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/Polynomial/Eval.lean | Polynomial.eval₂_bit0 | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\n⊢ eval₂ f x (bit0 p) = bit0 (eval₂ f x p)",
"tactic": "rw [bit0, eval₂_add, bit0]"
}
] | [
104,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq_le | [
{
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"state_before": "a : ℕ\na1 : 1 < a\ni j n : ℕ\nij : i ≤ j\nj2n : j ≤ 2 * n\nh : xn a1 i ≡ xn a1 j [MOD xn a1 n]\nntriv : ¬(a = 2 ∧ n = 1 ∧ i = 0 ∧ j = 2)\nnpos : n = 0\n⊢ i = j",
"tactic": "simp_all"
},
{
"state_after": "a : ℕ\na1 : 1 < a\ni j n : ℕ\nij : i ≤ j\nj2n ... | [
767,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
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Mathlib/Data/Finset/Basic.lean | Finset.coe_filter | [] | [
2742,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2741,
1
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Mathlib/Data/Num/Lemmas.lean | ZNum.cast_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\na : ZNum\n⊢ ↑(0 + a) = ↑0 + ↑a",
"tactic": "cases a <;> exact (_root_.zero_add _).symm"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\nb : ZNum\n⊢ ↑(b + 0) = ↑b +... | [
1336,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_eq_cancel | [
{
"state_after": "ctx : Context\nm₁ m₂ : Poly\nh : denote_eq ctx (m₁, m₂)\n⊢ denote_eq ctx (cancel m₁ m₂)",
"state_before": "ctx : Context\nm₁ m₂ : Poly\nh : denote_eq ctx (m₁, m₂)\n⊢ denote_eq ctx (cancel m₁ m₂)",
"tactic": "simp"
},
{
"state_after": "case h\nctx : Context\nm₁ m₂ : Poly\nh : de... | [
416,
44
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
415,
1
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Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.multinomial_spec | [] | [
57,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.sInf_coe | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/Data/Set/Lattice.lean | iInf_iUnion | [] | [
2243,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2242,
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.germ_stalk_specializes' | [] | [
338,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_sub_const | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type ?u.38982\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nv₁ v₂ v₃ v : V\n⊢ ∠ (v₁ - v) (v₂ - v) (v₃ - v) = ∠ v₁ v₂ v₃",
"tactic": "simpa only [vsub_eq_sub] using angle... | [
112,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_center | [] | [
790,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
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Mathlib/Topology/MetricSpace/MetrizableUniformity.lean | UniformSpace.metrizable_uniformity | [
{
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259,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_preimage_singleton | [] | [
340,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.comp | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\ng : β → γ\nhg : UniformInducing g\nf : α → β\nhf : UniformInducing f\n⊢ comap (fun x => ((g ∘ f) x.fst, (g ∘ f) x.snd)) (𝓤 γ) =\n comap ((fun x => (g x.fst, g x.snd)) ∘ fun x => (f... | [
73,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
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Mathlib/Data/Int/Cast/Lemmas.lean | Pi.int_apply | [] | [
356,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
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] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.invOf_eq_nonsing_inv | [
{
"state_after": "l : Type ?u.127855\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA B : Matrix n n α\ninst✝ : Invertible A\nthis : Invertible (det A) := detInvertibleOfInvertible A\n⊢ ⅟A = A⁻¹",
"state_before": "l : Type ?u.127855\nm : Type u\nn : Ty... | [
272,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableOn.congr | [] | [
922,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.dvd_gcd | [] | [
87,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.eq_of_length_le | [] | [
421,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
420,
1
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | measurable_measure_prod_mk_right | [] | [
196,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | add_tsub_cancel_iff_le | [] | [
318,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.sSup_mem | [] | [
142,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_monotone | [] | [
671,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Data/List/Cycle.lean | List.isRotated_next_eq | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl l' : List α\nh : l ~r l'\nhn : Nodup l\nk : ℕ\nhk : k < length l\nhx : nthLe l k hk ∈ l\n⊢ next l (nthLe l k hk) hx = next l' (nthLe l k hk) (_ : nthLe l k hk ∈ l')",
"state_before": "α : Type u_1\ninst✝ : Decidab... | [
434,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_cast | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : n = m\ni : Fin n\n⊢ ↑(↑(cast h) i) = ↑i",
"tactic": "simp"
}
] | [
1070,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.card_div_choose_le_card_shadow_div_choose | [
{
"state_after": "case inl\n𝕜 : Type u_2\nα : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\nr : ℕ\nhr : r ≠ 0\nh𝒜 : Set.Sized r ↑𝒜\nhr' : Fintype.card α < r\n⊢ ↑(card 𝒜) / ↑(Nat.choose (Fintype.card α) r) ≤ ↑(card ((∂ ) 𝒜)) / ↑(Nat.choose (Fint... | [
113,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.dual_id | [] | [
1567,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
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] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_card_le | [] | [
1299,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Algebra/Group/Units.lean | divp_left_inj | [] | [
478,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.union_distrib_iInter₂_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.181670\nγ : Type ?u.181673\nι : Sort u_2\nι' : Sort ?u.181679\nι₂ : Sort ?u.181682\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.181692\nκ₂ : ι → Sort ?u.181697\nκ' : ι' → Sort ?u.181702\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ (s ∪ ⋂ (i : ι) (j ... | [
1404,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1403,
1
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.lintegral_lt_top_of_boundedContinuous_to_real | [] | [
696,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.image_subset_compact_of_bounded | [
{
"state_after": "no goals",
"state_before": "𝕜₁ : Type u_3\n𝕜₂ : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜₁\ninst✝⁶ : SeminormedRing 𝕜₂\nσ₁₂ : 𝕜₁ →+* 𝕜₂\nM₁ : Type u_4\nM₂ : Type u_2\nM₃ : Type ?u.72218\ninst✝⁵ : SeminormedAddCommGroup M₁\ninst✝⁴ : TopologicalSpace M₂\ninst✝³ : AddCommMonoid M₂\ni... | [
135,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Order/CompleteLattice.lean | Prod.swap_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.212863\nγ : Type ?u.212866\nι : Sort u_3\nι' : Sort ?u.212872\nκ : ι → Sort ?u.212877\nκ' : ι' → Sort ?u.212882\ninst✝¹ : SupSet α\ninst✝ : SupSet β\nf : ι → α × β\n⊢ swap (iSup f) = ⨆ (i : ι), swap (f i)",
"tactic": ... | [
1883,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1882,
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Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousWithinAt_tsum | [
{
"state_after": "α : Type u_1\ninst✝¹ : TopologicalSpace α\nβ : Type ?u.131928\ninst✝ : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Type u_2\nf : ι → α → ℝ≥0∞\nh : ∀ (i : ι), LowerSemicontinuousWithinAt (f i) s x\n⊢ LowerSemicontinuousWithinAt (fun x' => ⨆ (s : Finset ι), ∑ i in s, f i x') s x",... | [
642,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
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Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasFDerivAt.iterate | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type ?u.140011\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.140106\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.1... | [
234,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.set_integral_dirac | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.1496551\n𝕜 : Type ?u.1496554\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : CompleteSpace E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : SMulCommClass ℝ 𝕜 E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : N... | [
1617,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1611,
1
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteVerts_inter_verts_left_eq | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.276164\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns : Set V\n⊢ deleteVerts G' (G'.verts ∩ s) = deleteVerts G' s",
"tactic": "ext <;> simp (config := { contextual := true }) [imp_false]"
}
] | [
1249,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
1
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Mathlib/Data/Real/EReal.lean | EReal.neg_le_neg_iff | [] | [
796,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
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Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.snd_exp | [
{
"state_after": "no goals",
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158,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.vec_single_eq_const | [] | [
196,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivaryOn_const_left | [] | [
136,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/Covering.lean | IsCoveringMap.quotientMap | [] | [
178,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.neg_snd | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.testBit_bitwise' | [
{
"state_after": "f : Bool → Bool → Bool\nh : f false false = false\nk : ℕ\n⊢ ∀ (m n : ℕ), testBit (bitwise' f m n) k = f (testBit m k) (testBit n k)",
"state_before": "f : Bool → Bool → Bool\nh : f false false = false\nm n k : ℕ\n⊢ testBit (bitwise' f m n) k = f (testBit m k) (testBit n k)",
"tactic": ... | [
500,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
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Mathlib/Data/Bool/Basic.lean | Bool.xor_not_left | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (a : Bool), xor (!a) a = true",
"tactic": "decide"
}
] | [
274,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/Analysis/Convex/PartitionOfUnity.lean | exists_continuous_forall_mem_convex_of_local | [
{
"state_after": "ι : Type ?u.6042\nX : Type u_2\nE : Type u_1\ninst✝⁷ : TopologicalSpace X\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : NormalSpace X\ninst✝³ : ParacompactSpace X\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nt : X → Set E\nht : ∀ (x : X), Convex... | [
63,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.nhds_basis_ball | [] | [
941,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_append | [] | [
112,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mex_not_mem_range | [] | [
2012,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2011,
1
] |
Mathlib/GroupTheory/NoncommPiCoprod.lean | MonoidHom.independent_range_of_coprime_order | [
{
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274,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.nsmul_eq_iff | [] | [
183,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Topology/Order/Basic.lean | Filter.Tendsto.max | [] | [
703,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
11
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Mathlib/Logic/Relation.lean | Relation.reflTransGen_iff_eq_or_transGen | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.24500\nγ : Type ?u.24503\nδ : Type ?u.24506\nr : α → α → Prop\na b c d : α\nh : ReflTransGen r a b\n⊢ b = a ∨ TransGen r a b\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.24500\nγ : Type ?u.24503\nδ : Type ?u.24506\nr : α → α → Prop\na b c d : α\nh : b ... | [
524,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_Iio | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.248450\ninst✝ : Fintype ι\na : ℝ\nn : ℕ\n⊢ ↑n = ↑↑volume (Ioo (a - ↑n) a)",
"tactic": "simp"
}
] | [
166,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.foldl_cons | [] | [
1368,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_of_open | [] | [
653,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.le_pow_toAddSubmonoid | [
{
"state_after": "case inl\nι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n : A\n⊢ M.toAddSubmonoid ^ 0 ≤ (M ^ 0).toAddSubmonoid\n\ncase inr\nι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : S... | [
432,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.totalVariation_absolutelyContinuous_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.93781\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nμ : Measure α\nh : totalVariation s ≪ μ\n⊢ (toJordanDecomposition s).posPart ≪ μ ∧ (toJordanDecomposition s).negPart ≪ μ\n\ncase mpr\nα : Type u_1\nβ : Type ?u.93781\ninst✝ : MeasurableSpace α\ns : Signed... | [
548,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
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Mathlib/Topology/Basic.lean | tendsto_nhds_limUnder | [] | [
1531,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
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Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.distrib' | [
{
"state_after": "case top\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : CanonicallyOrderedCommSemiring α\na b : WithTop α\n⊢ (a + b) * ⊤ = a * ⊤ + b * ⊤\n\ncase coe\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : CanonicallyOrderedCommSemiring α\na b : WithTop α\nc : α\n⊢ (a + b) * ↑c = a * ↑c + b * ↑c",
"... | [
195,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
9
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Mathlib/GroupTheory/GroupAction/Group.lean | smul_left_cancel | [] | [
166,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image2_eq_seq | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort ?u.275320\nι' : Sort ?u.275323\nι₂ : Sort ?u.275326\nκ : ι → Sort ?u.275331\nκ₁ : ι → Sort ?u.275336\nκ₂ : ι → Sort ?u.275341\nκ' : ι' → Sort ?u.275346\nf : α → β → γ\ns : Set α\nt : Set β\nx✝ : γ\n⊢ x✝ ∈ image2 f s t ↔ x✝ ∈ seq (f '' ... | [
2010,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2008,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_eq_of_associated | [
{
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"state_before": "d✝ d : ℤ\nhd : d ≤ 0\nx y : ℤ√d\nh : Associated x y\n⊢ norm x = norm y",
"tactic": "obtain ⟨u, rfl⟩ := h"
},
{
"state_after": "no goals",
"state_before": "case intro\nd✝ d : ℤ... | [
630,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Order/Basic.lean | LinearOrder.toPartialOrder_injective | [
{
"state_after": "case refl\nι : Type ?u.13117\nα✝ : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.13128\nr : α✝ → α✝ → Prop\nα : Type u_1\nA B : LinearOrder α\nA_le A_lt : α → α → Prop\nle_refl✝¹ : ∀ (a : α), a ≤ a\nle_trans✝¹ : ∀ (a b c : α), a ≤ b → b ≤ c → a ≤ c\nlt_iff_le_not_le✝¹ : ∀ (a b : α), a < b ↔ ... | [
647,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | tangentCone_congr | [] | [
140,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_injective | [] | [
3115,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3114,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.IsTerminal.strict_hom_ext | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasStrictTerminalObjects C\nI : C\nhI : IsTerminal I\nA : C\nf g : I ⟶ A\nthis : IsIso f\n⊢ f = g",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasStrictTerminalObjects C\nI : C\nhI : IsTerminal I\nA : C\nf g : I ⟶ A\n⊢ f = g",
"ta... | [
198,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Logic/Relation.lean | Relation.transitive_reflTransGen | [] | [
548,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.addEquiv_symm | [] | [
277,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.cons_injective2 | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nx y : α\ns t : Stream' α\nh : x :: s = y :: t\n⊢ x = y",
"tactic": "rw [← nth_zero_cons x s, h, nth_zero_cons]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nx y : α\ns t ... | [
101,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.liftOn_mk | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.bijOn_iInter_of_directed | [] | [
1642,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.mem_append_stream_right | [] | [
559,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | SemilinearIsometryClass.continuous | [] | [
92,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderiv_id | [] | [
1033,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnity.coe_injective | [] | [
105,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/BoundedOrder.lean | antitone_le | [] | [
571,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.eq_rec_on_eq | [] | [
1043,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sub_equiv_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf1 f2 g1 g2 : CauSeq β abv\nhf : f1 ≈ f2\nhg : g1 ≈ g2\n⊢ f1 - g1 ≈ f2 - g2",
"tactic": "simpa only [sub_eq_add_neg] using add_equiv_add hf ... | [
483,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.surj_on_of_inj_on_of_ncard_le | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ns t✝ : Set α\na b✝ x y : α\nf✝ : α → β\nt : Set β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂\nhst : ncard t ≤ ncard s\nht : autoParam (Set.Finite t) _auto✝\nb :... | [
431,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotent_iff_finite_descending_central_series | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ (∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤) ↔ ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ Group.IsNilpotent G ↔ ∃ n H, IsDescendingC... | [
278,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | combo_mem_ball_of_ne | [
{
"state_after": "case inl\n𝕜 : Type ?u.41739\nE : Type u_1\ninst✝⁴ : NormedLinearOrderedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : StrictConvexSpace ℝ E\nx y z : E\na b : ℝ\nhne : x ≠ y\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\nhx : x ∈ closedBall z 0... | [
163,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.piecewise_ite | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.84669\nι : Sort ?u.84672\nπ : α → Type ?u.84677\nδ : α → Sort ?u.84682\ns✝ : Set α\nf g : (i : α) → δ i\ninst✝¹ : (j : α) → Decidable (j ∈ s✝)\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nf₁ f₂ : α → β\ninst✝ : (i : α) → Decidable (i ∈ s)\nh₁ : Map... | [
1449,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.sub_succ' | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.ord_aleph_eq_enum_card | [
{
"state_after": "⊢ StrictMono (ord ∘ aleph) ∧ range (ord ∘ aleph) = {b | ord (card b) = b ∧ ω ≤ b}",
"state_before": "⊢ ord ∘ aleph = enumOrd {b | ord (card b) = b ∧ ω ≤ b}",
"tactic": "rw [← eq_enumOrd _ ord_card_unbounded']"
},
{
"state_after": "⊢ range (ord ∘ aleph) = {b | ord (card b) = b ∧... | [
401,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousAt.add | [] | [
947,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Topology/Constructions.lean | nhds_pi | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.196613\nδ : Type ?u.196616\nε : Type ?u.196619\nζ : Type ?u.196622\nι : Type u_1\nπ : ι → Type u_2\nκ : Type ?u.196633\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π i)\nf : α → (i : ι) → π i\na : (i : ι) ... | [
1218,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | LipschitzWith.to_rightInverse | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.138257\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nK : ℝ≥0\nf : α → β\nhf : LipschitzWith K f\ng : β → α\nhg : Function.RightInverse g f\nx y : β\n⊢ edist x y ≤ ↑K * edist (g x) (g y)",
"tactic": "sim... | [
256,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.ext_iff | [] | [
758,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signAux_mul | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nf g : Perm (Fin n)\n⊢ signAux (f * g) = signAux f * signAux g⁻¹",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nf g : Perm (Fin n)\n⊢ signAux (f * g) = signAux f * signAux g",
"tactic": "rw [← signAux_inv g]... | [
423,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.ext | [] | [
266,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Finset.aemeasurable_prod | [
{
"state_after": "no goals",
"state_before": "M : Type u_3\nι : Type u_1\nα : Type u_2\ninst✝² : CommMonoid M\ninst✝¹ : MeasurableSpace M\ninst✝ : MeasurableMul₂ M\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf : ι → α → M\ns : Finset ι\nhf : ∀ (i : ι), i ∈ s → AEMeasurable (f i)\n⊢ AEMeasurable fun... | [
957,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.map_liftQ | [
{
"state_after": "case intro.mk.intro\nR : Type u_1\nM : Type u_3\nr : R\nx✝ y : M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\np p' : Submodule R M\nR₂ : Type u_2\nM₂ : Type u_4\ninst✝³ : Ring R₂\ninst✝² : AddCommGroup M₂\ninst✝¹ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq✝ : Submodule R₂ M₂\ninst✝ : ... | [
469,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_X_pow_add_C | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\nn : ℕ\nhn : 0 < n\nr : R\n✝ : Nontrivial R\n⊢ leadingCoeff (X ^ n + ↑C r) = 1",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\nn : ℕ\nhn : 0 < n\nr : R\n⊢ leadingCoeff (X ^ n + ↑C r) = 1... | [
1428,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1424,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | PreErgodic.prob_eq_zero_or_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\ninst✝ : IsProbabilityMeasure μ\nhf : PreErgodic f\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ ↑↑μ s = 0 ∨ ↑↑μ s = 1",
"tactic": "simpa [hs] using hf.measure_self_or_compl... | [
75,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | DenseRange.topologicalClosure_map_submodule | [
{
"state_after": "R₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.327240\ninst✝²³ : Semiring R₁\ninst✝²² : Semiring R₂\ninst✝²¹ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nM₁ : Type u_3\ninst✝²⁰ : TopologicalSpace M₁\ninst✝¹⁹ : AddCommMonoid M₁\nM'₁ : Type ?u.327327\ninst✝¹⁸ : TopologicalSpace ... | [
568,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.injective | [] | [
850,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.compl_toMeasurable_compl_ae_eq | [] | [
245,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_X_pow_eq_nat_cast_mul | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommSemiring R\nn : ℕ\n⊢ (↑derivative^[Nat.zero]) (X ^ n) = ↑(Nat.descFactorial n Nat.zero) * X ^ (n - Nat.zero)\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝... | [
508,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.Parallel.direction_eq | [
{
"state_after": "case intro\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns₁ : AffineSubspace k P\nv : V\n⊢ direction s₁ = direction (map (↑(constVAdd k P v)) s₁)",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3... | [
1750,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1747,
1
] |
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