file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
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Mathlib/Order/Hom/Bounded.lean | map_eq_top_iff | [
{
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145,
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142,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.comap_symm | [] | [
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37
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.range_const | [
{
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162,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_cons_none | [] | [
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.id_apply | [] | [
774,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Control/Fold.lean | Traversable.foldr_map | [] | [
383,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_eq_bot | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | Monotone.mul_strictMono' | [] | [
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55
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Mathlib/Data/Option/NAry.lean | Option.map_map₂_antidistrib | [
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184,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.univ_inaccessible | [
{
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{
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},
{
... | [
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24
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Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.coe_decompose_mul_of_left_mem_of_not_le | [
{
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304,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
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Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.rangeS_top_iff_surjective | [
{
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93
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Mathlib/Algebra/Hom/Iterate.lean | RingHom.iterate_map_neg | [] | [
164,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Topology/Support.lean | HasCompactSupport.smul_right | [
{
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Mathlib/Data/Set/Basic.lean | Set.diff_union_diff_cancel | [] | [
1590,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientMap_surjective | [
{
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418,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.image_eq_target_inter_inv_preimage | [] | [
273,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
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Mathlib/Analysis/InnerProductSpace/Projection.lean | norm_sq_eq_add_norm_sq_projection | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.959328\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\nx : E\nS : Submodule 𝕜 E\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace { x... | [
1036,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.mem_iff | [] | [
265,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
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Mathlib/NumberTheory/Padics/Hensel.lean | T_def | [
{
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127,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Order/CompleteLattice.lean | le_iSup_iff | [
{
"state_after": "no goals",
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173,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.one_apply | [] | [
137,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
9
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots_le_map_of_injective | [
{
"state_after": "case pos\nR : 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\nhf : Function.Injective ↑f\nhp0 : p = 0\n⊢ ↑Multiset.card (roots p) ≤ ↑Multiset.card (roots (map f... | [
1206,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
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] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.symm_self_id_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nβ : Y ≅ Z\n⊢ α.symm ≪≫ α ≪≫ β = β",
"tactic": "rw [← trans_assoc, symm_self_id, refl_trans]"
}
] | [
213,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.bsize | [
{
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"state_before": "l m r : List Char\n⊢ Substring.bsize\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len l },\n stopPos := { byteIdx := utf8Len l + utf8Len m } } =\n utf8Len m",
"tactic": "simp [Substring.bsize, Nat.add_sub_cancel_left]"
}
... | [
813,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
812,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.flip' | [
{
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"state_before": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\nh : ν ≤ n\n⊢ bernsteinPolynomial R n ν = Polynomial.comp (bernsteinPolynomial R n (n - ν)) (1 - X)",
"tactic": "simp [← flip _ _ _ h, Polynomial.comp_assoc]"
}
] | [
89,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/Data/Nat/Basic.lean | Nat.div_eq_iff_eq_mul_right | [] | [
659,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
11
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Mathlib/Order/Bounds/OrderIso.lean | OrderIso.isGLB_preimage | [] | [
65,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.sinh | [] | [
168,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_pf_left | [
{
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"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₃ b c a₁ : R\na₂ ... | [
359,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
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] |
Mathlib/Algebra/GroupPower/Order.lean | one_le_pow_iff | [] | [
238,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | Finite.of_summable_const | [
{
"state_after": "ι : Type u_2\nκ : Type ?u.66748\nα : Type u_1\ninst✝³ : LinearOrderedAddCommGroup α\ninst✝² : TopologicalSpace α\ninst✝¹ : Archimedean α\ninst✝ : OrderClosedTopology α\nb : α\nhb : 0 < b\nhf : Summable fun x => b\nH : ∀ (s : Finset ι), card s • b ≤ ∑' (x : ι), b\n⊢ Finite ι",
"state_before... | [
274,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Order/RelClasses.lean | IsPreorder.swap | [] | [
100,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/Analysis/Convex/Exposed.lean | IsExposed.antisymm | [] | [
102,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
11
] |
Mathlib/Logic/Basic.lean | Ne.dite_eq_right_iff | [] | [
1181,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1180,
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Mathlib/Analysis/Convex/StrictConvexSpace.lean | norm_combo_lt_of_ne | [
{
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178,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Basic.lean | List.getLast_pmap | [
{
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Mathlib/MeasureTheory/Group/Arithmetic.lean | List.aemeasurable_prod | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
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Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.mul_apply | [] | [
131,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_Ioc | [
{
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"tactic": "rw [← Icc_diff_left, ← Icc_diff_left, image_diff (upda... | [
154,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/Data/Finset/Basic.lean | Finset.coe_sdiff | [] | [
2116,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2115,
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Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.isDomain | [] | [
439,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
11
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Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.LeftExactFunctor.forget_obj | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mk_eq_mk_iff | [] | [
294,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.comp_left | [] | [
80,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Init/Propext.lean | eq_false_intro | [] | [
29,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
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] |
src/lean/Init/SimpLemmas.lean | or_false | [] | [
90,
91
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
90,
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Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | Real.Angle.coe_expMapCircle | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ ↑(expMapCircle ↑x✝) = ↑(cos ↑x✝) + ↑(sin ↑x✝) * I",
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"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ ↑(expMa... | [
126,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.disjoint_atBot_atTop | [
{
"state_after": "case intro.intro\nι : Type ?u.4780\nι' : Type ?u.4783\nα : Type u_1\nβ : Type ?u.4789\nγ : Type ?u.4792\ninst✝¹ : PartialOrder α\ninst✝ : Nontrivial α\nx y : α\nhne : x ≠ y\n⊢ Disjoint atBot atTop",
"state_before": "ι : Type ?u.4780\nι' : Type ?u.4783\nα : Type u_1\nβ : Type ?u.4789\nγ : T... | [
125,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.empty_vecAlt0 | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nm n o : ℕ\nm' : Type ?u.51912\nn' : Type ?u.51915\no' : Type ?u.51918\nα : Type u_1\nh : 0 = 0 + 0\n⊢ vecAlt0 h ![] = ![]",
"tactic": "simp"
}
] | [
403,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Init/Function.lean | Function.Bijective.comp | [] | [
82,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_units_conj | [] | [
532,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.isSymm_mul_transpose_self | [] | [
60,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Init/Data/Int/Basic.lean | Int.ofNat_mul_out | [] | [
51,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
11
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.FinMeasAdditive.smul_measure | [
{
"state_after": "α : Type u_1\nE : Type ?u.29157\nF : Type ?u.29160\nF' : Type ?u.29163\nG : Type ?u.29166\n𝕜 : Type ?u.29169\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ℝ F'\n... | [
139,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.card_insertNone | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4974\ns : Finset α\n⊢ card (↑insertNone s) = card s + 1",
"tactic": "simp [insertNone]"
}
] | [
82,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Classification.lean | IsAlgClosed.ringEquivOfCardinalEqOfCharZero | [
{
"state_after": "case a\nK L : Type\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : IsAlgClosed K\ninst✝² : IsAlgClosed L\ninst✝¹ : CharZero K\ninst✝ : CharZero L\nhK : ℵ₀ < (#K)\nhKL : (#K) = (#L)\n⊢ Nonempty (K ≃+* L)",
"state_before": "K L : Type\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : IsAlgClosed K... | [
193,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | ae_eq_restrict_iff_indicator_ae_eq | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.5024740\nδ : Type ?u.5024743\nι : Type ?u.5024746\nR : Type ?u.5024749\nR' : Type ?u.5024752\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns t : Set α\nf : α → β\ninst✝ : Zero β\ng : α → β\nhs : MeasurableSet s\n⊢ (∀ᵐ (x : α) ∂μ, x ∈ s → f x ... | [
4706,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4698,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.bot_eq_zero | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
src/lean/Init/Prelude.lean | Fin.eq_of_val_eq | [] | [
1753,
31
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1752,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.norm_lt_iff | [] | [
235,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.of_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.25485\nm : MeasurableSpace α\nM✝ : Type ?u.25491\ninst✝⁵ : AddCommMonoid M✝\ninst✝⁴ : TopologicalSpace M✝\ninst✝³ : T2Space M✝\nv✝ : VectorMeasure α M✝\nf : ℕ → Set α\nM : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : TopologicalSpace M\n... | [
202,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Set.Finite.smul_set | [] | [
108,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearEquiv.piCongrRight_symm | [] | [
369,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Surjective.forall | [] | [
195,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
11
] |
Mathlib/Data/Nat/PrimeFin.lean | Nat.infinite_setOf_prime | [] | [
25,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_inj_iff | [] | [
663,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Algebra/Associated.lean | Associates.coe_unit_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.291289\nγ : Type ?u.291292\nδ : Type ?u.291295\ninst✝ : CommMonoid α\nu : (Associates α)ˣ\n⊢ ↑u = 1",
"tactic": "simp"
}
] | [
882,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.smul_le_smul | [] | [
650,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sinh_three_mul | [
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ sinh (3 * x) = 4 * sinh x ^ 3 + 3 * sinh x",
"state_before": "x y : ℂ\n⊢ sinh (3 * x) = 4 * sinh x ^ 3 + 3 * sinh x",
"tactic": "have h1 : x + 2 * x = 3 * x := by ring"
},
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ sinh x * cosh (2 *... | [
792,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.equiv_refl | [] | [
169,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.ofRealAm_coe | [] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | IsGLB.iUnion_Ioi_eq | [] | [
193,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_smul | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.187403\nδ : Type ?u.187406\nι : Type ?u.187409\nR : Type ?u.187412\nR' : Type ?u.187415\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nμ : Measure α\nf : α → β... | [
1209,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
11
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.isPrimitiveRoot_iff' | [
{
"state_after": "case mp\nM : Type ?u.3462472\nN : Type ?u.3462475\nG : Type ?u.3462478\nR : Type u_1\nS : Type ?u.3462484\nF : Type ?u.3462487\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk✝ l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh✝ : IsPrimitiveRoot ζ✝ k✝\ninst✝ : IsDomain R\nk... | [
788,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.cantorFunction_injective | [
{
"state_after": "c : ℝ\nf✝ g✝ : ℕ → Bool\nn : ℕ\nh1 : 0 < c\nh2 : c < 1 / 2\nf g : ℕ → Bool\nhfg : cantorFunction c f = cantorFunction c g\n⊢ f = g",
"state_before": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\nh1 : 0 < c\nh2 : c < 1 / 2\n⊢ Function.Injective (cantorFunction c)",
"tactic": "intro f g hfg"
},
{
... | [
199,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | deriv_ne_zero | [] | [
124,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
9
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.comp_one | [
{
"state_after": "case h\nα : Type ?u.214013\nβ : Type ?u.214016\nM : Type u_1\nN : Type u_2\nP : Type u_3\nG : Type ?u.214028\nH : Type ?u.214031\nF : Type ?u.214034\ninst✝⁴ : Group G\ninst✝³ : CommGroup H\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : MulOneClass P\nf : N →* P\nx✝ : M\n⊢ ↑(comp f 1)... | [
1517,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_lowerSemicontinuousAt_antitone | [] | [
353,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | norm_sup_sub_sup_le_add_norm | [
{
"state_after": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\na b c d : α\n⊢ ‖a ⊔ b - c ⊔ d‖ ≤ ‖abs (a - c)‖ + ‖abs (b - d)‖",
"state_before": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\na b c d : α\n⊢ ‖a ⊔ b - c ⊔ d‖ ≤ ‖a - c‖ + ‖b - d‖",
"tactic": "rw [← norm_abs_eq_norm (a - c), ← norm... | [
146,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\n⊢ padicValNat p n = 0 ↔ p = 1 ∨ n = 0 ∨ ¬p ∣ n",
"tactic": "simp only [padicValNat, dite_eq_right_iff, PartENat.get_eq_iff_eq_coe, Nat.cast_zero,\n multiplicity_eq_zero, and_imp, pos_iff_ne_zero, Ne.def, ← or_iff_not_imp_left]"
}
] | [
91,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.haar_singleton | [
{
"state_after": "case h.e'_2.h.e'_3\n𝕜 : Type ?u.585203\nG : Type u_1\nH : Type ?u.585209\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : MeasurableSpace H\ninst✝⁴ : Group G\ninst✝³ : TopologicalSpace G\nμ : Measure G\ninst✝² : IsHaarMeasure μ\ninst✝¹ : TopologicalGroup G\ninst✝ : BorelSpace G\ng : G\n⊢ {g} = (fun h =>... | [
724,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.mod_add_div' | [
{
"state_after": "R : Type u\ninst✝ : EuclideanDomain R\nm k : R\n⊢ m % k + k * (m / k) = m",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\nm k : R\n⊢ m % k + m / k * k = m",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : EuclideanDom... | [
134,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | zpow_sub₀ | [
{
"state_after": "no goals",
"state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nha : a ≠ 0\nz1 z2 : ℤ\n⊢ a ^ (z1 - z2) = a ^ z1 / a ^ z2",
"tactic": "rw [sub_eq_add_neg, zpow_add₀ ha, zpow_neg, div_eq_mul_inv]"
}
] | [
164,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.nhdsWithin_target_inter | [] | [
268,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.tendsto_iff_tendstoUniformly | [
{
"state_after": "α : Type u₁\nβ : Type u₂\ninst✝² : TopologicalSpace α\ninst✝¹ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nι : Type u₃\np : Filter ι\nF : ι → C(α, β)\ninst✝ : CompactSpace α\n⊢ (∀ (K : Set α), IsCompact K → TendstoUniformlyOn (fun i a => ↑(F i) a) (↑f) p K) ↔\n TendstoUniforml... | [
440,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_re | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ (log x).re = Real.log (↑abs x)",
"tactic": "simp [log]"
}
] | [
36,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toPartENat_apply_of_lt_aleph0 | [] | [
1857,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1856,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousOn.mono | [] | [
691,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_const | [] | [
1556,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1554,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.tendsto_indicator_ge | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.15743\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf : α → β\nx : α\nn : ℕ\nhn : n ≥ ⌈↑‖f x‖₊⌉₊ + 1\n⊢ Set.indicator {x | ↑n ≤ ↑‖f x‖₊} f x = 0",
"state_before": "α : Type u_2\nβ : Type u_1\nι : Type ?u.15743\nm : MeasurableSp... | [
168,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Finset/Functor.lean | Finset.seq_def | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_smul | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Path.not_mem_edges_of_loop | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nv : V\ne : Sym2 V\np : Path G v v\n⊢ ¬e ∈ Walk.edges ↑p",
"tactic": "simp [p.loop_eq]"
}
] | [
1331,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1330,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.Bijective.iterate | [] | [
102,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_disjoint | [] | [
585,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.comp_bijective | [] | [
387,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_isTop | [] | [
2393,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2392,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_mul_of_ediv_eq_right | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nH1 : b ∣ a\nH2 : a / b = c\n⊢ a = b * c",
"tactic": "rw [← H2, Int.mul_ediv_cancel' H1]"
}
] | [
739,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
738,
11
] |
Mathlib/Order/FixedPoints.lean | OrderHom.isLeast_lfp | [] | [
100,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
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