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/Data/Set/Function.lean | Set.restrict_eq_iff | [] | [
64,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Analysis/Convex/Star.lean | starConvex_iff_forall_pos | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.15199\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y z : E\ns : Set E\nhx : x ∈ s\n⊢ (∀ ⦃y : E⦄, y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ s) → Sta... | [
176,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Topology/Maps.lean | Embedding.discreteTopology | [
{
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"state_before": "α : Type ?u.127326\nβ : Type ?u.127329\nγ : Type ?u.127332\nδ : Type ?u.127335\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\nX : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ntY : TopologicalSpace Y\ninst✝ : Discr... | [
264,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
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Mathlib/Order/Heyting/Basic.lean | sdiff_le_hnot | [] | [
997,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
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Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsNat.to_isRat | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Ring α\nn✝ : ℕ\n⊢ 1 * ↑1 = 1",
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},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Ring α\nn✝ : ℕ\n⊢ ↑1 * 1 = 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_be... | [
154,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx0 : x ≤ 0\nhpx : -(π / 2) ≤ x\n⊢ 0 ≤ -x",
"tactic": "linarith"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx0 : x ≤ 0\nhpx : -(π / 2) ≤ x\n⊢ -x ≤ π / 2",
"tactic": "linarith"
}
] | [
957,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
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Mathlib/Order/Hom/Basic.lean | OrderHom.const_comp | [] | [
394,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
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Mathlib/Data/Nat/Count.lean | Nat.count_le_cardinal | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ Cardinal.mk { k // k < n ∧ p k } ≤ Cardinal.mk ↑{k | p k}",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ ↑(count p n) ≤ Cardinal.mk ↑{k | p k}",
"tactic": "rw [count_eq_card_fintype, ← Cardinal.mk_fintype]"
},
{
... | [
125,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_right_of_ge' | [] | [
796,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_eq_span_of_subset | [] | [
207,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.lt_def | [] | [
64,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.NatTrans.removeUnop_id | [] | [
371,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.mem_support_pure_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3232\nγ : Type ?u.3235\na a' : α\n⊢ a' ∈ support (pure a) ↔ a' = a",
"tactic": "simp"
}
] | [
56,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.tan_add_mul_I | [
{
"state_after": "no goals",
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"tactic": ... | [
142,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Algebra/Group/Defs.lean | mul_inv_rev | [] | [
1028,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
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Mathlib/Order/Partition/Finpartition.lean | Finpartition.card_bind | [
{
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407,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.aeval_T | [
{
"state_after": "no goals",
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"tactic": "rw [aeval_def, eval₂_eq_eval_map, map_T]"
}
] | [
33,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_map_of_injective | [
{
"state_after": "no goals",
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"... | [
256,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Std/Data/Int/DivMod.lean | Int.fdiv_zero | [] | [
53,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
50,
19
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Mathlib/LinearAlgebra/Alternating.lean | LinearMap.compMultilinearMap_alternatization | [
{
"state_after": "case H\nR : Type u_1\ninst✝¹⁴ : Semiring R\nM : Type u_4\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\nN : Type ?u.744012\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : Module R N\nP : Type ?u.744042\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\nM' : Type ?u.744072\ninst✝⁷ : AddCommGroup M'\ninst... | [
921,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.int_even_mul_periodic | [] | [
399,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_sub | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ a - b - c = a - (b + c)",
"tactic": "simp [Int.sub_eq_add_neg, Int.add_assoc]"
}
] | [
361,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
360,
11
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_inj | [] | [
117,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Quotient.congr_mk | [] | [
971,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
9
] |
Mathlib/Data/List/Sigma.lean | List.mem_keys_kinsert | [
{
"state_after": "no goals",
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"tactic": "by_cases h : a = a' <;> simp [h]"
}
] | [
575,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | norm_image_of_norm_zero | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type u_3\n𝕜₃ : Type ?u.1293\nE : Type u_4\nEₗ : Type ?u.1299\nF : Type u_5\nFₗ : Type ?u.1305\nG : Type ?u.1308\nGₗ : Type ?u.1311\n𝓕 : Type u_1\ninst✝¹⁶ : SeminormedAddCommGroup E\ninst✝¹⁵ : SeminormedAddCommGroup Eₗ\ninst✝¹⁴ : SeminormedAddCommGroup F\ninst✝¹³ : Semino... | [
60,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_addMonoidHom_mk | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/Topology/Separation.lean | Continuous.closedEmbedding | [] | [
1338,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
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Mathlib/Data/List/Basic.lean | List.indexOf_append_of_not_mem | [
{
"state_after": "case nil\nι : Type ?u.82162\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na : α\nh✝ : ¬a ∈ l₁\nh : ¬a ∈ []\n⊢ indexOf a ([] ++ l₂) = length [] + indexOf a l₂\n\ncase cons\nι : Type ?u.82162\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List ... | [
1227,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
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] |
Mathlib/Algebra/CharP/Basic.lean | sub_pow_char_pow_of_commute | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : Ring R\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP R p\nn : ℕ\nx y : R\nh : Commute x y\n⊢ (x - y) ^ p ^ n = x ^ p ^ n - y ^ p ^ n",
"tactic": "induction n with\n| zero => simp\n| succ n n_ih =>\n rw [pow_succ', pow_mul, pow_... | [
272,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.equivFunOnFinite_single | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.138459\nγ : Type ?u.138462\nι : Type ?u.138465\nM : Type u_2\nM' : Type ?u.138471\nN : Type ?u.138474\nP : Type ?u.138477\nG : Type ?u.138480\nH : Type ?u.138483\nR : Type ?u.138486\nS : Type ?u.138489\ninst✝² : Zero M\na a' : α\nb : M\ninst✝¹ : DecidableEq α\... | [
516,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Topology/Order/Basic.lean | frontier_lt_subset_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderClosedTopology α\nf g : β → α\ninst✝ : TopologicalSpace β\nhf : Continuous f\nhg : Continuous g\n⊢ frontier {b | f b < g b} ⊆ {b | f b = g b}",
"tactic": "... | [
647,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.subtype_card | [] | [
124,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTransposeAddEquiv_symm | [] | [
2270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2268,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | prime_factors_irreducible | [
{
"state_after": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\na : α\nf : Multiset α\nha : Irreducible a\npfa : (∀ (b : α), b ∈ f → Prime b) ∧ Multiset.prod f ~ᵤ a\nthis : DecidableEq α\n⊢ ∃ p, a ~ᵤ p ∧ f = {p}",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\na : α\nf : Multiset α\n... | [
278,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.prod_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\na b : FactorSet α\n⊢ FactorSet.prod a... | [
1553,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1546,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.deriv_of_open | [] | [
2134,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2132,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_pow_eq_monomial | [
{
"state_after": "case zero\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ X ^ Nat.zero = ↑(monomial Nat.zero) 1\n\ncase succ\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nhn : X ^ n = ↑(monomial n) 1\n⊢ X ^ Nat.succ n = ↑(monomial (Nat.succ n)) 1",
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890,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_eq_zero_symm | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1186924\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑(starRingEnd 𝕜) (inner y x) = 0 ↔ inner y x = 0",
"state_b... | [
453,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.basicOpen_eq_zeroLocus_compl | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nr : A\nx : ProjectiveSpectrum 𝒜\n⊢ x ∈ ↑(basicOpen 𝒜 r) ↔ ¬r ∈ ↑x.asHomogeneousIdeal",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : C... | [
409,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
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Std/Data/String/Lemmas.lean | String.Pos.add_byteIdx | [] | [
97,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
97,
9
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_prod | [] | [
760,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
8
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.add_apply | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Set/Finite.lean | Set.iInf_iSup_of_antitone | [] | [
1519,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1516,
1
] |
Mathlib/CategoryTheory/Skeletal.lean | CategoryTheory.ThinSkeleton.map_iso_eq | [] | [
318,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.nonempty_iso_symm | [] | [
136,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.contDiffAt | [] | [
1341,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Data/List/Basic.lean | List.all₂_map_iff | [
{
"state_after": "no goals",
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"tactic": "induction l <;> simp [*]"
}
] | [
4282,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4281,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.commute_X | [] | [
1389,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
1
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Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.ext_ring | [
{
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401,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
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Mathlib/Order/SymmDiff.lean | compl_symmDiff_self | [] | [
770,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
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Mathlib/Algebra/Order/Kleene.lean | le_kstar | [] | [
240,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translate_inv_apply | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.liftNC_mul | [] | [
1302,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
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Mathlib/Topology/Sober.lean | IsIrreducible.genericPoint_closure_eq | [] | [
141,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Tactic/GCongr.lean | Nat.cast_le_cast | [] | [
140,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.comp_smul_apply | [] | [
450,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.inner_eq_mul_norm_of_angle_eq_zero | [
{
"state_after": "no goals",
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"tactic": "simp [← cos_angle_mul_norm_mul_norm, h]"
}
] | [
247,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Data/Real/Pointwise.lean | Real.mul_iSup_of_nonpos | [] | [
131,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.inv_Ioo_0_left | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : LinearOrderedField α\na✝ a : α\nha : 0 < a\nx : α\n⊢ x ∈ (Ioo 0 a)⁻¹ ↔ x ∈ Ioi a⁻¹",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a : α\nha : 0 < a\n⊢ (Ioo 0 a)⁻¹ = Ioi a⁻¹",
"tactic": "ext x"
},
{
"state_after": "no goals",
... | [
768,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
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Mathlib/Data/Set/Basic.lean | Set.setOf_eq_eq_singleton | [] | [
1262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
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src/lean/Init/Control/Lawful.lean | bind_pure | [
{
"state_after": "m : Type u_1 → Type u_2\nα : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m α\n⊢ (do\n let a ← x\n pure (id a)) =\n x",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m α\n⊢ x >>= pure = x",
"tactic": "show x ... | [
60,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
58,
9
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Mathlib/Topology/LocalExtr.lean | IsLocalExtr.comp_mono | [] | [
228,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
8
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | lt_or_lt_of_mul_lt_mul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4096\ninst✝³ : LinearOrder α\ninst✝² : Mul α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na₁ a₂ b₁ b₂ : α\n⊢ a₂ ≤ a₁ ∧ b₂ ≤ b₁ → a₂ * b₂ ≤ a₁ * b₁",
"state_be... | [
88,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/Order/Interval.lean | Interval.mul_bot | [] | [
219,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/Ring/Units.lean | IsUnit.sub_iff | [] | [
108,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Std/Data/List/Lemmas.lean | List.get?_inj | [
{
"state_after": "no goals",
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"tactic": "induction xs generalizing i j with\n| nil => cases h₀\n| cons x xs ih =>\n match i, j with\n | 0, 0 => rfl\n | i+1, j+1 => s... | [
566,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
551,
1
] |
Mathlib/Order/WithBot.lean | WithBot.unbot_coe | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.empty_smul | [] | [
1305,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_add_int | [
{
"state_after": "no goals",
"state_before": "x✝ y✝ z x : ℝ\nhx : x ≠ 0\ny : ℝ\nn : ℤ\n⊢ x ^ (y + ↑n) = x ^ y * x ^ n",
"tactic": "rw [rpow_def, rpow_def, Complex.ofReal_add,\nComplex.cpow_add _ _ (Complex.ofReal_ne_zero.mpr hx), Complex.ofReal_int_cast,\nComplex.cpow_int_cast, ← Complex.ofReal_zpow, mu... | [
330,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.Q_f_0_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ HomologicalComplex.Hom.f (Q q) 0 = 0",
"tactic": "simp only [HomologicalComplex.sub_f_apply, HomologicalComplex.id_f, Q, P_f_0_eq, sub_self]"
}
] | [
103,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.of_exists_prime_factors | [] | [
342,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.tensor_comp | [
{
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279,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_mul_le_iff' | [
{
"state_after": "no goals",
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"tactic": "rw [inv_mul_le_iff h, mul_comm]"
}
] | [
183,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.tanh_mul_I | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ tanh (x * I) = tan x * I",
"tactic": "rw [tanh_eq_sinh_div_cosh, cosh_mul_I, sinh_mul_I, mul_div_right_comm, tan]"
}
] | [
824,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Computability/Language.lean | Language.kstar_eq_iSup_pow | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.98971\nγ : Type ?u.98974\nl✝ m : Language α\na b x✝ : List α\nl : Language α\nx : List α\n⊢ x ∈ l∗ ↔ x ∈ ⨆ (i : ℕ), l ^ i",
"state_before": "α : Type u_1\nβ : Type ?u.98971\nγ : Type ?u.98974\nl✝ m : Language α\na b x : List α\nl : Language α\n⊢ l∗ = ⨆ (i ... | [
270,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | multiplicity_prime_eq_multiplicity_image_by_factor_orderIso | [
{
"state_after": "M : Type u_1\ninst✝⁶ : CancelCommMonoidWithZero M\nN : Type u_2\ninst✝⁵ : CancelCommMonoidWithZero N\ninst✝⁴ : UniqueFactorizationMonoid N\ninst✝³ : UniqueFactorizationMonoid M\ninst✝² : DecidableRel fun x x_1 => x ∣ x_1\ninst✝¹ : DecidableRel fun x x_1 => x ∣ x_1\ninst✝ : DecidableEq (Associa... | [
354,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.eq_inv_of_hom_inv_id | [] | [
361,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | Algebra.coe_lmul_eq_mul | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_upwards | [] | [
186,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.preimage_mul_left_one' | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.682735\nα : Type u_1\nβ : Type ?u.682741\nγ : Type ?u.682744\ninst✝ : Group α\ns t : Finset α\na b : α\n⊢ preimage 1 ((fun x x_1 => x * x_1) a⁻¹)\n (_ : Set.InjOn ((fun x x_1 => x * x_1) a⁻¹) ((fun x x_1 => x * x_1) a⁻¹ ⁻¹' ↑1)) =\n {a}",
... | [
1239,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | continuousAt_dslope_of_ne | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : b ≠ a\n⊢ ContinuousAt (dslope f a) b ↔ ContinuousAt f b",
"tactic": "simp only [← continuousWithi... | [
118,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.40518\nf✝ : α ↪ β\ns✝ : Finset α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α ↪ β\na : α\ns : Finset α\n⊢ map f (insert a s) = insert (↑f a) (map f s)",
"tactic": "simp only [insert_eq, map_union, map_singleto... | [
230,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_sum_fiber_le_of_sum_le_nsmul | [] | [
367,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\n⊢ Unbounded (fun x x_1 => x ≤ x_1) s ↔ ∀ (a : α), ∃ b, b ∈ s ∧ a < b",
"tactic": "simp only [Unbounded, not_le]"
}
] | [
47,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_mk' | [] | [
219,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_one | [
{
"state_after": "β : Type ?u.215364\nA : Type ?u.215367\nG : Type ?u.215370\nM : Type ?u.215373\nR : Type u_1\ninst✝ : OrderedSemiring R\na x y : R\nn✝ m : ℕ\nh₀ : 0 ≤ a\nh₁ : a < 1\nn : ℕ\nx✝ : n + 1 ≠ 0\n⊢ a * a ^ n < 1",
"state_before": "β : Type ?u.215364\nA : Type ?u.215367\nG : Type ?u.215370\nM : Ty... | [
433,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.Monic.comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nhp : Monic p\nhq : Monic q\nh : natDegree q ≠ 0\n⊢ Monic (Polynomial.comp p q)",
"tactic": "rw [Monic.def, leadingCoeff_comp h, Monic.def.1 hp, Monic.def... | [
829,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_eq_lsub | [
{
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1770,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1766,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.limNthHom_spec | [
{
"state_after": "p : 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\nε : ℝ\nhε : 0 < ε\n⊢ ∃ N, ∀ (n : ℕ), n ≥ N → ‖limNt... | [
589,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nndist_eq_of_L2 | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.291243\n𝕜' : Type ?u.291246\nι : Type u_2\nα : ι → Type ?u.291254\nβ✝ : ι → Type ?u.291259\ninst✝² : Fintype ι\ninst✝¹ : Fact (1 ≤ p)\nβ : ι → Type u_1\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx y : PiLp 2 β\n⊢ dist x y = Real.sqrt (∑ x_1 : ι, dist (x x_1) (y x_... | [
614,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Order/CompleteLattice.lean | Antitone.map_iSup_le | [] | [
1006,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.sum_map_mul_left | [] | [
128,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.forall_mem_zpowers | [] | [
73,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Set/Prod.lean | Set.fst_image_prod | [] | [
359,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Frequently.and_eventually | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.159948\nι : Sort x\np q : α → Prop\nf : Filter α\nhp : ∃ᶠ (x : α) in f, p x\nhq : ∀ᶠ (x : α) in f, q x\nh : ∀ᶠ (x : α) in f, ¬(fun x => p x ∧ q x) x\n⊢ ∀ (x : α), ¬(fun x => p x ∧ q x) x → q x → ¬(fun x => p x) x",
"state_before": "α : Type u... | [
1284,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1281,
1
] |
Mathlib/Logic/Basic.lean | ball_and | [] | [
1101,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_succ_right | [
{
"state_after": "S : Type u\ninst✝ : Semiring S\nn : ℕ\nh : pochhammer ℕ (n + 1) = pochhammer ℕ n * (X + ↑n)\n⊢ pochhammer S (n + 1) = pochhammer S n * (X + ↑n)\n\ncase h\nS : Type u\ninst✝ : Semiring S\nn : ℕ\n⊢ pochhammer ℕ (n + 1) = pochhammer ℕ n * (X + ↑n)",
"state_before": "S : Type u\ninst✝ : Semiri... | [
109,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.centralizer_eq_univ | [] | [
152,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Order/CompleteLattice.lean | OrderIso.map_iInf | [] | [
973,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
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