file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/Filter/Basic.lean | Filter.mem_principal | [] | [
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73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
9
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Mathlib/Topology/Order/Basic.lean | nhds_top_basis | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ :... | [
1141,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.coe_preimage_infty | [
{
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"tactic": "ext"
},
{
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] | [
170,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_le_multiplicity_of_dvd_right | [] | [
259,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Combinatorics/SimpleGraph/Hasse.lean | SimpleGraph.hasse_adj | [] | [
49,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/Data/Finset/Basic.lean | Finset.union_subset | [] | [
1371,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.range_inr | [
{
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171,
39
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164,
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Mathlib/Algebra/BigOperators/Pi.lean | Finset.prod_apply | [] | [
47,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.nnnorm | [] | [
2054,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2053,
1
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Mathlib/Data/Nat/Cast/Basic.lean | Nat.one_le_cast | [
{
"state_after": "no goals",
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"tactic": "rw [← cast_one, cast_le]"
}
] | [
146,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | hasFDerivAt_of_tendsto_locally_uniformly_on' | [
{
"state_after": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_4\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_3\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E → E →L[𝕜] G\nx : E\ninst✝ : ... | [
421,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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Mathlib/Data/Finset/Pointwise.lean | Finset.subset_mul_right | [] | [
802,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
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Mathlib/Data/Fintype/Card.lean | Fintype.card_ne_zero | [] | [
547,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/Topology/UniformSpace/Basic.lean | Uniform.continuousAt_iff'_left | [
{
"state_after": "no goals",
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"tactic": "rw [ContinuousAt, tendsto_nhds_left]"... | [
1930,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1928,
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Mathlib/Data/Finset/Lattice.lean | Finset.max'_le_iff | [] | [
1368,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
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Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.image_ι_comp_eq_zero | [
{
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"tactic": "simp [h]"
}
] | [
348,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | parallelogram_law_with_norm | [
{
"state_after": "𝕜 : Type ?u.2512953\nE : Type u_1\nF : Type ?u.2512959\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⊢ ↑re (inner (x + y) (x + y)) + ↑re (inner (x - y) (x - y))... | [
1125,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
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Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.Independent.linearIndependent | [
{
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562,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.neg_smul | [
{
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1113,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
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Mathlib/Data/List/Pairwise.lean | List.pwFilter_subset | [] | [
402,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
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Mathlib/Order/SymmDiff.lean | bihimp_right_inj | [] | [
689,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.spanSingleton_div_spanSingleton | [
{
"state_after": "no goals",
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159,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.diam_image | [] | [
597,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_toSubring | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/LinearAlgebra/Pi.lean | LinearMap.vecCons_apply | [] | [
582,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.invOn_invFunOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.67189\nι : Sort ?u.67192\nπ : α → Type ?u.67197\ns s₁ s₂ : Set α\nt : Set β\nf : α → β\ninst✝ : Nonempty α\nh : SurjOn f s t\n⊢ LeftInvOn (invFunOn f s) f (invFunOn f s '' t)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.67189\nι : Sort ... | [
1268,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.coe_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.95849\nγ : Type ?u.95852\nι : Sort ?u.95855\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Set α\nhs : Set.Nonempty s\n⊢ ↑(sInf s) = ⨅ (a : α) (_ : a ∈ s), ↑a",
"tactic": "rw [coe_sInf' hs, sInf_image]"
}
] | [
1232,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.lower_comm | [] | [
522,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sumCongr_mul | [] | [
191,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_countAddMonoidHom | [] | [
2399,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2398,
1
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Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_mono | [] | [
203,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isUpperSet_Ici | [] | [
211,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge | [
{
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778,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_subtype_iff_indicator | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.29909\nδ : Type ?u.29912\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf g : β → α\na b : α\ns✝ : Finset β\ns : Set β\n⊢ HasSum (f ∘ Subtype.val) a ↔ HasSum (Set.indicator s f) a",
"tactic": "rw [← Set.indicat... | [
160,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_dist_of_mem_uniformity | [
{
"state_after": "no goals",
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... | [
47,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
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Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.mono | [
{
"state_after": "no goals",
"state_before": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\nK₁ K₂ : Compacts G\nh : ↑K₁ ⊆ ↑K₂\n⊢ (fun s => ↑(toFun μ s)) K₁ ≤ (fun s => ↑(toFun μ s)) K₂",
"tactic": "simp [apply_eq_coe_toFun, μ.mono' _ _ h]"
}
] | [
99,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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Mathlib/Data/Finset/Basic.lean | Finset.induction_on | [] | [
1220,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
11
] |
Mathlib/Data/PEquiv.lean | Equiv.toPEquiv_apply | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_eq_bot | [
{
"state_after": "no goals",
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"tactic": "simpa using @pi_inf_principal_univ_pi_eq_bot ι α f fun _ => univ"
}
] | [
157,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.AwayMap.lift_eq | [] | [
1277,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | nndist_vsub_vsub_le | [
{
"state_after": "no goals",
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192,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/Data/List/Rotate.lean | List.head?_rotate | [
{
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"tactic": "rw [← get?_zero, get?_rotate (n.zero_le.trans_lt h), zero_add, Nat.mod_eq_of_lt h]"
}
] | [
267,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_mul_nat_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← cast_coe_nat, irrational_mul_rat_iff, Nat.cast_ne_zero]"
}
] | [
629,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
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Mathlib/Computability/Primrec.lean | Nat.Primrec'.prim_iff | [] | [
1546,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1545,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein_lt_self | [
{
"state_after": "α : Type ?u.71541\nβ : Type ?u.71544\nγ : Type ?u.71547\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\ni : (Quotient.out o).α\n⊢ typein (fun x x_1 => x < x_1) i < type fun x x_1 => x < x_1",
"state_before": "α : Type ?u.71541\nβ : Type ?u.71544\nγ : Type ?u.71547\nr : ... | [
448,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.subtype_coe_map_comap | [
{
"state_after": "no goals",
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"tactic": "rw [map_comap,... | [
2283,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2282,
1
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Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.Decomposition.inductionOn | [
{
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97,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/Algebra/Module/BigOperators.lean | Multiset.sum_smul_sum | [
{
"state_after": "case empty\nα : Type ?u.20507\nβ : Type ?u.20510\nR : Type u_1\nM : Type u_2\nι : Type ?u.20519\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nr s : R\nx y : M\nt : Multiset M\n⊢ sum 0 • sum t = sum (map (fun p => p.fst • p.snd) (0 ×ˢ t))\n\ncase cons\nα : Type ?u.20507\nβ... | [
38,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiable_cosh | [] | [
154,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.le_sInf | [
{
"state_after": "case f\nC : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : WellPowered C\ninst✝ : HasWidePullbacks C\nA : C\ns : Set (Subobject A)\nf : Subobject A\nk : ∀ (g : Subobject A), g ∈ s → f ≤ g\n⊢ underlying.obj f ⟶ underlying.obj (sInf s)\n\ncase w\nC : Type u₁\... | [
659,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_row_iff | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\ni : ℕ\nc : ℕ × ℕ\n⊢ c ∈ row μ i ↔ c ∈ μ ∧ c.fst = i",
"tactic": "simp [row]"
}
] | [
290,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.monic_integralNormalization | [] | [
88,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/RingTheory/MatrixAlgebra.lean | MatrixEquivTensor.toFunAlgHom_apply | [
{
"state_after": "R : Type u\ninst✝⁴ : CommSemiring R\nA : Type v\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\na : A\nm : Matrix n n R\n⊢ AddHom.toFun (lift (toFunBilinear R A n)).toAddHom (a ⊗ₜ[R] m) = a • Matrix.map m ↑(algebraMap R A)",
"state_before"... | [
86,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.IsTrail.even_countp_edges_iff | [
{
"state_after": "case nil\nV : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu✝ v : V\np : Walk G u✝ v\nht✝ : IsTrail p\nx u : V\nht : IsTrail Walk.nil\n⊢ Even (List.countp (fun e => decide (x ∈ e)) (edges Walk.nil)) ↔ u ≠ u → x ≠ u ∧ x ≠ u\n\ncase cons\nV : Type u_1\nG : SimpleGraph V\ninst✝ : Decidable... | [
85,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/DirectLimit.lean | AddCommGroup.DirectLimit.lift_of | [] | [
346,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.splitFun_comp | [] | [
246,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.eventually | [] | [
481,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
11
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.Preadditive.exact_iff_homology_zero | [
{
"state_after": "V : Type u\ninst✝⁵ : Category V\ninst✝⁴ : HasImages V\ninst✝³ : HasZeroObject V\ninst✝² : Preadditive V\ninst✝¹ : HasKernels V\ninst✝ : HasCokernels V\nA B C : V\nf : A ⟶ B\ng : B ⟶ C\nh : Exact f g\nthis : Epi (imageToKernel f g (_ : f ≫ g = 0))\n⊢ homology f g (_ : f ≫ g = 0) ≅ 0",
"stat... | [
97,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/List/Sigma.lean | List.kerase_append_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nx✝ : List (Sigma β)\nh : a ∈ keys []\n⊢ kerase a ([] ++ x✝) = kerase a [] ++ x✝",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": "α : Type u\... | [
526,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.tendsto_setToFun_filter_of_dominated_convergence | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1756095\nG : Type ?u.1756098\n𝕜 : Type ?u.1756101\np : ℝ≥0∞\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedAddCommGroup F'\ninst✝³ : NormedSpace ℝ F'\ninst... | [
1784,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
1
] |
Mathlib/Algebra/GeomSum.lean | op_geom_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Semiring α\nx : α\nn : ℕ\n⊢ op (∑ i in range n, x ^ i) = ∑ i in range n, op x ^ i",
"tactic": "simp"
}
] | [
85,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.lift_coe | [] | [
937,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.interedges_biUnion | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.12270\nι : Type u_1\nκ : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝³ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝² : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\ninst✝¹ : DecidableEq α\ninst✝ : ... | [
125,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.pi_condition | [
{
"state_after": "case h\nC : Type u\ninst✝² : Category C\nI : MulticospanIndex C\nK : Multifork I\ninst✝¹ : HasProduct I.left\ninst✝ : HasProduct I.right\nb✝ : I.R\n⊢ (Pi.lift (ι K) ≫ MulticospanIndex.fstPiMap I) ≫ Pi.π I.right b✝ =\n (Pi.lift (ι K) ≫ MulticospanIndex.sndPiMap I) ≫ Pi.π I.right b✝",
"st... | [
417,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Order/Heyting/Basic.lean | hnot_sup_self | [] | [
1067,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.strongEpi_factorThruImage_of_strongEpiMonoFactorisation | [] | [
960,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_comp | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\nS R✝ : Sieve X\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nR : Sieve ((F ⋙ G).obj X)\nY✝ : C\nf✝ : Y✝ ⟶ X\n⊢ (functorPullback (F ⋙ G) R).arrows f✝ ↔ (functorPullback F (functorPullback... | [
612,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | IsOpen.tendstoLocallyUniformlyOn_iff_forall_tendsto | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx✝ : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\nhs : IsOpen s\nx : α\nhx : x ∈ s\n⊢ Tendsto (fun y => (f y.snd, F y.fst y... | [
622,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
8
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean | Real.sin_gt_sub_cube | [
{
"state_after": "x : ℝ\nh : 0 < x\nh' : x ≤ 1\nhx : abs x = x\n⊢ x - x ^ 3 / 4 < sin x",
"state_before": "x : ℝ\nh : 0 < x\nh' : x ≤ 1\n⊢ x - x ^ 3 / 4 < sin x",
"tactic": "have hx : |x| = x := abs_of_nonneg h.le"
},
{
"state_after": "x : ℝ\nh : 0 < x\nh' : x ≤ 1\nhx : abs x = x\nthis : -(abs x... | [
75,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_mono | [] | [
473,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_coeIdeal | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.injective | [] | [
559,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
11
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.induction_on' | [
{
"state_after": "ι : Type u_1\nι₂ : Type ?u.91649\nι₃ : Type ?u.91652\nR : Type u_2\ninst✝⁷ : CommSemiring R\nR₁ : Type ?u.91661\nR₂ : Type ?u.91664\ns : ι → Type u_3\ninst✝⁶ : (i : ι) → AddCommMonoid (s i)\ninst✝⁵ : (i : ι) → Module R (s i)\nM : Type ?u.91854\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nE ... | [
220,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.algHom_ext | [] | [
790,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_congr_of_surjective | [] | [
449,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.mem_iff | [
{
"state_after": "R : Type u_1\nA : Type ?u.59390\ninst✝¹ : AddGroup R\ninst✝ : StarAddMonoid R\nx : R\n⊢ x ∈ (selfAdjoint R).toAddSubmonoid.toAddSubsemigroup.carrier ↔ star x = x",
"state_before": "R : Type u_1\nA : Type ?u.59390\ninst✝¹ : AddGroup R\ninst✝ : StarAddMonoid R\nx : R\n⊢ x ∈ selfAdjoint R ↔ s... | [
304,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_le_range | [] | [
2978,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2977,
1
] |
Mathlib/Order/Lattice.lean | sup_le_sup | [] | [
230,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.hasBasis_nhds_zero | [] | [
227,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
11
] |
Mathlib/Algebra/Group/Units.lean | mul_divp_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c a : α\nu : αˣ\n⊢ a * (↑u * ↑u⁻¹) = a",
"tactic": "rw [Units.mul_inv, mul_one]"
}
] | [
473,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Topology/PathConnected.lean | Path.truncate_const_continuous_family | [
{
"state_after": "X✝ : Type ?u.469179\nY : Type ?u.469182\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.469197\nγ✝ : Path x y\nX : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\nt : ℝ\nkey : Continuous fun x => (t, x)\n⊢ Continuous ↿(truncate γ t)",
"state... | [
681,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasProducts_of_opposite | [] | [
367,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.addOrderOf_coe_rat | [
{
"state_after": "𝕜 : Type u_1\nB : Type ?u.192515\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\np q✝ : 𝕜\nhp : Fact (0 < p)\nq : ℚ\nthis : ↑↑q.den ≠ 0\n⊢ addOrderOf ↑(↑q * p) = q.den",
"state_before": "𝕜 : Type u_1\nB : Type ?u.192515\ninst✝² : LinearOrderedFie... | [
417,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.eqOn_of_eqOn_frontier | [] | [
426,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.linMulLin_apply | [] | [
582,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.sdiff | [] | [
250,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Std/Classes/Order.lean | Std.OrientedCmp.cmp_eq_eq_symm | [
{
"state_after": "α✝ : Sort u_1\ncmp : α✝ → α✝ → Ordering\nx y : α✝\ninst✝ : OrientedCmp cmp\n⊢ cmp y x = Ordering.swap Ordering.eq ↔ cmp y x = Ordering.eq",
"state_before": "α✝ : Sort u_1\ncmp : α✝ → α✝ → Ordering\nx y : α✝\ninst✝ : OrientedCmp cmp\n⊢ cmp x y = Ordering.eq ↔ cmp y x = Ordering.eq",
"ta... | [
35,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
34,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_add_le' | [
{
"state_after": "case inl\nα : Type u_1\nE : Type u_2\nF : Type ?u.3024839\nG : Type ?u.3024842\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → E\nhf : AEStronglyMeasurable f μ\nhg : AEStronglyMea... | [
827,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_atBot_of_monotone | [] | [
1305,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.bddBelow | [] | [
335,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_toAddEquiv | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | LinearLocallyFiniteOrder.isMax_of_succFn_le | [
{
"state_after": "ι : Type u_1\ninst✝¹ : LinearOrder ι\ninst✝ : LocallyFiniteOrder ι\ni : ι\nhi : succFn i ≤ i\nj : ι\nx✝ : i ≤ j\nhij_lt : i < j\n⊢ False",
"state_before": "ι : Type u_1\ninst✝¹ : LinearOrder ι\ninst✝ : LocallyFiniteOrder ι\ni : ι\nhi : succFn i ≤ i\n⊢ IsMax i",
"tactic": "refine' fun j... | [
103,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.eq_σ_comp_of_not_injective | [
{
"state_after": "n : ℕ\nΔ' : SimplexCategory\nθ : [n + 1] ⟶ Δ'\nhθ : ∃ x x_1, ↑(Hom.toOrderHom θ) x = ↑(Hom.toOrderHom θ) x_1 ∧ ¬x = x_1\n⊢ ∃ i θ', θ = σ i ≫ θ'",
"state_before": "n : ℕ\nΔ' : SimplexCategory\nθ : [n + 1] ⟶ Δ'\nhθ : ¬Function.Injective ↑(Hom.toOrderHom θ)\n⊢ ∃ i θ', θ = σ i ≫ θ'",
"tact... | [
663,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_le_norm_add_const_of_dist_le' | [] | [
658,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.ofRelIsoLT_apply | [] | [
1038,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_image | [
{
"state_after": "case h\nf : ZFSet → ZFSet\nH : Definable 1 f\nx x✝ : ZFSet\n⊢ x✝ ∈ toSet (image f x) ↔ x✝ ∈ f '' toSet x",
"state_before": "f : ZFSet → ZFSet\nH : Definable 1 f\nx : ZFSet\n⊢ toSet (image f x) = f '' toSet x",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": ... | [
1257,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1254,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_zero | [] | [
106,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sep_univ | [] | [
1459,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.mono_left | [] | [
78,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_nonneg | [] | [
651,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
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