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/Fin/VecNotation.lean | Matrix.vecCons_const | [] | [
191,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.coe_le_coe | [] | [
314,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\nP : Type w₂\ninst✝¹⁴ : CommRing R\ninst✝¹³ : LieRing L\ninst✝¹² : LieAlgebra R L\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : AddCommGroup N\ninst✝⁹ : AddCommGroup P\ninst✝⁸ : Module R M\ninst✝⁷ : Module R N\ninst✝⁶ : Mod... | [
824,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.subalgebraConjInvariant | [
{
"state_after": "case intro.intro\n𝕜 : Type u_1\nX : Type u_2\ninst✝¹ : IsROrC 𝕜\ninst✝ : TopologicalSpace X\nS : Set C(X, 𝕜)\nhS : ∀ (f : C(X, 𝕜)), f ∈ S → ↑(AlgHom.compLeftContinuous ℝ ↑conjAe (_ : Continuous ↑conjCle)) f ∈ S\nf : C(X, 𝕜)\nhf : f ∈ ↑(Subalgebra.restrictScalars ℝ (Algebra.adjoin 𝕜 S)).t... | [
369,
67
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354,
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Mathlib/LinearAlgebra/Span.lean | LinearMap.map_injective | [] | [
897,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_add_prod_le | [
{
"state_after": "ι : Type u_1\nα : Type ?u.156140\nβ : Type ?u.156143\nM : Type ?u.156146\nN : Type ?u.156149\nG : Type ?u.156152\nk : Type ?u.156155\nR : Type u_2\ninst✝ : OrderedCommSemiring R\nf✝ g✝ : ι → R\ns t : Finset ι\ni : ι\nf g h : ι → R\nhi : i ∈ s\nh2i : g i + h i ≤ f i\nhgf : ∀ (j : ι), j ∈ s → j ... | [
641,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
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Mathlib/Order/Filter/Pointwise.lean | Filter.pure_vsub_pure | [] | [
1140,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.uniformInducing | [] | [
177,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
11
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearDependent_comp_subtype | [] | [
378,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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Mathlib/Data/Complex/Exponential.lean | Complex.cosh_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh (-x) = cosh x",
"tactic": "simp [add_comm, cosh, exp_neg]"
}
] | [
623,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_sup | [] | [
355,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.min_order_le_order_add | [
{
"state_after": "case pos\nΓ✝ : Type ?u.666994\nR : Type u_2\ninst✝² : PartialOrder Γ✝\ninst✝¹ : AddMonoid R\nΓ : Type u_1\ninst✝ : LinearOrderedCancelAddCommMonoid Γ\nx y : HahnSeries Γ R\nhxy : x + y ≠ 0\nhx : x = 0\n⊢ min (order x) (order y) ≤ order (x + y)\n\ncase neg\nΓ✝ : Type ?u.666994\nR : Type u_2\nin... | [
394,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_finset_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.948084\nδ : Type ?u.948087\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nι : Type u_1\ns : Finset ι\nf : ι → α → β\nhf : ∀ (i : ι), i ∈ s ... | [
676,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
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Mathlib/Data/PFun.lean | PFun.id_comp | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
588,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
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Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.decomposeAux_coe | [
{
"state_after": "case mk\nM : Type u_1\nι : Type u_3\nR : Type u_2\ninst✝⁴ : DecidableEq M\ninst✝³ : AddMonoid M\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : CommSemiring R\nf : M →+ ι\ni : ι\nx : AddMonoidAlgebra R M\nhx : x ∈ gradeBy R (↑f) i\n⊢ ↑(decomposeAux f) ↑{ val := x, property := hx } =\n ... | [
183,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Computability/Partrec.lean | Computable.of_eq | [] | [
283,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coeff_coe | [
{
"state_after": "case ofNat\nR : Type u\nR' : Type ?u.236572\ninst✝¹ : Semiring R\ninst✝ : Ring R'\nf g : PowerSeries R\nf' g' : PowerSeries R'\na✝ : ℕ\n⊢ HahnSeries.coeff (↑(ofPowerSeries ℤ R) f) (Int.ofNat a✝) =\n if Int.ofNat a✝ < 0 then 0 else ↑(coeff R (Int.natAbs (Int.ofNat a✝))) f\n\ncase negSucc\nR ... | [
226,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Sum/Basic.lean | Function.Injective.sum_elim | [] | [
563,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Algebra/Order/SMul.lean | Tactic.smul_nonneg_of_pos_of_nonneg | [] | [
309,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
9
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_ne_zero_iff | [] | [
344,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Filter/Archimedean.lean | tendsto_nat_cast_atTop_atTop | [] | [
42,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_eq_lsub_iff_succ | [
{
"state_after": "case refine'_1\nα : Type ?u.324464\nβ : Type ?u.324467\nγ : Type ?u.324470\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\nh : sup f = lsub f\n⊢ ∀ (a : Ordinal), a < lsub f → succ a < lsub f\n\ncase refine'_2\nα : Type ?u.324464\nβ : Type ?u.324467\nγ : Type... | [
1652,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1639,
1
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Mathlib/Data/List/Zip.lean | List.get?_zip_with | [
{
"state_after": "case nil\nα : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.94446\nε : Type ?u.94449\nf : α → β → γ\nl₂✝ : List β\ni✝ : ℕ\nl₂ : List β\ni : ℕ\n⊢ get? (zipWith f [] l₂) i = Option.bind (Option.map f (get? [] i)) fun g => Option.map g (get? l₂ i)\n\ncase cons\nα : Type u\nβ : Type u_1\nγ : Typ... | [
377,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
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Mathlib/Data/Set/Image.lean | Set.mem_image_iff_of_inverse | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.45305\nι : Sort ?u.45308\nι' : Sort ?u.45311\nf✝ : α → β\ns✝ t : Set α\nf : α → β\ng : β → α\nb : β\ns : Set α\nh₁ : LeftInverse g f\nh₂ : Function.RightInverse g f\n⊢ b ∈ g ⁻¹' s ↔ g b ∈ s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4... | [
414,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Set.infinite_iff_exists_gt | [] | [
844,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
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] |
Mathlib/Algebra/Group/Units.lean | Units.mk_val | [] | [
162,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.continuous_totalSpaceMk | [] | [
274,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Algebra/Lie/Semisimple.lean | LieAlgebra.isSemisimple_iff_no_abelian_ideals | [
{
"state_after": "R : Type u\nL : Type v\ninst✝² : CommRing R\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\n⊢ (∀ (I : LieIdeal R L), IsSolvable R { x // x ∈ ↑I } → I = ⊥) ↔\n ∀ (I : LieIdeal R L), IsLieAbelian { x // x ∈ ↑I } → I = ⊥",
"state_before": "R : Type u\nL : Type v\ninst✝² : CommRing R\ninst✝¹ :... | [
78,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
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Mathlib/GroupTheory/Congruence.lean | Con.to_submonoid_inj | [] | [
805,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.hasLimitsOfShape_of_equivalence | [
{
"state_after": "case has_limit\nJ : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF : J ⥤ C\nJ' : Type u₂\ninst✝¹ : Category J'\ne : J ≌ J'\ninst✝ : HasLimitsOfShape J C\n⊢ autoParam (∀ (F : J' ⥤ C), HasLimit F) _auto✝",
"state_before": "J : Type u₁\ninst... | [
610,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
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] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.tensor_μ_def₁ | [
{
"state_after": "C : Type u₁\ninst✝⁸ : Category C\ninst✝⁷ : MonoidalCategory C\ninst✝⁶ : BraidedCategory C\nD : Type u₂\ninst✝⁵ : Category D\ninst✝⁴ : MonoidalCategory D\ninst✝³ : BraidedCategory D\nE : Type u₃\ninst✝² : Category E\ninst✝¹ : MonoidalCategory E\ninst✝ : BraidedCategory E\nX₁ X₂ Y₁ Y₂ : C\n⊢ ((α... | [
393,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.mem_rmap | [] | [
77,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMap₂_symm | [] | [
404,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Std/Logic.lean | exists_prop | [] | [
483,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
482,
9
] |
Mathlib/RingTheory/Localization/Module.lean | LinearIndependent.localization_localization | [
{
"state_after": "R : Type u_2\nRₛ : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing Rₛ\ninst✝⁸ : Algebra R Rₛ\nS : Submonoid R\nhT : IsLocalization S Rₛ\nA : Type u_3\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\nAₛ : Type u_5\ninst✝⁵ : CommRing Aₛ\ninst✝⁴ : Algebra A Aₛ\ninst✝³ : Algebra Rₛ Aₛ\ninst✝² : Algeb... | [
93,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.prime_C_iff_of_fintype | [
{
"state_after": "R✝ : Type u\nS : Type ?u.283331\nσ✝ : Type v\nM : Type w\ninst✝⁵ : CommRing R✝\ninst✝⁴ : CommRing S\ninst✝³ : AddCommGroup M\ninst✝² : Module R✝ M\nr✝ : R✝\nR : Type u\nσ : Type v\nr : R\ninst✝¹ : CommRing R\ninst✝ : Fintype σ\nf : (d : ℕ) → (MvPolynomial (Fin d) R)[X] ≃* MvPolynomial (Fin (d ... | [
790,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
9
] |
Mathlib/Analysis/ODE/Gronwall.lean | norm_le_gronwallBound_of_norm_deriv_right_le | [] | [
147,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_add | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\nh₁ : a ∣ b\nh₂ : a ∣ c\nd : Nat\nhd : b = a * d\ne : Nat\nhe : c = a * e\n⊢ b + c = a * (d + e)",
"tactic": "simp [Nat.left_distrib, hd, he]"
}
] | [
668,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
667,
11
] |
Mathlib/Data/Opposite.lean | Opposite.unop_op | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mul_meas_ge_le_pow_norm' | [] | [
1801,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1798,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd | [
{
"state_after": "case intro\nR : Type u_1\ninst✝ : CommRing R\nd n : ℕ\nh : d ∈ Nat.properDivisors n\nhd : d ∣ n\nhdn : d < n\n⊢ (X ^ d - 1) * ∏ x in Nat.divisors n \\ Nat.divisors d, cyclotomic x R = X ^ n - 1",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nd n : ℕ\nh : d ∈ Nat.properDivisors n\n⊢ (X... | [
441,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.SchurZassenhausInduction.step7 | [
{
"state_after": "G : Type u\ninst✝² : Group G\ninst✝¹ : Fintype G\nN : Subgroup G\ninst✝ : Normal N\nh1 : Nat.coprime (Fintype.card { x // x ∈ N }) (index N)\nh2 :\n ∀ (G' : Type u) [inst : Group G'] [inst_1 : Fintype G'],\n Fintype.card G' < Fintype.card G →\n ∀ {N' : Subgroup G'} [inst_2 : Normal N'... | [
265,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
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] |
Mathlib/Data/Finset/Basic.lean | Finset.disjiUnion_cons | [] | [
3470,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3463,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | exists_extension_of_le_sublinear | [
{
"state_after": "𝕜 : Type ?u.285824\nE : Type u_1\nF : Type ?u.285830\nG : Type ?u.285833\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : { x // x ∈ f.domain }), ↑f x ≤ N... | [
859,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
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] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.convex | [] | [
68,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_singleton | [] | [
117,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ring_inverse_equiv | [
{
"state_after": "R : Type u_1\nM : Type u_2\nM₂ : Type ?u.1961009\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : TopologicalSpace M₂\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : TopologicalAddGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R M₂\ne : M ≃L[R] M\n⊢ Ring.inverse ↑(↑(MulEquiv.... | [
2525,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2521,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | Monotone.le_csSup_image | [] | [
1247,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
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Mathlib/Topology/Support.lean | LocallyFinite.exists_finset_nhd_mulSupport_subset | [
{
"state_after": "case intro.intro\nX : Type u_2\nα : Type ?u.34493\nα' : Type ?u.34496\nβ : Type ?u.34499\nγ : Type ?u.34502\nδ : Type ?u.34505\nM : Type ?u.34508\nE : Type ?u.34511\nR : Type u_3\nι : Type u_1\nU : ι → Set X\ninst✝¹ : TopologicalSpace X\ninst✝ : One R\nf : ι → X → R\nhlf : LocallyFinite fun i ... | [
338,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/GroupTheory/Abelianization.lean | rank_closureCommutatorRepresentatives_le | [
{
"state_after": "G : Type u\ninst✝¹ : Group G\ninst✝ : Finite ↑(commutatorSet G)\n⊢ Group.rank { x // x ∈ closureCommutatorRepresentatives G } ≤ Nat.card ↑(commutatorSet G) + Nat.card ↑(commutatorSet G)",
"state_before": "G : Type u\ninst✝¹ : Group G\ninst✝ : Finite ↑(commutatorSet G)\n⊢ Group.rank { x // ... | [
290,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_sub_one | [
{
"state_after": "case zero\nn m : ℕ\na : Fin (zero + 1)\n⊢ ↑(a - 1) = if a = 0 then zero else ↑a - 1\n\ncase succ\nn m n✝ : ℕ\na : Fin (Nat.succ n✝ + 1)\n⊢ ↑(a - 1) = if a = 0 then Nat.succ n✝ else ↑a - 1",
"state_before": "n✝ m n : ℕ\na : Fin (n + 1)\n⊢ ↑(a - 1) = if a = 0 then n else ↑a - 1",
"tactic... | [
1957,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1949,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.Ioi_add_bij | [
{
"state_after": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d x✝ : M\nh : x✝ ∈ Ioi (a + d)\n⊢ x✝ ∈ (fun x => x + d) '' Ioi a",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x + d) (Ioi a... | [
44,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.getRight_inl | [] | [
101,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
9
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.empty_mul | [] | [
357,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.flip_iff | [] | [
461,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_pure | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_mul_neg | [
{
"state_after": "case pos\nR : Type u_2\ninst✝³ : CommRing R\nx : R\nB : Type u_1\ninst✝² : CommRing B\ninst✝¹ : Algebra R B\ninst✝ : IsLocalization.Away x B\nd : ℤ\nhd : d ≤ 0\n⊢ selfZpow x B d * selfZpow x B (-d) = 1\n\ncase neg\nR : Type u_2\ninst✝³ : CommRing R\nx : R\nB : Type u_1\ninst✝² : CommRing B\nin... | [
287,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.moveRight_neg | [
{
"state_after": "case mk\nα✝ β✝ : Type u_1\na✝¹ : α✝ → PGame\na✝ : β✝ → PGame\ni : LeftMoves (mk α✝ β✝ a✝¹ a✝)\n⊢ moveRight (-mk α✝ β✝ a✝¹ a✝) (↑toRightMovesNeg i) = -moveLeft (mk α✝ β✝ a✝¹ a✝) i",
"state_before": "x : PGame\ni : LeftMoves x\n⊢ moveRight (-x) (↑toRightMovesNeg i) = -moveLeft x i",
"tac... | [
1278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv | [] | [
1454,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1452,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_bsup | [] | [
1501,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.ereal_toReal | [] | [
2007,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2005,
1
] |
Mathlib/Computability/DFA.lean | DFA.evalFrom_split | [
{
"state_after": "case intro.intro.intro\nα : Type u\nσ : Type v\nM : DFA α σ\ninst✝ : Fintype σ\nx : List α\ns t : σ\nhlen : Fintype.card σ ≤ List.length x\nhx : evalFrom M s x = t\nn m : Fin (Fintype.card σ + 1)\nhneq : n ≠ m\nheq : evalFrom M s (List.take (↑n) x) = evalFrom M s (List.take (↑m) x)\n⊢ ∃ q a b ... | [
138,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.uncurry_eq | [] | [
221,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.IsClique.mono | [
{
"state_after": "α : Type u_1\nG H : SimpleGraph α\ns t : Set α\nh : G ≤ H\n⊢ Set.Pairwise s G.Adj → Set.Pairwise s H.Adj",
"state_before": "α : Type u_1\nG H : SimpleGraph α\ns t : Set α\nh : G ≤ H\n⊢ IsClique G s → IsClique H s",
"tactic": "simp_rw [isClique_iff]"
},
{
"state_after": "no goal... | [
78,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_sub | [
{
"state_after": "no goals",
"state_before": "n m : Nat\nh : n ≤ m\nk : Nat\n⊢ subNatNat (m - n) k = subNatNat m (k + n)",
"tactic": "rwa [← subNatNat_add_add _ _ n, Nat.sub_add_cancel]"
}
] | [
234,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
233,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_id | [] | [
999,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.preimage_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\ns t : Finset β\nhs : InjOn f (f ⁻¹' ↑s)\nht : InjOn f (f ⁻¹' ↑t)\n⊢ ↑(preimage (s ∩ t) f\n (_ : ∀ (x₁ : α), x₁ ∈ f ⁻¹' ↑(s ∩ t) → ∀ (x₂ : α), x₂ ∈ f ... | [
64,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_zero_left' | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1400160\nG : Type ?u.1400163\n𝕜 : Type ?u.1400166\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 ... | [
1368,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | liftFun_vecCons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : ℕ\nr : α → α → Prop\ninst✝ : IsTrans α r\nf : Fin (n + 1) → α\na : α\n⊢ ((fun x x_1 => x < x_1) ⇒ r) (vecCons a f) (vecCons a f) ↔ r a (f 0) ∧ ((fun x x_1 => x < x_1) ⇒ r) f f",
"tactic": "simp only [liftFun_iff_succ r, forall_fin_succ, con... | [
27,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.lt_cof_power | [
{
"state_after": "α : Type ?u.195035\nr : α → α → Prop\na b : Cardinal\nha : ℵ₀ ≤ a\nb1 : 1 < b\nb0 : b ≠ 0\n⊢ a < Ordinal.cof (ord (b ^ a))",
"state_before": "α : Type ?u.195035\nr : α → α → Prop\na b : Cardinal\nha : ℵ₀ ≤ a\nb1 : 1 < b\n⊢ a < Ordinal.cof (ord (b ^ a))",
"tactic": "have b0 : b ≠ 0 := (... | [
1247,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.leadingCoeff_of_c_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.557467\nF : Type ?u.557470\nK : Type ?u.557473\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\n⊢ leadingCoeff (toPoly P) = P.d",
"tactic": "rw [of_c_eq_zero ha hb hc, leadingCoe... | [
236,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.fderivWithin | [] | [
87,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
] |
Mathlib/Algebra/Lie/BaseChange.lean | LieAlgebra.ExtendScalars.bracket_def | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
9
] |
Std/Data/Array/Init/Lemmas.lean | Array.toList_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\narr : Array α\n⊢ toList arr = arr.data",
"tactic": "simp [toList, foldr_eq_foldr_data]"
}
] | [
96,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
95,
9
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.exists_eq_const | [
{
"state_after": "case inl\nX : Type u_1\nY : Type u_2\nZ : Type ?u.5782\nα : Type ?u.5785\ninst✝² : TopologicalSpace X\ninst✝¹ : PreconnectedSpace X\ninst✝ : Nonempty Y\nf : X → Y\nhf : IsLocallyConstant f\nh : IsEmpty X\n⊢ ∃ y, f = Function.const X y\n\ncase inr\nX : Type u_1\nY : Type u_2\nZ : Type ?u.5782\n... | [
179,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_smul_span_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nF : Type ?u.45639\nG : Type ?u.45642\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI✝ J : Ideal R\nN P : Submodule R M\nI : Ideal R\nm x : M\nhx : x ∈ I • span R {m}\nm1 m2 : M\nx✝¹ : ∃ y, y ∈ I ∧ y • m = m1\nx✝ ... | [
146,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.eq_of_eq_counts | [] | [
1507,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1505,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.19547\nβ : Type ?u.19550\nG : Type u_1\ninst✝ : DivInvMonoid G\na✝ b✝ c✝ a b c : G\n⊢ a * (b / c) = a * b / c",
"tactic": "simp only [mul_assoc, div_eq_mul_inv]"
}
] | [
325,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.comp₂ | [
{
"state_after": "no goals",
"state_before": "f : ℕ → ℕ → ℕ\nhf : Primrec' fun v => f (Vector.head v) (Vector.head (Vector.tail v))\nn : ℕ\ng h : Vector ℕ n → ℕ\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v => f (g v) (h v)",
"tactic": "simpa using hf.comp' (hg.cons <| hh.cons Primrec'.nil)"
}
] | [
1442,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublistsLen_of_length_lt | [] | [
341,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.coe_fold_l | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2887\nop : α → α → α\nhc : IsCommutative α op\nha : IsAssociative α op\nb : α\nl : List α\n⊢ List.foldl (fun x y => op y x) b l = List.foldl op b l",
"tactic": "simp [hc.comm]"
}
] | [
49,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.104729\nα : Type ?u.104732\nβ : Type ?u.104735\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\nx : ℤ\n⊢ fract x = OfNat.ofNat 0 x",
"tactic": "simp [fract]"
}
] | [
624,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.modify_WF | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → β → β\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nk : α\nh : Bucket.WF m.buckets\n⊢ Bucket.WF\n (Bucket.update\n (Bucket.update m.buckets (mkIdx (_ : 0 < Array.size m.buckets.val) (UInt64.toUSize (hash k))).val AssocList.nil\n (_ :\n ... | [
281,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
273,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_lsub_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.321274\nβ : Type ?u.321277\nγ : Type ?u.321280\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\na : Ordinal\n⊢ a < lsub f ↔ ∃ i, a ≤ f i",
"tactic": "simpa only [not_forall, not_lt, not_le] using not_congr (@lsu... | [
1605,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1603,
1
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.eventualRange_eq_iff | [
{
"state_after": "J : Type u\ninst✝¹ : Category J\nF : J ⥤ Type v\ni j k : J\ns : Set (F.obj i)\ninst✝ : IsCofilteredOrEmpty J\nf : i ⟶ j\n⊢ (∀ (i_1 : J) (j_1 : i_1 ⟶ j), range (F.map f) ⊆ range (F.map j_1)) ↔\n ∀ ⦃k : J⦄ (g : k ⟶ i), range (F.map f) ⊆ range (F.map (g ≫ f))",
"state_before": "J : Type u\... | [
227,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.diff_right | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\ninst✝ : DecidableEq α\nl₁ l₂ t : List α\nh : l₁ ~ l₂\n⊢ List.diff l₁ t ~ List.diff l₂ t",
"tactic": "induction t generalizing l₁ l₂ h <;> simp [*, Perm.erase]"
}
] | [
797,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.comm | [] | [
71,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.count_sum' | [
{
"state_after": "ι : Type ?u.936144\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝ : DecidableEq α\ns : Finset β\na : α\nf : β → Multiset α\n⊢ count a (sum (map (fun x => f x) s.val)) = sum (map (fun x => count a (f x)) s.val)",
"state_before": "ι : Type ?u.936144\nβ ... | [
2147,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2144,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_of_nonpos | [] | [
626,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Algebra/Order/Invertible.lean | invOf_le_one | [] | [
43,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.empty_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.148810\nγ : Type ?u.148813\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t t₁ t₂ u v : Finset α\na b : α\ns : Finset α\nx : α\n⊢ x ∈ ∅ ∨ x ∈ s ↔ x ∈ s",
"tactic": "simp"
}
] | [
1442,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1441,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_inj | [] | [
186,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.vecMul_stdBasis | [
{
"state_after": "R : Type u_3\ninst✝² : Semiring R\nl : Type ?u.4510\nm : Type u_1\nn : Type u_2\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nM : Matrix m n R\ni : m\nj : n\nthis : ∑ i' : m, (if i = i' then 1 else 0) * M i' j = M i j\n⊢ vecMul (↑(LinearMap.stdBasis R (fun x => R) i) 1) M j = M i j",
"state_... | [
108,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.u_biSup_of_lu_eq_self | [] | [
831,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_div_cancel''' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.71563\nβ : Type ?u.71566\nG : Type u_1\ninst✝ : CommGroup G\na✝ b✝ c d a b : G\n⊢ a * b / a = b",
"tactic": "rw [div_eq_inv_mul, inv_mul_cancel_left]"
}
] | [
963,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioi_pred | [] | [
731,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.285420\nr : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\nn : σ\n⊢ degreeOf n 0 = 0",
"tactic": "classical simp only [degreeOf_def, degrees_zero, Multiset.count_zero]"
},
... | [
512,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.basicOpen_mul_le_right | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nf g : A\n⊢ basicOpen 𝒜 f ⊓ basicOpen 𝒜 g ≤ basicOpen 𝒜 g",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : Com... | [
433,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.228585\nβ : Type ?u.228588\nγ : Type ?u.228591\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\n⊢ ord 1 = 1",
"tactic": "simpa using ord_nat 1"
}
] | [
1436,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1436,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ofLeftInverse_symm_apply | [] | [
2725,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2723,
1
] |
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