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/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_reindexRange | [
{
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"state_before": "R : Type u_2\ninst✝¹⁰ : CommSemiring R\nl : Type ?u.2593072\nm : Type ?u.2593075\nn : Type u_3\ninst✝⁹ : Fintype n\ninst✝⁸ : Fintype m\ninst✝⁷ : DecidableEq n\nM₁ : Type u_1\nM₂ : Type ?u.2593099\ninst✝⁶ : AddCommMonoid M₁\ninst✝⁵ : AddCommMonoid M₂\ninst✝⁴ : Mo... | [
793,
98
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1
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Mathlib/Data/Nat/Cast/Defs.lean | Nat.cast_succ | [] | [
116,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Logic/Relation.lean | Relation.TransGen.head'_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.21585\nγ : Type ?u.21588\nδ : Type ?u.21591\nr : α → α → Prop\na b c d : α\nh : TransGen r a c\n⊢ ∃ b, r a b ∧ ReflTransGen r b c",
"state_before": "α : Type u_1\nβ : Type ?u.21585\nγ : Type ?u.21588\nδ : Type ?u.21591\nr : α → α → Prop\na b c d : α\n⊢ TransGen r ... | [
434,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Order/Hom/Basic.lean | OrderHom.snd_comp_prod | [] | [
470,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_sInf | [
{
"state_after": "case h\nι : Sort ?u.112949\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\ns : Set (Subgraph G)\ne : Sym2 V\n⊢ e ∈ edgeSet (sInf s) ↔ e ∈ (⋂ (G' : Subgraph G) (_ : G' ∈ s), edgeSet G') ∩ SimpleGraph.edgeSet G",
"state_before": "ι : Sort ?u.112949\nV : Type u\nW : T... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousLinearMap.smul_compLp | [
{
"state_after": "case h\nα : Type u_5\nE : Type u_4\nF : Type u_2\nG : Type ?u.5700489\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedAddCommGroup G\ng : E → F\nc✝ : ℝ≥0\n𝕜 : Type u_3\ninst✝⁶ : Nontriviall... | [
1004,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_fderiv | [] | [
351,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
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Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.comp.mk_get | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nP : MvPFunctor n\nQ : Fin2 n → MvPFunctor m\nα β : TypeVec m\nx : Obj (comp P Q) α\n⊢ mk (get x) = x",
"tactic": "rfl"
}
] | [
153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | CommGroupCat.mono_iff_ker_eq_bot | [] | [
423,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
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Mathlib/Topology/Homotopy/Contractible.lean | ContinuousMap.Nullhomotopic.comp_left | [
{
"state_after": "case intro\nX : Type u_3\nY : Type u_1\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : C(Y, Z)\ng : C(X, Y)\ny : Z\nhy : Homotopic f (const Y y)\n⊢ Nullhomotopic (comp f g)",
"state_before": "X : Type u_3\nY : Type u_1\nZ : Type u_2\... | [
47,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
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Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_and_eq | [] | [
20,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
20,
1
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.SemanticallyEquivalent.ex | [
{
"state_after": "L : Language\nT : Theory L\nα : Type w\nn : ℕ\nφ ψ : BoundedFormula L α (n + 1)\nh : SemanticallyEquivalent T φ ψ\n⊢ ∀ (M : ModelType T) (v : α → ↑M) (xs : Fin n → ↑M),\n (∃ a, BoundedFormula.Realize φ v (Fin.snoc xs a)) ↔ ∃ a, BoundedFormula.Realize ψ v (Fin.snoc xs a)",
"state_before"... | [
475,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
11
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_single | [
{
"state_after": "no goals",
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801,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | eq_Icc_csInf_csSup_of_connected_bdd_closed | [] | [
260,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk | [
{
"state_after": "case a\nR : Type u\ninst✝ : CommRing R\nI J : Ideal R\nh : I ≤ J\nx✝ : R\n⊢ ↑(RingHom.comp (↑(quotQuotEquivQuotOfLE h)) (quotQuotMk I J)) x✝ = ↑(Ideal.Quotient.mk J) x✝",
"state_before": "R : Type u\ninst✝ : CommRing R\nI J : Ideal R\nh : I ≤ J\n⊢ RingHom.comp (↑(quotQuotEquivQuotOfLE h)) ... | [
638,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.mem_map | [] | [
752,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixingSubmonoid_fixedPoints_gc | [] | [
72,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAt_iff_tendsto | [] | [
286,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.mul_int_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nhm : m ≠ 0\n⊢ LiouvilleWith p (x * ↑m) ↔ LiouvilleWith p x",
"tactic": "rw [← Rat.cast_coe_int, mul_rat_iff (Int.cast_ne_zero.2 hm)]"
}
] | [
153,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousOn_symm | [] | [
106,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_mul_eq_coe | [] | [
1169,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
8
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.equivIsoLimit_apply | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | SemiconjBy.units_zpow_right | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.391210\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝² : Monoid M\ninst✝¹ : Group G\ninst✝ : Ring R\na : M\nx y : Mˣ\nh : SemiconjBy a ↑x ↑y\nn : ℕ\n⊢ SemiconjBy a ↑(x ^ ↑n) ↑(y ^ ↑n)",
"t... | [
1057,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\np1 p2 : P\nhp1 : p1 ∈ s\nhp2 : p2 ∈ s\nr1 r2 : ℝ\nv : V\nhv : v ∈ (direction s)ᗮ\n⊢ dist (r1 •... | [
515,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integrable_of_integral_tendsto_of_nonneg_ae | [] | [
476,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.IsCobounded.inter | [] | [
196,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.sub_int | [] | [
278,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coe_reindex | [] | [
428,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.eq_coe_norm_of_nonneg | [
{
"state_after": "case intro\nE : Type ?u.1183703\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz : ℝ\nhz : 0 ≤ ↑z\n⊢ ↑z = ↑‖↑z‖",
"state_before": "E : Type ?u.1183703\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz : ℂ\nhz : 0 ≤ z\n⊢ z = ↑‖z‖",
"tactic": "lift z to ℝ using hz.2.sy... | [
443,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | norm_eq_iInf_iff_inner_eq_zero | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.265347\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\nu v : E\nhv : v ∈ K\nthis : InnerProductSpace ℝ E := InnerProductSpace.isROrCTo... | [
376,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_one_of_mul_eq_one_right | [] | [
854,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
853,
1
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Mathlib/Data/Fin/Basic.lean | Fin.rev_eq | [
{
"state_after": "case h\nn✝ m n a : ℕ\ni : Fin (n + 1)\nh : n = a + ↑i\n⊢ ↑(↑rev i) = ↑{ val := a, isLt := (_ : a < Nat.succ n) }",
"state_before": "n✝ m n a : ℕ\ni : Fin (n + 1)\nh : n = a + ↑i\n⊢ ↑rev i = { val := a, isLt := (_ : a < Nat.succ n) }",
"tactic": "ext"
},
{
"state_after": "case h... | [
492,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.one_zpow | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\n⊢ 1 ^ ↑n = 1",
"tactic": "rw [zpow_ofNat, one_pow]"
},
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\nins... | [
84,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.symm | [] | [
97,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.single_apply | [] | [
361,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Order/Bounded.lean | Set.Bounded.rel_mono | [] | [
93,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/RingTheory/Adjoin/FG.lean | isNoetherianRing_of_fg | [] | [
211,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.gc_map_comap | [] | [
327,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.mk_coe | [] | [
175,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Order/Atoms.lean | bot_covby_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2959\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\na b x : α\n⊢ ⊥ ⋖ a ↔ IsAtom a",
"tactic": "simp only [Covby, bot_lt_iff_ne_bot, IsAtom, not_imp_not]"
}
] | [
101,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ωSup_le_iff | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nγ : Type ?u.8324\ninst✝ : OmegaCompletePartialOrder α\nc : Chain α\nx : α\na✝ : ωSup c ≤ x\ni✝ : ℕ\n⊢ ↑c i✝ ≤ x\n\ncase mpr\nα : Type u\nβ : Type v\nγ : Type ?u.8324\ninst✝ : OmegaCompletePartialOrder α\nc : Chain α\nx : α\na✝ : ∀ (i : ℕ), ↑c i ≤ x\n⊢ ωSup c ≤ ... | [
226,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_congr_left | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.6274\ninst✝ : PseudoEMetricSpace α\nx y z : α\nh : edist x y = 0\n⊢ edist x z = edist y z",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.6274\ninst✝ : PseudoEMetricSpace α\nx y z : α\nh : edist x y = 0\n⊢ edist z x = edist z y",
"tactic": "rw... | [
119,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_sdiff_sub | [] | [
343,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
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Mathlib/Algebra/Category/Ring/Basic.lean | CategoryTheory.Iso.commRingIsoToRingEquiv_toRingHom | [
{
"state_after": "case a\nX Y : CommRingCat\ni : X ≅ Y\nx✝ : ↑X\n⊢ ↑(RingEquiv.toRingHom (commRingCatIsoToRingEquiv i)) x✝ = ↑i.hom x✝",
"state_before": "X Y : CommRingCat\ni : X ≅ Y\n⊢ RingEquiv.toRingHom (commRingCatIsoToRingEquiv i) = i.hom",
"tactic": "ext"
},
{
"state_after": "no goals",
... | [
482,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulStrictMono_iff_posMulMonoRev | [] | [
296,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
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Mathlib/Data/Set/Finite.lean | Set.finite_iUnion | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : Finite ι\nf : ι → Set α\nH : ∀ (i : ι), Set.Finite (f i)\nthis : (i : ι) → Fintype ↑(f i)\n⊢ Set.Finite (⋃ (i : ι), f i)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : Finite ι\nf : ι → Set α\nH : ∀ (i : ι)... | [
777,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.coe_toLocallyBoundedMap | [] | [
384,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Nat/Parity.lean | Function.Involutive.iterate_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → α\nn : ℕ\nhf : Involutive f\nhne : f ≠ id\nH : f^[n] = f\nhn : Even n\n⊢ f = id",
"tactic": "rwa [hf.iterate_even hn, eq_comm] at H"
}
] | [
326,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.top_prod | [
{
"state_after": "no goals",
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809,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Order/CompleteLattice.lean | Prod.fst_iSup | [] | [
1875,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1874,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_subset_uIcc_iff_le | [] | [
1024,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
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Mathlib/Analysis/NormedSpace/Pointwise.lean | exists_dist_eq | [
{
"state_after": "𝕜 : Type ?u.200626\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx✝ y z✝ : E\nδ ε : ℝ\nx z : E\na b : ℝ\nha : 0 ≤ a\nhb : 0 ≤ b\nhab : a + b = 1\n⊢ dist x (a • x + b • z) = b * dist x z ∧ dist (a • x + b • z) z =... | [
161,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mul_le | [] | [
542,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Algebra/Associated.lean | associated_mul_unit_right_iff | [] | [
510,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Topology/UnitInterval.lean | projIcc_eq_one | [] | [
190,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.coe_cast_hom | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_nat_eq_last | [
{
"state_after": "n✝ m n : ℕ\n⊢ { val := n % (n + 1), isLt := (_ : n % (n + 1) < n + 1) } = { val := n, isLt := (_ : n < Nat.succ n) }",
"state_before": "n✝ m n : ℕ\n⊢ ↑n = last n",
"tactic": "rw [← Fin.ofNat_eq_val, Fin.ofNat'', Fin.last]"
},
{
"state_after": "no goals",
"state_before": "n✝... | [
820,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
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Mathlib/Topology/Algebra/StarSubalgebra.lean | elementalStarAlgebra.isClosed | [] | [
204,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
11
] |
Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.dNext_cochainComplex | [
{
"state_after": "ι : Type ?u.364174\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf✝ g : C ⟶ D\nh k : D ⟶ E\ni : ι\nP Q : CochainComplex V ℕ\nf : (i j : ℕ) → X P i ⟶ X Q j\nj : ℕ\n⊢ d P j (ComplexShape.next (ComplexShape.up ℕ) j) ≫ f (ComplexShape.... | [
591,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.unitors_equal | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\n⊢ (λ_ (𝟙_ C)).hom = (ρ_ (𝟙_ C)).hom",
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}
] | [
72,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_union | [
{
"state_after": "no goals",
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1728,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1725,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots_le_map | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝³ : CommRing A\ninst✝² : CommRing B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\np : A[X]\nf : A →+* B\nh : map f p ≠ 0\n⊢ ↑Multiset.card (Multiset.map (↑f) (roots p)) ≤ ↑Multiset.card (roots (map f p))",
"st... | [
1199,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Terminal.lean | CategoryTheory.Limits.PreservesTerminal.iso_hom | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAt_zero_of_eventually_const | [] | [
1137,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.asGroupHom_apply | [
{
"state_after": "no goals",
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"tactic": "simp only [asGroupHom, MonoidHom.coe_toHomUnits]"
... | [
344,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.toSheafify_naturality | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q : Cᵒᵖ ⥤ D\nη : P ⟶ Q\n⊢ η ≫ toPlus J Q ≫ plusMap J (to... | [
500,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Algebra/Module/GradedModule.lean | DirectSum.Gmodule.one_smul' | [
{
"state_after": "ι : Type u_1\nA : ι → Type u_2\nM : ι → Type u_3\ninst✝⁵ : AddMonoid ι\ninst✝⁴ : (i : ι) → AddCommMonoid (A i)\ninst✝³ : (i : ι) → AddCommMonoid (M i)\ninst✝² : DecidableEq ι\ninst✝¹ : GMonoid A\ninst✝ : Gmodule A M\nx : ⨁ (i : ι), M i\n⊢ ↑(smulAddMonoidHom A M) 1 = AddMonoidHom.id (⨁ (i : ι),... | [
122,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
9
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_diff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.32157\ninst✝ : PartialOrder α\na b c x : α\n⊢ x ∈ Icc a b \\ {a} ↔ x ∈ Ioc a b",
"tactic": "simp [lt_iff_le_and_ne, eq_comm, and_right_comm]"
}
] | [
776,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Arrow.middle_spec | [] | [
667,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.exists_bilinForm_self_ne_zero | [
{
"state_after": "case intro\nS : Type ?u.666424\nR : Type u_1\nR₁ : Type ?u.666430\nM : Type u_2\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nhtwo : Invertible 2\nB : BilinForm R M\nQ : QuadraticForm R M\nhB₁✝ hB₁ : ↑(QuadraticForm.associatedHom ℕ) Q ≠ 0\n⊢ ∃ x, ¬IsOrtho (↑(QuadraticForm.asso... | [
1074,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_bot | [] | [
698,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.not_infinite_add | [] | [
610,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.toLin_symm | [] | [
516,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.inv_unit_app_app | [] | [
683,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/RingTheory/ReesAlgebra.lean | monomial_mem_adjoin_monomial | [
{
"state_after": "case zero\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI✝ I : Ideal R\nn : ℕ\nr✝ : R\nhr✝ : r✝ ∈ I ^ n\nr : R\nhr : r ∈ I ^ Nat.zero\n⊢ ↑(monomial Nat.zero) r ∈ Algebra.adjoin R ↑(Submodule.map (monomial 1) I)\n\ncase succ\nR M : Type u\ninst✝² : CommRing R\... | [
98,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.empty_ssubset_singleton | [] | [
724,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.eq_pow_of_mul_eq_pow_bit1 | [] | [
415,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Set/Image.lean | Set.compl_range_inr | [] | [
946,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_mul | [] | [
331,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_iUnion_iff | [] | [
1714,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1710,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_iff_eq_or_lt | [] | [
841,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.IsCompressed.eq | [] | [
125,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
11
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.sum_fst | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid.right | [] | [
1108,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
8
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le | [
{
"state_after": "case intro\nR✝ : Type u\nS : Type v\nT : Type w\na b : R✝\nn : ℕ\ninst✝² : CommRing R✝\ninst✝¹ : IsDomain R✝\np✝ q✝ : R✝[X]\nR : Type u_1\ninst✝ : CommRing R\np q : R[X]\nhp : Monic p\nhdeg : natDegree q ≤ natDegree p\nr : R[X]\nhr : q = p * r\n⊢ q = ↑C (leadingCoeff q) * p",
"state_before... | [
1040,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousAt.add' | [
{
"state_after": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\nβ : Type ?u.183589\ninst✝³ : Preorder β\nf✝ g✝ : α → β\nx : α\ns t : Set α\ny z : β\nι : Type ?u.183615\nγ : Type u_2\ninst✝² : LinearOrderedAddCommMonoid γ\ninst✝¹ : TopologicalSpace γ\ninst✝ : OrderTopology γ\nf g : α → γ\nhcont : ContinuousAt (fun ... | [
909,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_piecewise | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubalgebra.exists_nested_lieIdeal_ofLe_normalizer | [
{
"state_after": "R : Type u_1\nL : Type u_2\nM : Type ?u.59016\nM' : Type ?u.59019\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : Lie... | [
166,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_zero | [] | [
206,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_sum | [] | [
1157,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | ball_inter_right | [] | [
647,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_unop | [
{
"state_after": "no goals",
"state_before": "𝕂 : Type u_2\n𝔸 : Type u_1\ninst✝⁵ : Field 𝕂\ninst✝⁴ : Ring 𝔸\ninst✝³ : Algebra 𝕂 𝔸\ninst✝² : TopologicalSpace 𝔸\ninst✝¹ : TopologicalRing 𝔸\ninst✝ : T2Space 𝔸\nx : 𝔸ᵐᵒᵖ\n⊢ exp 𝕂 (MulOpposite.unop x) = MulOpposite.unop (exp 𝕂 x)",
"tactic": "simp... | [
135,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | support_factorization | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : UniqueFactorizationMonoid α\ninst✝¹ : NormalizationMonoid α\ninst✝ : DecidableEq α\nn : α\n⊢ (factorization n).support = Multiset.toFinset (normalizedFactors n)",
"tactic": "simp [factorization, Mul... | [
2027,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2025,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapSMul_single | [] | [
1438,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1437,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.castAddHom_int | [] | [
255,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.mul_self_le_mul_self | [] | [
285,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_normalizer_iff' | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.381690\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.381699\ninst✝ : AddGroup A\nH K : Subgroup G\ng : G\nh : g ∈ normalizer H\nn : G\n⊢ n * g ∈ H ↔ g * n ∈ H",
"tactic": "rw [h, mul_assoc, mul_inv_cancel_right]"
},
{
"... | [
2167,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2165,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.ediam_image_inter_le | [] | [
185,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.prod_mono_right | [] | [
1611,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1610,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | MonoidHom.range_eq_top_of_cancel | [
{
"state_after": "A : Type u\nB : Type v\ninst✝¹ : CommGroup A\ninst✝ : CommGroup B\nf : A →* B\nh : ∀ (u v : B →* B ⧸ range f), comp u f = comp v f → u = v\n⊢ comp 1 f = comp (QuotientGroup.mk' (range f)) f\n\nA : Type u\nB : Type v\ninst✝¹ : CommGroup A\ninst✝ : CommGroup B\nf : A →* B\nh : 1 = QuotientGroup.... | [
57,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
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