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/Order/Filter/AtTopBot.lean | Filter.extraction_of_eventually_atTop | [] | [
475,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.sub_rat | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\n⊢ Irrational (x - ↑q)",
"tactic": "simpa only [sub_eq_add_neg, cast_neg] using h.add_rat (-q)"
}
] | [
280,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_iSup | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nf : ι → Subgraph G\n⊢ edgeSet (⨆ (i : ι), f i) = ⋃ (i : ι), edgeSet (f i)",
"tactic": "simp [iSup]"
}
] | [
574,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_empty_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.18102\nβ : Type u_3\nβ' : Type ?u.18108\nγ : Type u_1\nγ' : Type ?u.18114\nδ : Type ?u.18117\nδ' : Type ?u.18120\nε : Type ?u.18123\nε' : Type ?u.18126\nζ : Type ?u.18129\nζ' : Type ?u.18132\nν : Type ?u.18135\nf f' : α → β → γ\ng g' :... | [
154,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_bot | [] | [
259,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Fuzzy.not_equiv' | [] | [
941,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_nil | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.bijective_iff_surjective_and_card | [] | [
675,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.id_map | [] | [
68,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
11
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_self | [
{
"state_after": "no goals",
"state_before": "⊢ 0 - 0 = 0",
"tactic": "rw [Nat.sub_zero]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ succ n - succ n = 0",
"tactic": "rw [succ_sub_succ, Nat.sub_self n]"
}
] | [
252,
54
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
250,
19
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.findGreatest_eq_iff | [
{
"state_after": "case zero\nm✝ n k l : ℕ\nP Q : ℕ → Prop\ninst✝ : DecidablePred P\nm : ℕ\n⊢ Nat.findGreatest P zero = m ↔ m ≤ zero ∧ (m ≠ 0 → P m) ∧ ∀ ⦃n : ℕ⦄, m < n → n ≤ zero → ¬P n\n\ncase succ\nm✝ n k✝ l : ℕ\nP Q : ℕ → Prop\ninst✝ : DecidablePred P\nk : ℕ\nihk : ∀ {m : ℕ}, Nat.findGreatest P k = m ↔ m ≤ k ... | [
624,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | polyEquivTensor_apply | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Part.lean | Part.bind_dom | [] | [
669,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Order/Hom/Bounded.lean | map_eq_bot_iff | [
{
"state_after": "F : Type u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.7624\nδ : Type ?u.7627\ninst✝⁴ : LE α\ninst✝³ : OrderBot α\ninst✝² : PartialOrder β\ninst✝¹ : OrderBot β\ninst✝ : OrderIsoClass F α β\nf : F\na : α\nthis : BotHomClass F α β := OrderIsoClass.toBotHomClass\n⊢ ↑f a = ⊥ ↔ a = ⊥",
"state_be... | [
155,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_with_zero_eq | [] | [
1527,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1527,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_mul | [] | [
522,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.isClosed_ker | [] | [
979,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_lt_lift | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nc : Cardinal\n⊢ ℵ₀ < lift c ↔ ℵ₀ < c",
"tactic": "rw [← lift_aleph0.{u,v}, lift_lt]"
}
] | [
1266,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1265,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | zero_zpow | [
{
"state_after": "case a\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\nn : ℕ\nh : ↑n ≠ 0\n⊢ n ≠ 0",
"state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\nn : ℕ\nh : ↑n ≠ 0\n⊢ 0 ^ ↑n = 0",
"tactic": "rw [zpow_ofNat, zero_pow']"
},
{
"state_after": "no goals",
"state_before": "case a\nG₀ : Typ... | [
68,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Std/Data/List/Lemmas.lean | List.eraseP_append_left | [
{
"state_after": "case neg\nα : Type u_1\np : α → Bool\na : α\npa : p a = true\nx : α\nxs l₂ : List α\nh : a ∈ x :: xs\nh' : ¬p x = true\n⊢ eraseP p (xs ++ l₂) = eraseP p xs ++ l₂",
"state_before": "α : Type u_1\np : α → Bool\na : α\npa : p a = true\nx : α\nxs l₂ : List α\nh : a ∈ x :: xs\n⊢ eraseP p (x :: ... | [
974,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
969,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.haarContent_self | [
{
"state_after": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup G\ninst✝ : T2Space G\nK₀ : PositiveCompacts G\n⊢ { val := 1, property := (_ : (fun r => 0 ≤ r) 1) } = 1",
"state_before": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : Topologica... | [
567,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_ne | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ i i' : ι\nf : Π₀ (i : ι), β i\nh : i' ≠ i\n⊢ ↑(erase i f) i' = ↑f i'",
"tactic": "simp [h]"
... | [
756,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | IsGLB.mul_left | [
{
"state_after": "case inl\nι : Type ?u.130842\nα : Type u_1\nβ : Type ?u.130848\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\ns : Set α\nha✝ : 0 ≤ a\nhs : IsGLB s b\nha : 0 < a\n⊢ IsGLB ((fun b => a * b) '' s) (a * b)\n\ncase inr\nι : Type ?u.130842\nα : Type u_1\nβ : Type ?u.130848\ninst✝ : Linea... | [
664,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommFoldr_eq_foldr | [
{
"state_after": "case h\nF : Type ?u.2925\nι : Type ?u.2928\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.2937\nf : α → β → β\nop : α → α → α\nh : LeftCommutative f\nb : β\na✝ : List α\n⊢ noncommFoldr f (Quotient.mk (List.isSetoid α) a✝)\n (_ :\n ∀ (x : α),\n x ∈ {x | x ∈ Quotient.mk (List.isSe... | [
76,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.coe_zero | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mem_Ioo_self_sub_add | [] | [
1293,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_map_of_mem | [] | [
1420,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1419,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.fderivWithin_aeval | [] | [
197,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
11
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_abs | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.20890\nι : Type ?u.20893\nα : Type u_1\nβ : Type ?u.20899\ninst✝ : LinearOrderedRing α\na b n : ℤ\n⊢ ↑(abs a) = abs ↑a",
"tactic": "simp [abs_eq_max_neg]"
}
] | [
174,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovaryOn_const_left | [] | [
132,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Icc_left | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : Preorder α\na b✝ c b : α\n⊢ (⋃ (a : α), Icc a b) = Iic b",
"tactic": "simp only [← Ici_inter_Iic, ← iUnion_inter, iUnion_Ici, univ_inter]"
}
] | [
88,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.one_lt_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17835\ninst✝¹ : OrderedSemiring α\ninst✝ : CharZero α\nm n : ℕ\n⊢ 1 < ↑n ↔ 1 < n",
"tactic": "rw [← cast_one, cast_lt]"
}
] | [
142,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.eq_top_iff | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS : Subalgebra R A\nh : S = ⊤\nx : A\n⊢ x ∈ ⊤",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring ... | [
912,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.subset_support_append_left | [
{
"state_after": "no goals",
"state_before": "V✝ : Type u\nV' : Type v\nV'' : Type w\nG✝ : SimpleGraph V✝\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nV : Type u\nG : SimpleGraph V\nu v w : V\np : Walk G u v\nq : Walk G v w\n⊢ support p ⊆ support (append p q)",
"tactic": "simp only [Walk.support_append,... | [
618,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.leftInverse | [] | [
266,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
11
] |
Mathlib/Data/Dfinsupp/Basic.lean | AddMonoidHom.map_dfinsupp_sumAddHom | [] | [
2317,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2314,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_smul | [
{
"state_after": "case inl\nE : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1927122\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : ... | [
361,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_dist | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\nn k : ℕ\nhnk : n ≤ k\nhex : ∃ m, k = n + m\n⊢ ‖newton_seq k - newton_seq n‖ ≤ ‖Polynomial.eval a (↑Polynomial... | [
329,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
9
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_C | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : R\nf : R[X]\nx : R\n⊢ ↑(taylor r) (↑C x) = ↑C x",
"tactic": "simp only [taylor_apply, C_comp]"
}
] | [
54,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.pow_right_iff | [] | [
215,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_self' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑n + 1 = 0",
"tactic": "rw [← Nat.cast_add_one, nat_cast_self (n + 1)]"
}
] | [
137,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/Lattice.lean | Prod.fst_inf | [] | [
1274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | DifferentiableAt.arsinh | [] | [
260,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Control/Bifunctor.lean | Bifunctor.id_snd | [] | [
87,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTriv_apply | [] | [
687,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsLocalization.localization_localization_eq_iff_exists | [
{
"state_after": "R : Type u_3\ninst✝⁹ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nP : Type ?u.134353\ninst✝⁶ : CommRing P\nN : Submonoid S\nT : Type u_2\ninst✝⁵ : CommRing T\ninst✝⁴ : Algebra R T\ninst✝³ : Algebra S T\ninst✝² : IsScalarTower R S T\ninst✝¹ : IsLocaliz... | [
119,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.ClosedUnder.inter | [] | [
79,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.coeff_eq_zero_of_totalDegree_lt | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.477178\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q f : MvPolynomial σ R\nd : σ →₀ ℕ\nh : ∀ (b : σ →₀ ℕ), b ∈ support f → (sum b fun x e => e) < ∑ i in d.support, ↑d i\n⊢ coeff d f = 0\n\nR : Type u\nS : Type v\nσ : Type u_1\... | [
780,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorLeftHomEquiv_symm_naturality | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nX X' Y Y' Z : C\ninst✝ : ExactPairing Y Y'\nf : X ⟶ X'\ng : X' ⟶ Y ⊗ Z\n⊢ (𝟙 Y' ⊗ f ≫ g) ≫ (α_ Y' Y Z).inv ≫ (ε_ Y Y' ⊗ 𝟙 Z) ≫ (λ_ Z).hom =\n (𝟙 Y' ⊗ f) ≫ (𝟙 Y' ⊗ g) ≫ (α_ Y' Y Z).inv ≫ (ε_ Y Y' ⊗ 𝟙 Z) ≫ (λ_ Z).hom",
"s... | [
390,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.mul_sub_left_distrib | [
{
"state_after": "no goals",
"state_before": "n m k : Nat\n⊢ n * (m - k) = n * m - n * k",
"tactic": "rw [Nat.mul_comm, Nat.mul_sub_right_distrib, Nat.mul_comm m n, Nat.mul_comm n k]"
}
] | [
717,
83
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
716,
11
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_toSubMulAction | [] | [
177,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_add | [] | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasStrictFDerivAt.const_sub | [
{
"state_after": "no goals",
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600,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_injective | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.8097\nA : Type u_1\ninst✝⁵ : Semiring A\ninst✝⁴ : SetLike σ A\ninst✝³ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : GradedRing 𝒜\nI : Ideal A\nx✝¹ x✝ : HomogeneousIdeal 𝒜\nx :... | [
88,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/Topology/Semicontinuous.lean | IsOpen.lowerSemicontinuous_indicator | [
{
"state_after": "α : Type u_1\ninst✝² : TopologicalSpace α\nβ : Type u_2\ninst✝¹ : Preorder β\nf g : α → β\nx✝ : α\ns t : Set α\ny z✝ : β\ninst✝ : Zero β\nhs : IsOpen s\nhy : 0 ≤ y\nx : α\nz : β\nhz : z < indicator s (fun _x => y) x\n⊢ ∀ᶠ (x' : α) in 𝓝 x, z < indicator s (fun _x => y) x'",
"state_before":... | [
209,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | rothNumberNat_isBigOWith_id | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.197857\nα : Type ?u.197860\nβ : Type ?u.197863\n𝕜 : Type ?u.197866\nE : Type ?u.197869\ns : Finset ℕ\nk n : ℕ\n⊢ ∀ (x : ℕ), ‖↑(↑rothNumberNat x)‖ ≤ ‖↑x‖",
"tactic": "simpa only [Real.norm_coe_nat, Nat.cast_le] using rothNumberNat_le"
}
] | [
517,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.index_nonempty | [
{
"state_after": "case intro.intro\nι : Type u_1\nι' : Type ?u.464205\nR : Type u_2\nR₂ : Type ?u.464211\nK : Type ?u.464214\nM : Type u_3\nM' : Type ?u.464220\nM'' : Type ?u.464223\nV : Type u\nV' : Type ?u.464228\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ni... | [
581,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_sdiff_inf | [
{
"state_after": "ι : Type ?u.27143\nα : Type u_1\nβ : Type ?u.27149\nπ : ι → Type ?u.27154\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a \\ (b ⊔ a ⊓ b) ⊔ b \\ (a ⊔ a ⊓ b) = a ∆ b",
"state_before": "ι : Type ?u.27143\nα : Type u_1\nβ : Type ?u.27149\nπ : ι → Type ?u.27154\ninst✝ : GeneralizedCohe... | [
176,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_sigma | [] | [
868,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.isLeft_eq_false | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.6615\nδ : Type ?u.6618\nx y : α ⊕ β\n⊢ isLeft x = false ↔ isRight x = true",
"tactic": "cases x <;> simp"
}
] | [
130,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.lipschitzOnWith_of_nnnorm_fderivWithin_le | [] | [
534,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Topology/Order/Basic.lean | Antitone.map_iSup_of_continuousAt | [] | [
2734,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2730,
1
] |
Mathlib/Data/List/Count.lean | List.filter_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl✝ : List α\ninst✝ : DecidableEq α\nl : List α\na : α\n⊢ filter (fun x => decide (a = x)) l = replicate (count a l) a",
"tactic": "simpa only [eq_comm] using filter_eq' l a"
}
] | [
292,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.continuousLinearMap_comp | [] | [
223,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_subset_singleton | [] | [
953,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q a : R[X]\n⊢ a.toFinsupp = 0 ↔ a = 0",
"tactic": "rw [← toFinsupp_zero, toFinsupp_inj]"
}
] | [
266,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
src/lean/Init/Core.lean | HEq.ndrecOn | [] | [
616,
10
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
615,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | continuous_mul_right | [] | [
105,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Differentiable.differentiableOn | [] | [
618,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Analysis/Calculus/FDerivSymmetric.lean | second_derivative_symmetric | [] | [
326,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/Set/Image.lean | Set.Subsingleton.preimage | [] | [
1224,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.ne_iff | [] | [
90,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.tendsto | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.56525\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → F\nx : E\nhf... | [
174,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
11
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_empty | [] | [
2345,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2345,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_upperSemicontinuousAt | [] | [
846,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.apply_mk | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : OrderTop α\na b c d : α\nha : a ≠ ⊤\nhab : Codisjoint a b\nh : a = b\n⊢ Codisjoint a a",
"tactic": "rwa [← h] at hab"
}
] | [
275,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.357626\nγ : Type ?u.357629\nι : Type ?u.357632\nM : Type u_1\nM' : Type ?u.357638\nN : Type ?u.357641\nP : Type ?u.357644\nG : Type ?u.357647\nH : Type ?u.357650\nR : Type ?u.357653\nS : Type ?u.357656\ninst✝ : Zero M\np : α → Prop\nf :... | [
896,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Std/Data/Array/Lemmas.lean | Array.getElem_ofFn_go | [
{
"state_after": "no goals",
"state_before": "n : Nat\nα : Type ?u.131979\nf : Fin n → α\ni : Nat\nacc : Array α\nk : Nat\nhki : k < n\nhin : i ≤ n\nhi : i = size acc\nhacc : ∀ (j : Nat) (hj : j < size acc), acc[j] = f { val := j, isLt := (_ : j < n) }\nthis : size acc + (n - size acc) = n\n⊢ k < size (ofFn... | [
298,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
282,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_inv | [] | [
806,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | AntitoneOn.mul' | [] | [
1367,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_single_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.46826\nγ : Type ?u.46829\nι : Type ?u.46832\nM : Type u_2\nM' : Type ?u.46838\nN : Type ?u.46841\nP : Type ?u.46844\nG : Type ?u.46847\nH : Type ?u.46850\nR : Type ?u.46853\nS : Type ?u.46856\ninst✝ : Zero M\na a' : α\nb : M\n⊢ (single ... | [
366,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/Convex/Independent.lean | convexIndependent_set_iff_inter_convexHull_subset | [
{
"state_after": "case mp\n𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.39598\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns✝ t s : Set E\n⊢ ConvexIndependent 𝕜 Subtype.val → ∀ (t : Set E), t ⊆ s → s ∩ ↑(convexHull 𝕜).toOrderHom t ⊆ t\n\ncase mpr\n𝕜 : Type u_2\nE : Type u_1\nι : Ty... | [
155,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_sum | [] | [
699,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | one_smul_eq_id | [] | [
489,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.zero_lxor' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ lxor' 0 n = n",
"tactic": "simp only [Bool.xor_false_left, Nat.bitwise'_zero_left, eq_self_iff_true, Bool.cond_true, lxor']"
}
] | [
190,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.coeFn_toL1 | [] | [
1359,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.coe_zero | [] | [
258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Real.norm_of_nonneg | [] | [
1715,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Module.isTorsionBySet_iff_torsionBySet_eq_top | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set R\na : R\nh : torsionBySet R M s = ⊤\nx : M\n⊢ x ∈ ⊤",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set R\na... | [
332,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_eq_zero_comm | [] | [
268,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Constructions.lean | map_fst_nhds | [] | [
704,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.aux_pid_of_ufd_of_unique_irreducible | [
{
"state_after": "case principal\nR✝ : Type ?u.50365\nR : Type u\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : UniqueFactorizationMonoid R\nh₁ : ∃ p, Irreducible p\nh₂ : ∀ ⦃p q : R⦄, Irreducible p → Irreducible q → Associated p q\n⊢ ∀ (S : Ideal R), Submodule.IsPrincipal S",
"state_before": "R✝ : Type ... | [
283,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/PFun.lean | PFun.mem_toSubtype_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.52355\nδ : Type ?u.52358\nε : Type ?u.52361\nι : Type ?u.52364\nf✝ : α →. β\np : β → Prop\nf : α → β\na : α\nb : Subtype p\n⊢ b ∈ toSubtype p f a ↔ ↑b = f a",
"tactic": "rw [toSubtype_apply, Part.mem_mk_iff, exists_sub... | [
559,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_toReal_eq_iff | [
{
"state_after": "α : Type ?u.25366\nβ : Type ?u.25369\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : ENNReal.ofReal (ENNReal.toReal a) = a\n⊢ ENNReal.ofReal (ENNReal.toReal a) ≠ ⊤",
"state_before": "α : Type ?u.25366\nβ : Type ?u.25369\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : ENNReal.ofReal (ENNReal.toReal a) = a\n⊢ a ≠ ⊤",
... | [
305,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/CategoryTheory/Functor/Const.lean | CategoryTheory.Functor.const.opObjUnop_inv_app | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.ProjectivePlane.lineCount_eq_lineCount | [
{
"state_after": "case intro\nP : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P L\ninst✝¹ : Finite P\ninst✝ : Finite L\np q : P\nval✝ : Fintype P\n⊢ lineCount L p = lineCount L q",
"state_before": "P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P ... | [
418,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Pi.norm_def' | [] | [
2458,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2457,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀ | [] | [
153,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_lt_top | [] | [
302,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
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