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/Logic/Equiv/Set.lean | Equiv.subset_image' | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα : Type u_1\nβ : Type u_2\ne : α ≃ β\ns : Set α\nt : Set β\n⊢ s ⊆ ↑e.symm '' t ↔ ↑e.symm.symm '' s ⊆ t",
"tactic": "rw [e.symm.subset_image]"
},
{
"state_after": "no goals",
"state_before": "α✝ : Sort u\nβ✝ ... | [
74,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_le | [] | [
447,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_top | [] | [
622,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Data/Set/Image.lean | Set.compl_image | [] | [
530,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_X_left_apply | [] | [
1463,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.dvd_ofDigits_sub_ofDigits | [
{
"state_after": "case nil\nn : ℕ\nα : Type u_1\ninst✝ : CommRing α\na b k : α\nh : k ∣ a - b\n⊢ k ∣ ofDigits a [] - ofDigits b []\n\ncase cons\nn : ℕ\nα : Type u_1\ninst✝ : CommRing α\na b k : α\nh : k ∣ a - b\nd : ℕ\nL : List ℕ\nih : k ∣ ofDigits a L - ofDigits b L\n⊢ k ∣ ofDigits a (d :: L) - ofDigits b (d :... | [
502,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Order/Bounds/Basic.lean | upperBounds_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns✝ t : Set α\na✝ b a : α\ns : Set α\n⊢ upperBounds (insert a s) = Ici a ∩ upperBounds s",
"tactic": "rw [insert_eq, upperBounds_union, upperBounds_singleton]"
}
] | [
973,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_zero_of_empty | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.306222\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : PseudoMetricSpace β\ninst✝¹ : PseudoMetricSpace γ\nf g : α →ᵇ β\nx : α\nC : ℝ\ninst✝ : IsEmpty α\n⊢ dist f g = 0",
"tactic": "rw [(ext isEmptyElim : f = g), dist_se... | [
250,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.lift_sub_val_mem_span | [
{
"state_after": "case intro\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\nr : R\nn k : ℕ\nhk : ∀ (n_1 : ℕ), n_1 ≥ k → ‖l... | [
635,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | nonpos_of_mul_nonpos_right | [] | [
833,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.surjective | [] | [
362,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.injective | [] | [
143,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.sub | [] | [
1894,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1891,
11
] |
Mathlib/Order/WellFounded.lean | Function.not_lt_argminOn | [] | [
212,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.subset_def | [
{
"state_after": "α : Type u_1\nl₁ l₂ : Lists' α true\nH : ∀ (a : Lists α), a ∈ toList l₁ → a ∈ l₂\n⊢ ofList (toList l₁) ⊆ l₂",
"state_before": "α : Type u_1\nl₁ l₂ : Lists' α true\nH : ∀ (a : Lists α), a ∈ toList l₁ → a ∈ l₂\n⊢ l₁ ⊆ l₂",
"tactic": "rw [← of_toList l₁]"
},
{
"state_after": "α : ... | [
212,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Equiv.Perm.decomposeFin_symm_apply_one | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ne : Perm (Fin (n + 1))\np : Fin (n + 2)\n⊢ ↑(↑decomposeFin.symm (p, e)) 1 = ↑(swap 0 p) (Fin.succ (↑e 0))",
"tactic": "rw [← Fin.succ_zero_eq_one, Equiv.Perm.decomposeFin_symm_apply_succ e p 0]"
}
] | [
63,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.id_comp | [] | [
480,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_comm | [
{
"state_after": "ι : Sort ?u.35598\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\n⊢ ((⨆ (x : α) (_ : x ∈ s), infEdist x t) ⊔ ⨆ (y : α) (_ : y ∈ t), infEdist y s) =\n (⨆ (y : α) (_ : y ∈ t), infEdist y s) ⊔ ⨆ (x : α) (_ : x ∈ s), infEd... | [
277,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Std/Logic.lean | eq_iff_iff | [] | [
53,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
53,
9
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumDualDistrib_inr | [] | [
622,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_distrib_subset_right | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u_4\nα' : Type u_6\nβ : Type u_5\nβ' : Type u_7\nγ : Type u_3\nγ' : Type ?u.46897\nδ : Type u_2\nδ' : Type ?u.46903\nε : Type u_1\nε' : Type ?u.46909\nζ : Type ?u.46912\nζ' : Type ?u.46915\nν : Type ?u.46918\nf✝ f' : α → β → γ\ng✝ ... | [
394,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.xor_iff_ne | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ {x y : Bool}, xor x y = true ↔ x ≠ y",
"tactic": "decide"
}
] | [
301,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_max' | [
{
"state_after": "F : Type ?u.352825\nα : Type u_1\nβ : Type ?u.352831\nγ : Type ?u.352834\nι : Type ?u.352837\nκ : Type ?u.352840\ninst✝ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ns : Finset αᵒᵈ\nhs : Finset.Nonempty s\n⊢ ↑(↑ofDual (max' s hs)) = ↑(min' (image (↑ofDual) s) (_ : Finset.Nonem... | [
1444,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.proj_some_index | [] | [
424,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
src/lean/Init/Data/Fin/Basic.lean | Fin.mlt | [] | [
36,
22
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
32,
9
] |
Mathlib/Algebra/Order/Field/Power.lean | Nat.zpow_ne_zero_of_pos | [] | [
56,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | generateFrom_eq_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.808243\nβ : Type u_2\nβ' : Type ?u.808249\nγ : Type ?u.808252\nE : Type ?u.808255\ninst✝⁵ : MeasurableSpace α\ninst✝⁴ : MeasurableSpace α'\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace β'\ninst✝¹ : MeasurableSpace γ\nμ μ' : Mea... | [
141,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.orderEmbeddingToFun_apply | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isUpperSet_iInter₂ | [] | [
165,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_cons | [] | [
1405,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | MeasureTheory.SimpleFunc.edist_approxOn_mono | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.64039\nE : Type ?u.64042\nF : Type ?u.64045\n𝕜 : Type ?u.64048\ninst✝⁴ : MeasurableSpace α\ninst✝³ : PseudoEMetricSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : MeasurableSpace β\nf✝ f : β → α\nhf : Measurable f\ns : Set α\ny₀ : α\nh₀ : y₀ ∈ s\ninst... | [
174,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | rotation_symm | [] | [
59,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.apriori_edist_iterate_efixedPoint_le' | [] | [
221,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.toSubring_subtype_eq_subtype | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_hasFDerivAt_iff' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ... | [
234,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.prodMap_smul | [] | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_nonpos_iff | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\n⊢ sinh x ≤ 0 ↔ x ≤ 0",
"tactic": "simpa only [sinh_zero] using @sinh_le_sinh x 0"
}
] | [
709,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_comp_le_hammingDist | [] | [
136,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.degree_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⊢ degree (p * q) = degree (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 : R[X]\n... | [
184,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.tendsto_nhds_top_iff_real | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.12287\ninst✝ : TopologicalSpace α✝\nα : Type u_1\nm : α → EReal\nf : Filter α\n⊢ (∀ (i : ℝ), True → ∀ᶠ (x : α) in f, m x ∈ Ioi ↑i) ↔ ∀ (x : ℝ), ∀ᶠ (a : α) in f, ↑x < m a",
"tactic": "simp only [true_implies, mem_Ioi]"
}
] | [
151,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.opRingEquiv_op_X | [] | [
56,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | ContinuousLinearMap.dslope_comp | [
{
"state_after": "case inl\n𝕜 : Type u_2\nE : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf✝ : 𝕜 → E\na b✝ : 𝕜\ns : Set 𝕜\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E →L[𝕜] F\ng : 𝕜 → E\nb : 𝕜\nH : b = b → Diffe... | [
55,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.bot_coeSubmodule | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.neg_mem_iff | [] | [
656,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_subset_thickening' | [] | [
1111,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1109,
1
] |
Mathlib/Order/BooleanAlgebra.lean | inf_compl_eq_bot' | [] | [
558,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.ofLinearEquiv_symm | [] | [
619,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.exp_inr | [
{
"state_after": "case hx\n𝕜 : Type u_3\nR : Type u_1\nM : Type u_2\ninst✝¹⁷ : IsROrC 𝕜\ninst✝¹⁶ : NormedRing R\ninst✝¹⁵ : AddCommGroup M\ninst✝¹⁴ : NormedAlgebra 𝕜 R\ninst✝¹³ : Module R M\ninst✝¹² : Module Rᵐᵒᵖ M\ninst✝¹¹ : SMulCommClass R Rᵐᵒᵖ M\ninst✝¹⁰ : Module 𝕜 M\ninst✝⁹ : IsScalarTower 𝕜 R M\ninst✝⁸... | [
128,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.644630\n⊢ leadingCoeff X = 1",
"tactic": "simpa only [pow_one] using @leadingCoeff_X_pow R _ 1"
}
] | [
822,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.toOrdinal_min | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.coe_ne_one | [] | [
84,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_eq_zero_iff | [] | [
268,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Order/Atoms.lean | OrderEmbedding.isCoatom_of_map_top_of_image | [] | [
708,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.trans_apply | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.foldl_eq' | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\nf : β → α → β\nl₁ l₂ : List α\np : l₁ ~ l₂\nx y : α\nt₁ t₂ : List α\n_p : t₁ ~ t₂\nr :\n (∀ (x : α), x ∈ t₁ → ∀ (y : α), y ∈ t₁ → ∀ (z : β), f (f z x) y = f (f z y) x) →\n ∀ (b : β), foldl f b t₁ = foldl f b t₂\nH : ∀ (x_1 : α), x_1 ∈ y :: x :: t... | [
517,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | absorbs_zero_iff | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.204287\nE : Type u_2\nι : Sort ?u.204293\nκ : ι → Sort ?u.204298\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\n⊢ Absorbs 𝕜 s 0 → 0 ∈ s",
"state_before": "𝕜 : Type u_1\n𝕝 : Type ?u.204287\nE : Type u_2\nι : Sort... | [
398,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_subset_product_right | [] | [
102,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | integralClosure.isFractionRing_of_finite_extension | [] | [
379,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.neg | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nhuv : u ~[l] v\n⊢ ((fun x => -u x) - fun x => -v x) =o[l] fun x => -v x",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nhuv : u ~[l] v\n⊢ (fun x ... | [
186,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots' | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\nhp0 : p = 0\n⊢ ↑Multiset.card (roots p) ≤ natDegree p\n\ncase neg\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\nh... | [
547,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.coprime_primes | [] | [
675,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/List/Join.lean | List.sum_take_map_length_lt1 | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12788\nL : List (List α)\ni j : ℕ\nhi : i < length L\nhj : j < length (nthLe L i hi)\n⊢ sum (take i (map length L)) + j < sum (take (i + 1) (map length L))",
"tactic": "simp [hi, sum_take_succ, hj]"
}
] | [
164,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.P_f_naturality | [] | [
201,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Set/Function.lean | Set.BijOn.surjOn | [] | [
916,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/Init/Data/List/Basic.lean | List.headI_nil | [] | [
42,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
9
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.ext | [] | [
837,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Algebra/CharP/Algebra.lean | algebraRat.charP_zero | [] | [
80,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_iInter | [] | [
110,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/RepresentationTheory/Maschke.lean | LinearMap.equivariantProjection_apply | [
{
"state_after": "no goals",
"state_before": "k : Type u\ninst✝¹¹ : CommRing k\nG : Type u\ninst✝¹⁰ : Group G\nV : Type v\ninst✝⁹ : AddCommGroup V\ninst✝⁸ : Module k V\ninst✝⁷ : Module (MonoidAlgebra k G) V\ninst✝⁶ : IsScalarTower k (MonoidAlgebra k G) V\nW : Type w\ninst✝⁵ : AddCommGroup W\ninst✝⁴ : Module... | [
131,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_coe_eq | [] | [
339,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.tendsto_Lp_of_tendstoInMeasure | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type ?u.504674\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\np : ℝ≥0∞\nf : ℕ → α → β\ng : α → β\ninst✝ : IsFiniteMeasure μ\nhp : 1 ≤ p\nhp' : p ≠ ⊤\nhf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ\nhg : Memℒp g p\nhui : UnifIntegrable f p μ\... | [
620,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.set_smul_subset_set_smul_iff₀ | [] | [
1035,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | norm_fderiv_iteratedFDeriv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\... | [
1570,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.independent_of_dfinsupp_sumAddHom_injective' | [
{
"state_after": "ι : Type u_2\nR : Type ?u.632921\nS : Type ?u.632924\nM : ι → Type ?u.632929\nN : Type u_1\ndec_ι : DecidableEq ι\ninst✝² : Ring R\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\np : ι → AddSubgroup N\nh : Function.Injective ↑(sumAddHom fun i => AddSubgroup.subtype (p i))\n⊢ Independent (↑AddSub... | [
487,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_cons | [] | [
45,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | exists_lt_mul_self | [] | [
1940,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1937,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | Subgroup.isOpen_of_openSubgroup | [] | [
331,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.pair_unpair | [
{
"state_after": "n : ℕ\n⊢ pair\n (if n - sqrt n * sqrt n < sqrt n then (n - sqrt n * sqrt n, sqrt n)\n else (sqrt n, n - sqrt n * sqrt n - sqrt n)).fst\n (if n - sqrt n * sqrt n < sqrt n then (n - sqrt n * sqrt n, sqrt n)\n else (sqrt n, n - sqrt n * sqrt n - sqrt n)).snd =\n n",
... | [
60,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.Approx.agree_children | [
{
"state_after": "case intro\nF : PFunctor\nn : ℕ\na✝ : F.A\nx✝ : B F a✝ → CofixA F n\nx'✝ : B F a✝ → CofixA F (n + 1)\nhagree : ∀ (i : B F a✝), Agree (x✝ i) (x'✝ i)\ni : B F (head' (CofixA.intro a✝ x✝))\nj : B F (head' (CofixA.intro a✝ x'✝))\nh₀ : HEq i j\n⊢ Agree (children' (CofixA.intro a✝ x✝) i) (children' ... | [
95,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.Semiconj.iterate_right | [] | [
109,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | EquicontinuousAt.closure | [] | [
392,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Std/Data/String/Lemmas.lean | String.posOfAux_eq | [] | [
313,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
313,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mk_coeFn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.308002\nδ : Type ?u.308005\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α →ₘ[μ] β\n⊢ mk ↑f (_ : AEStronglyMeasurable (↑f) μ) = Quotient.mk'' (Quotient.out' f)",
... | [
171,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.zero_lt_coe | [] | [
415,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/LinearAlgebra/Pi.lean | Submodule.iSup_map_single | [
{
"state_after": "case intro\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\nι' : Type x'\ninst✝⁴ : Semiring R\nφ : ι → Type u_1\ninst✝³ : (i : ι) → AddCommMonoid (φ i)\ninst✝² : (i : ι) → Module R (φ i)\nI : Set ι\np q : (i : ι) ... | [
320,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.map_smulₛₗ | [] | [
224,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
11
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.iff_isOpen_fiber | [] | [
111,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/Order.lean | discreteTopology_bot | [] | [
276,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.smul_inj | [] | [
914,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.val_toFinset | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.455035\nγ : Type ?u.455038\ninst✝ : DecidableEq α\ns : Finset α\na✝ : α\n⊢ a✝ ∈ toFinset s.val ↔ a✝ ∈ s",
"state_before": "α : Type u_1\nβ : Type ?u.455035\nγ : Type ?u.455038\ninst✝ : DecidableEq α\ns : Finset α\n⊢ toFinset s.val = s",
"tactic": "ext"... | [
3218,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3216,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_eq_asc_factorial_div_factorial | [
{
"state_after": "n k : ℕ\n⊢ k ! * choose (n + k) k = k ! * (ascFactorial n k / k !)",
"state_before": "n k : ℕ\n⊢ choose (n + k) k = ascFactorial n k / k !",
"tactic": "apply mul_left_cancel₀ (factorial_ne_zero k)"
},
{
"state_after": "n k : ℕ\n⊢ ascFactorial n k = k ! * (ascFactorial n k / k !... | [
255,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_one_div_add_atTop_nhds_0_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.3724\nβ : Type ?u.3727\nι : Type ?u.3730\nthis : Tendsto (fun n => 1 / ↑(n + 1)) atTop (𝓝 0)\n⊢ Tendsto (fun n => 1 / (↑n + 1)) atTop (𝓝 0)",
"tactic": "simpa"
}
] | [
56,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_of_mul_le_of_nonneg_right | [] | [
435,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/Order.lean | le_of_nhds_le_nhds | [
{
"state_after": "α : Type u_1\nt t₁ t₂ : TopologicalSpace α\ns✝ : Set α\nh : ∀ (x : α), 𝓝 x ≤ 𝓝 x\ns : Set α\n⊢ (∀ (a : α), a ∈ s → s ∈ 𝓝 a) → ∀ (a : α), a ∈ s → s ∈ 𝓝 a",
"state_before": "α : Type u_1\nt t₁ t₂ : TopologicalSpace α\ns✝ : Set α\nh : ∀ (x : α), 𝓝 x ≤ 𝓝 x\ns : Set α\n⊢ IsOpen s → IsOpen... | [
306,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_union_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45790\ninst✝ : PartialOrder α\na b c x : α\n⊢ x ∈ Ioi a ∪ {a} ↔ x ∈ Ici a",
"tactic": "simp [eq_comm, le_iff_eq_or_lt]"
}
] | [
848,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Computability/NFA.lean | NFA.pumping_lemma | [
{
"state_after": "α : Type u\nσ σ' : Type v\nM : NFA α σ\ninst✝ : Fintype σ\nx : List α\nhx : x ∈ DFA.accepts (toDFA M)\nhlen : Fintype.card (Set σ) ≤ List.length x\n⊢ ∃ a b c,\n x = a ++ b ++ c ∧\n List.length a + List.length b ≤ Fintype.card (Set σ) ∧ b ≠ [] ∧ {a} * {b}∗ * {c} ≤ DFA.accepts (toDFA M)"... | [
135,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.zero_le | [
{
"state_after": "case mk\nα✝ β : Type u\na✝ : Cardinal\nα : Type u_1\n⊢ 0 ≤ Quot.mk Setoid.r α",
"state_before": "α β : Type u\n⊢ ∀ (a : Cardinal), 0 ≤ a",
"tactic": "rintro ⟨α⟩"
},
{
"state_after": "no goals",
"state_before": "case mk\nα✝ β : Type u\na✝ : Cardinal\nα : Type u_1\n⊢ 0 ≤ Quot... | [
657,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
11
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_sup | [] | [
923,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.int_cast_imI | [] | [
1005,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tail_interleave | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\ns₁ s₂ : Stream' α\n⊢ tail\n (corec\n (fun x =>\n match x with\n | (s₁, snd) => head s₁)\n (fun x =>\n match x with\n | (s₁, s₂) => (s₂, tail s₁))\n (s₁, s₂)) =\n corec\n (fun x =>\n ... | [
424,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
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