asIso (𝟙 Y)) ≪≫ rightDistributor Y fun j => f j... | [
218,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_smul | [
{
"state_after": "case h\nR : Type ?u.840053\nR' : Type ?u.840056\n𝕜 : Type u_1\n𝕜₂ : Type ?u.840062\n𝕜₃ : Type ?u.840065\n𝕝 : Type ?u.840068\nE : Type u_2\nE₂ : Type ?u.840074\nE₃ : Type ?u.840077\nF : Type ?u.840080\nG : Type ?u.840083\nι : Type ?u.840086\ninst✝² : SeminormedRing 𝕜\ninst✝¹ : AddCommGroup... | [
699,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.ringChar_ne_one | [
{
"state_after": "R : Type u_1\ninst✝¹ : NonAssocSemiring R\ninst✝ : Nontrivial R\nh : ringChar R = 1\n⊢ False",
"state_before": "R : Type u_1\ninst✝¹ : NonAssocSemiring R\ninst✝ : Nontrivial R\n⊢ ringChar R ≠ 1",
"tactic": "intro h"
},
{
"state_after": "R : Type u_1\ninst✝¹ : NonAssocSemiring R... | [
599,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_insert | [
{
"state_after": "case a\nα : Type u_1\ns✝ t✝ : Finset α\ninst✝ : DecidableEq α\ns : Finset α\na : α\nt : Finset α\n⊢ t ∈ powerset (insert a s) ↔ t ∈ powerset s ∪ image (insert a) (powerset s)",
"state_before": "α : Type u_1\ns✝ t : Finset α\ninst✝ : DecidableEq α\ns : Finset α\na : α\n⊢ powerset (insert a ... | [
115,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.inductionOn₂ | [] | [
148,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_coe | [] | [
2003,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2002,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.zero_mem_smul_finset | [] | [
2121,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2120,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_tri_right | [
{
"state_after": "n m : ℕ\n⊢ m ≤ dist n m + n",
"state_before": "n m : ℕ\n⊢ m ≤ n + dist n m",
"tactic": "rw [add_comm]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ m ≤ dist n m + n",
"tactic": "apply dist_tri_left"
}
] | [
61,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bitCasesOn_bit1 | [] | [
137,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.self_cast_nat_mul | [] | [
1111,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumEmpty_apply_inl | [] | [
401,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.ne_zero' | [
{
"state_after": "M : Type ?u.2763073\nN : Type ?u.2763076\nG : Type ?u.2763079\nR : Type u_1\nS : Type ?u.2763085\nF : Type ?u.2763088\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk l : ℕ\nζ : R\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ+\nhζ : IsPrimitiveRoot ζ ↑n\np : ℕ ... | [
635,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_mul_abs_self | [] | [
53,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Real/Basic.lean | Real.sInf_le_sSup | [
{
"state_after": "case inl\nx y : ℝ\nh₁ : BddBelow ∅\nh₂ : BddAbove ∅\n⊢ sInf ∅ ≤ sSup ∅\n\ncase inr\nx y : ℝ\ns : Set ℝ\nh₁ : BddBelow s\nh₂ : BddAbove s\nhne : Set.Nonempty s\n⊢ sInf s ≤ sSup s",
"state_before": "x y : ℝ\ns : Set ℝ\nh₁ : BddBelow s\nh₂ : BddAbove s\n⊢ sInf s ≤ sSup s",
"tactic": "rcas... | [
920,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sup_eq_right | [
{
"state_after": "case inl.intro.intro.intro\nα : Type u_1\ninst✝ : LinearOrderedField α\na b : CauSeq α abs\nε : α\nε0 : 0 < ε\ni : ℕ\nh : ∀ (j : ℕ), j ≥ i → ε ≤ ↑(b - a) j\n⊢ a ⊔ b ≈ b\n\ncase inr\nα : Type u_1\ninst✝ : LinearOrderedField α\na b : CauSeq α abs\nh : a ≈ b\n⊢ a ⊔ b ≈ b",
"state_before": "α ... | [
928,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
11
] |
Mathlib/Computability/TuringMachine.lean | Turing.mem_eval | [
{
"state_after": "case refine'_1\nσ : Type u_1\nf : σ → Option σ\na b : σ\nh : b ∈ eval f a\n⊢ Reaches f a b ∧ f b = none\n\ncase refine'_2\nσ : Type u_1\nf : σ → Option σ\na b : σ\nx✝ : Reaches f a b ∧ f b = none\nh₁ : Reaches f a b\nh₂ : f b = none\n⊢ b ∈ eval f a",
"state_before": "σ : Type u_1\nf : σ → ... | [
851,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_interior | [] | [
97,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_union_right | [] | [
592,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_pow_unitSphere | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.continuous_const | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.12251\ninst✝² : OmegaCompletePartialOrder α\ninst✝¹ : OmegaCompletePartialOrder β\ninst✝ : OmegaCompletePartialOrder γ\nf : α →o β\ng : β →o γ\nx : β\nc : Chain α\nz : β\n⊢ Function.const α x (ωSup c) ≤ z ↔ ∀ (i : ℕ), (Function.const α x ∘ ↑c) i ≤ z",
"s... | [
297,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.out_snd_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.34479\nγ : Type ?u.34482\ne : Sym2 α\n⊢ e = Quotient.mk (Rel.setoid α) ((Quotient.out e).snd, (Quotient.out e).fst)",
"tactic": "rw [eq_swap, Prod.mk.eta, e.out_eq]"
}
] | [
347,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.comp | [] | [
115,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.coe_toNNReal_ae_eq | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.1005622\nγ : Type ?u.1005625\nδ : Type ?u.1005628\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ≥0∞\nhf : ∀ᵐ (x : α) ∂μ, f x < ⊤\n⊢ ∀ (a : α), f a < ⊤ → ↑(ENNReal.toNN... | [
842,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.terminated_stable | [] | [
174,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | MulOpposite.dist_op | [] | [
1662,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/Data/Prod/TProd.lean | Set.elim_preimage_pi | [
{
"state_after": "ι : Type u\nα : ι → Type v\ni j : ι\nl✝ : List ι\nf : (i : ι) → α i\ninst✝ : DecidableEq ι\nl : List ι\nhnd : Nodup l\nh : ∀ (i : ι), i ∈ l\nt : (i : ι) → Set (α i)\nh2 : {i | i ∈ l} = univ\n⊢ TProd.elim' h ⁻¹' pi univ t = Set.tprod l t",
"state_before": "ι : Type u\nα : ι → Type v\ni j : ... | [
183,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.conjugatesOfSet_subset_normalClosure | [] | [
2460,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2459,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousOn_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.311983\nδ : Type ?u.311986\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\n⊢ ContinuousOn f s ↔ ∀ (x : α), x ∈ s → ∀ (t : Set β), Is... | [
598,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_eq_empty | [] | [
298,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.inductionOn | [] | [
142,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_mono | [] | [
340,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.coe_prodComm | [] | [
315,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Topology/Order/Basic.lean | Ico_mem_nhdsWithin_Iio | [] | [
471,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_subtype_and_compl | [] | [
1189,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g σ : Perm α\n⊢ support σ = ∅ ↔ σ = 1",
"tactic": "simp_rw [Finset.ext_iff, mem_support, Finset.not_mem_empty, iff_false_iff, not_not,\n Equiv.Perm.ext_iff, one_apply]"
}
] | [
308,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.lsub_lt_ord_lift_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.157402\nr : α → α → Prop\nι : Type u\nf : ι → Ordinal\nc : Cardinal\nhc : IsRegular c\nhι : lift (#ι) < c\n⊢ lift (#ι) < Ordinal.cof (ord c)",
"tactic": "rwa [hc.cof_eq]"
}
] | [
1063,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_nhdsWithin_iff | [] | [
1030,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_one_right' | [] | [
450,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_bound | [
{
"state_after": "x : ℝ\nhx : abs' x ≤ 1\n⊢ ↑Complex.abs ↑(sin x - (x - x ^ 3 / 6)) = ↑Complex.abs (Complex.sin ↑x - ↑(x - x ^ 3 / 6))",
"state_before": "x : ℝ\nhx : abs' x ≤ 1\n⊢ abs' (sin x - (x - x ^ 3 / 6)) = ↑Complex.abs (Complex.sin ↑x - ↑(x - x ^ 3 / 6))",
"tactic": "rw [← abs_ofReal]"
},
{
... | [
1864,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Order/WithBot.lean | WithBot.some_eq_coe | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | dfinsupp_sumAddHom_mem | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝³ : (i : ι) → AddZeroClass (β i)\ninst✝² : AddCommMonoid γ\nS : Type u_1\ninst✝¹ : SetLike S γ\ninst✝ : AddSubmonoidClass S γ\ns : S\nf : Π₀ (i : ι), β i\ng : (i : ι) → β i →+ γ\nh : ∀ (c : ι)... | [
1942,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1937,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | AddMonoidHom.completion_coe | [] | [
281,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Matrix/Hadamard.lean | Matrix.hadamard_one | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.17082\nγ : Type ?u.17085\nm : Type ?u.17088\nn : Type u_2\nR : Type ?u.17094\nA B C : Matrix m n α\ninst✝¹ : DecidableEq n\ninst✝ : MulZeroOneClass α\nM : Matrix n n α\ni j : n\n⊢ (M ⊙ 1) i j = diagonal (fun i => M i i) i j",
"state_before": "α : Type u_... | [
124,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Multiset/Pi.lean | Multiset.card_pi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nβ : α → Type u\nδ : α → Sort v\nm : Multiset α\nt : (a : α) → Multiset (β a)\n⊢ ↑card (pi 0 t) = prod (map (fun a => ↑card (t a)) 0)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type... | [
120,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | summable_geometric_of_norm_lt_1 | [] | [
298,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/PEquiv.lean | Equiv.toPEquiv_symm | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_or_fuzzy_of_lf | [] | [
935,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_eq_empty_of_le | [] | [
393,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.pair_mem_prod | [
{
"state_after": "no goals",
"state_before": "x y a b : ZFSet\n⊢ pair a b ∈ prod x y ↔ a ∈ x ∧ b ∈ y",
"tactic": "simp"
}
] | [
1349,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Analysis/BoxIntegral/Integrability.lean | MeasureTheory.SimpleFunc.hasBoxIntegral | [
{
"state_after": "case h_ind\nι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nI : Box ι\nl : IntegrationParams\nhl : l.bRiemann = false\ny : E\ns : Set (ι → ℝ)\nhs : MeasurableSet s\n⊢ HasIntegral I l (↑(... | [
184,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Continuous.comp_aestronglyMeasurable | [] | [
1259,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.length_sum | [] | [
672,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivAt.scomp_hasDerivWithinAt | [] | [
109,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.interedges_disjoint_right | [
{
"state_after": "𝕜 : Type ?u.7027\nι : Type ?u.7030\nκ : Type ?u.7033\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\ns : Finset α\nt t' : Finset β\nht : ∀ ⦃a : β⦄, a ∈ t → ¬a ... | [
101,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.cantorFunction_succ | [
{
"state_after": "c : ℝ\nf✝ g : ℕ → Bool\nn : ℕ\nf : ℕ → Bool\nh1 : 0 ≤ c\nh2 : c < 1\n⊢ (cantorFunctionAux c f 0 + ∑' (b : ℕ), cantorFunctionAux c f (b + 1)) =\n (bif f 0 then 1 else 0) + c * cantorFunction c fun n => f (n + 1)",
"state_before": "c : ℝ\nf✝ g : ℕ → Bool\nn : ℕ\nf : ℕ → Bool\nh1 : 0 ≤ c\n... | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_iInter_subset | [] | [
395,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Algebra/CharP/Basic.lean | RingHom.map_iterate_frobenius | [] | [
382,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.toNat_coe | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Topology/Sober.lean | isGenericPoint_iff_specializes | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.467\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nx y : α\nS U Z : Set α\n⊢ IsGenericPoint x S ↔ ∀ (y : α), x ⤳ y ↔ y ∈ S",
"tactic": "simp only [specializes_iff_mem_closure, IsGenericPoint, Set.ext_iff]"
}
] | [
57,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_all | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.142440\nι✝ : Sort x\nι : Type u_1\ninst✝ : Finite ι\nl : Filter α\np : ι → α → Prop\nval✝ : Fintype ι\n⊢ (∀ᶠ (x : α) in l, ∀ (i : ι), p i x) ↔ ∀ (i : ι), ∀ᶠ (x : α) in l, p i x",
"state_before": "α : Type u\nβ : Type v\nγ : Type w... | [
1160,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/RegularMono.lean | CategoryTheory.isIso_of_regularMono_of_epi | [] | [
152,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Logic/Basic.lean | PLift.down_inj | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na b : PLift α\nh : a = b\n⊢ a.down = b.down",
"tactic": "rw [h]"
}
] | [
84,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
9
] |
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