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/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Iic | [] | [
442,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv'_mul | [] | [
513,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.isInitialMul_inv | [] | [
114,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.21144\nα : Type u_1\ninst✝ : NonUnitalNonAssocSemiring α\ng f₁ f₂ : CentroidHom α\nhg : Injective ↑g\nh : comp g f₁ = comp g f₂\na : α\n⊢ ↑g (↑f₁ a) = ↑g (↑f₂ a)",
"tactic": "rw [← comp_apply, h, comp_apply]"
}
] | [
238,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_singleton | [] | [
39,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_iff'' | [
{
"state_after": "case h.e'_2\nι : Type u'\nι' : Type ?u.19688\nR : Type u_1\nK : Type ?u.19694\nM : Type u_2\nM' : Type ?u.19700\nM'' : Type ?u.19703\nV : Type u\nV' : Type ?u.19708\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module... | [
144,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/NumberTheory/LSeries.lean | Nat.ArithmeticFunction.LSeriesSummable_of_bounded_of_one_lt_re | [
{
"state_after": "f : ArithmeticFunction ℂ\nm : ℝ\nh : ∀ (n : ℕ), ↑Complex.abs (↑f n) ≤ m\nz : ℂ\nhz : 1 < z.re\n⊢ LSeriesSummable f ↑z.re",
"state_before": "f : ArithmeticFunction ℂ\nm : ℝ\nh : ∀ (n : ℕ), ↑Complex.abs (↑f n) ≤ m\nz : ℂ\nhz : 1 < z.re\n⊢ LSeriesSummable f z",
"tactic": "rw [← LSeriesSum... | [
105,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.dvd_of_mem_cycleType | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nn : ℕ\nh : n ∈ cycleType σ\n⊢ n ∣ Multiset.lcm (cycleType σ)",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nn : ℕ\nh : n ∈ cycleType σ\n⊢ n ∣ orderOf σ",
"tactic": "rw [← lcm_c... | [
183,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Nat/WithBot.lean | Nat.WithBot.add_eq_zero_iff | [
{
"state_after": "case none.none\n\n⊢ none + none = 0 ↔ none = 0 ∧ none = 0\n\ncase none.some\nval✝ : ℕ\n⊢ none + some val✝ = 0 ↔ none = 0 ∧ some val✝ = 0\n\ncase some.none\nval✝ : ℕ\n⊢ some val✝ + none = 0 ↔ some val✝ = 0 ∧ none = 0\n\ncase some.some\nval✝¹ val✝ : ℕ\n⊢ some val✝¹ + some val✝ = 0 ↔ some val✝¹ =... | [
31,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.isEquiv_iff_val_sub_one_lt_one | [
{
"state_after": "K : Type u_3\nF : Type ?u.3433435\nR : Type ?u.3433438\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type u_2\nΓ''₀ : Type ?u.3433450\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : LinearOrderedCommGroupWithZero Γ'₀\nv : Valuation K Γ₀\nv' ... | [
520,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | pullback_nonzero | [
{
"state_after": "G₀ : Type u\nM₀ : Type u_2\nM₀' : Type u_1\nG₀' : Type ?u.9044\ninst✝³ : MulZeroOneClass M₀\ninst✝² : Nontrivial M₀\na b : M₀\ninst✝¹ : Zero M₀'\ninst✝ : One M₀'\nf : M₀' → M₀\nzero : f 0 = 0\none : f 1 = 1\n⊢ ¬0 = 1",
"state_before": "G₀ : Type u\nM₀ : Type u_2\nM₀' : Type u_1\nG₀' : Type... | [
229,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.mod | [] | [
166,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
11
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_replicate | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\na : α\ni : Fin n\n⊢ get (replicate n a) i = a",
"tactic": "apply List.get_replicate"
}
] | [
130,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.liftAux_apply | [] | [
363,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | hasSum_geometric_of_lt_1 | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.68751\nβ : Type ?u.68754\nι : Type ?u.68757\nr : ℝ\nh₁ : 0 ≤ r\nh₂ : r < 1\nthis✝ : r ≠ 1\nthis : Tendsto (fun n => (r ^ n - 1) * (r - 1)⁻¹) atTop (𝓝 ((0 - 1) * (r - 1)⁻¹))\n⊢ Tendsto (fun n => ∑ i in Finset.range n, r ^ i) atTop (𝓝 (1 - r)⁻¹)",
... | [
188,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_dvd_prod_of_dvd | [
{
"state_after": "case h₁\nι : Type ?u.807675\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : CommMonoid β\nS : Finset α\ng1 g2 : α → β\nh✝ : ∀ (a : α), a ∈ S → g1 a ∣ g2 a\nh : ∀ (a : α), a ∈ ∅ → g1 a ∣ g2 a\n⊢ Finset.prod ∅ g1 ∣ Finset.prod ∅ g2\n\ncase h₂\nι : Type ?u.807... | [
1733,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1727,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_commute | [] | [
1062,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulRight_injective | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : Ring A\ninst✝¹ : Algebra R A\ninst✝ : NoZeroDivisors A\nx : A\nhx : x ≠ 0\nthis : Nontrivial A := { exists_pair_ne := Exists.intro x (Exists.intro 0 hx) }\n⊢ Function.Injective ↑(mulRight R x)",
"state_before": "R : Type u_2\nA ... | [
249,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.prod_mono | [] | [
662,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Analysis/Convex/Slope.lean | strictConcaveOn_iff_slope_strict_anti_adjacent | [] | [
237,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_mul_mul_le_card_mul_mul_card_div | [
{
"state_after": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA✝ B✝ C✝ A B C : Finset α\n⊢ card (A / C⁻¹) * card B ≤ card (A * B) * card (B * C⁻¹)",
"state_before": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA✝ B✝ C✝ A B C : Finset α\n⊢ card (A * C) * card B ≤ card (A * B) * ... | [
87,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | tendsto_right_nhds_uniformity | [] | [
860,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_prime_pow | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\np : ℕ\nhp : Fact (Nat.Prime p)\nhnot : ¬x ^ p ^ n = 1\nhfin : x ^ p ^ (n + 1) = 1\n⊢ orderOf x = p ^ (n + 1)",
"tactic": "apply minimalPeriod_eq_prime_pow <;> rwa [isP... | [
461,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_emptyset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.112728\nγ : Type ?u.112731\nι : Sort ?u.112734\nι' : Sort ?u.112737\nκ : ι → Sort ?u.112742\nκ' : ι' → Sort ?u.112747\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\nf : β → α\n⊢ (⨅ (x : β) (_ : x ∈ ∅), f x) = ⊤",
... | [
1405,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1405,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.hasSum_coe_one | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Algebra/Lie/Matrix.lean | lieEquivMatrix'_apply | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.77173\nα : Type u_1\nβ : Type ?u.77179\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\n⊢ 1 / a ≤ b ↔ 1 / b ≤ a",
"tactic": "simpa using inv_le ha hb"
}
] | [
436,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.eq_conj_eqToHom | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y : C\nf : X ⟶ Y\n⊢ f = eqToHom (_ : X = X) ≫ f ≫ eqToHom (_ : Y = Y)",
"tactic": "simp only [Category.id_comp, eqToHom_refl, Category.comp_id]"
}
] | [
295,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Algebra/Regular/Basic.lean | IsRegular.ne_zero | [] | [
255,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.map_sup | [] | [
741,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulReflectLT_iff_contravariant_pos | [
{
"state_after": "case inl\nα : Type u_1\na✝ b✝ c✝ d : α\ninst✝¹ : MulZeroClass α\ninst✝ : PartialOrder α\nh✝ : ContravariantClass { x // 0 < x } α (fun x y => ↑x * y) fun x x_1 => x < x_1\na : { x // 0 ≤ x }\nb c : α\nh : ↑a * b < ↑a * c\nha : 0 = ↑a\n⊢ b < c\n\ncase inr\nα : Type u_1\na✝ b✝ c✝ d : α\ninst✝¹ :... | [
473,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.finrank_directSum | [
{
"state_after": "R : Type u\nM✝ : Type v\nN : Type w\ninst✝¹⁴ : Ring R\ninst✝¹³ : StrongRankCondition R\ninst✝¹² : AddCommGroup M✝\ninst✝¹¹ : Module R M✝\ninst✝¹⁰ : Module.Free R M✝\ninst✝⁹ : Module.Finite R M✝\ninst✝⁸ : AddCommGroup N\ninst✝⁷ : Module R N\ninst✝⁶ : Module.Free R N\ninst✝⁵ : Module.Finite R N\... | [
114,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.source_inter_preimage_target_inter | [] | [
377,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.ext_iff_degree_le | [] | [
370,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_comp | [
{
"state_after": "α : Type ?u.362805\nβ : Type ?u.362808\nγ : Type ?u.362811\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no o' : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nhf : ∀ {i j : Ordinal} (hi : i < o) (hj : j < o), i ≤ j → f i hi ≤ f j hj\ng : (a : Ordinal) → a < o' → Ordinal\nhg : blsub o' ... | [
1951,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1943,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.linearMapAt_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁸ : Semiring R\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F TotalSpace.proj\nx : TotalSpace E\nb✝ : B\ny✝ : E b✝\ninst✝... | [
249,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_zero | [
{
"state_after": "case a.h\nl : Type ?u.264124\nm : Type u_2\nn : Type u_1\no : Type u_3\nm' : o → Type ?u.264138\nn' : o → Type ?u.264143\nR : Type ?u.264146\nS : Type ?u.264149\nα : Type v\nβ : Type w\nγ : Type ?u.264156\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype n\nM : Matrix m n α\ni✝ : m\nx✝ : ... | [
991,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
11
] |
Std/Data/Int/DivMod.lean | Int.emod_eq_zero_of_dvd | [] | [
682,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
681,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.ext | [] | [
205,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.neg_neg | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na : X ⟶ Y\n⊢ 0 - (0 - a) = a",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na : X ⟶ Y\n⊢ - -a = a",
"tactic": "rw [neg_def, neg_def]"
},
{
"state_after": "C... | [
386,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_nnnorm | [] | [
2049,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2048,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lt_one_iff_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.180662\nβ : Type ?u.180665\nγ : Type ?u.180668\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\n⊢ a < 1 ↔ a = 0",
"tactic": "simpa using @lt_succ_bot_iff _ _ _ a _ _"
}
] | [
1093,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.isOpen | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.19471\nσ : Type ?u.19474\nτ : Type ?u.19477\ninst✝ : TopologicalSpace α\nF : Realizer α\ns : F.σ\na : α\nm : a ∈ f F.F s\n⊢ 𝓝 a ≤ 𝓟 (f F.F s)",
"tactic": "simpa using F.mem_nhds.2 ⟨s, m, Subset.refl _⟩"
}
] | [
161,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
11
] |
Std/Logic.lean | Decidable.imp_iff_or_not | [] | [
559,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
558,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.comp_prod_comp_same | [] | [
418,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Topology/Homotopy/Equiv.lean | Homeomorph.coe_toHomotopyEquiv | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.nontrivial_of_einfsep_ne_top | [] | [
97,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate_eq_nil_iff | [
{
"state_after": "case zero\nα : Type u\nl✝ l : List α\n⊢ rotate l zero = [] ↔ l = []\n\ncase succ\nα : Type u\nl✝ : List α\nn : ℕ\nhn : ∀ {l : List α}, rotate l n = [] ↔ l = []\nl : List α\n⊢ rotate l (succ n) = [] ↔ l = []",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ rotate l n = [] ↔ l = []",
... | [
207,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.noncommProd_mem | [] | [
87,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.nondegenerate_iff_ker_eq_bot | [
{
"state_after": "R : Type ?u.1436438\nM : Type ?u.1436441\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type ?u.1436477\nM₁ : Type ?u.1436480\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_2\ninst✝¹⁰ : CommSemiring R₂\ninst✝⁹ : A... | [
1323,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1313,
1
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.card_dvd_of_le | [] | [
820,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubalgebra.topEquiv_apply | [] | [
1272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/Computability/Language.lean | Language.iSup_add | [] | [
229,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_plift_up | [] | [
238,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Order/BooleanAlgebra.lean | disjoint_sdiff_self_right | [] | [
217,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.isLeast_image2 | [] | [
1496,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1494,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.finiteDimensional_iSup_of_finset' | [
{
"state_after": "K : Type u_2\nL : Type u_3\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nE1 E2 : IntermediateField K L\nι : Type u_1\nf : ι → IntermediateField K L\ns : Finset ι\nh : ∀ (i : ι), i ∈ s → FiniteDimensional K { x // x ∈ f i }\nthis : ∀ (i : { i // i ∈ s }), FiniteDimensional K { x // ... | [
1250,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/Analysis/Normed/Field/InfiniteSum.lean | tsum_mul_tsum_eq_tsum_sum_antidiagonal_of_summable_norm | [] | [
99,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.unique | [
{
"state_after": "case intro\nr s : ℝ\nf : ℕ → ℝ\nhr : IsSt (ofSeq f) r\nhs : IsSt (ofSeq f) s\n⊢ r = s",
"state_before": "x : ℝ*\nr s : ℝ\nhr : IsSt x r\nhs : IsSt x s\n⊢ r = s",
"tactic": "rcases ofSeq_surjective x with ⟨f, rfl⟩"
},
{
"state_after": "case intro\nr s : ℝ\nf : ℕ → ℝ\nhr : Tendst... | [
279,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Topology/OmegaCompletePartialOrder.lean | notBelow_isOpen | [
{
"state_after": "α : Type u_1\ninst✝ : OmegaCompletePartialOrder α\ny : Scott α\nh : Monotone (notBelow y)\n⊢ IsOpen (notBelow y)",
"state_before": "α : Type u_1\ninst✝ : OmegaCompletePartialOrder α\ny : Scott α\n⊢ IsOpen (notBelow y)",
"tactic": "have h : Monotone (notBelow y) := by\n intro x y' h\n ... | [
110,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | exists_max_ideal_of_mem_nonunits | [
{
"state_after": "α : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nh : a ∈ nonunits α\nthis : Ideal.span {a} ≠ ⊤\n⊢ ∃ I, Ideal.IsMaximal I ∧ a ∈ I",
"state_before": "α : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nh : a ∈ nonunits α\n⊢ ∃ I, Ideal.IsMaximal I ∧ a ∈ I",
"tactic": "have : ... | [
864,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.bit0_div_two | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ bit0 n / 2 = n",
"tactic": "rw [← Nat.bit0_eq_bit0, bit0_eq_two_mul, two_mul_div_two_of_even (even_bit0 n)]"
}
] | [
246,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/LocalAtTarget.lean | Set.restrictPreimage_closedEmbedding | [] | [
64,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_constOfIsEmpty | [
{
"state_after": "case a\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁸ : Fintype ι\ninst✝¹⁷ : Fintype ι'\ninst✝¹⁶ : NontriviallyNormedField 𝕜\ninst✝¹⁵ : (i : ι) → NormedAddCommGroup (E... | [
534,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_pow | [] | [
447,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_eq_sqrt_inner | [] | [
1000,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Balanced.insert | [] | [
167,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
163,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.snd_linear | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.dvd_div_of_mul_dvd | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ m n k a b c : ℕ\nh : a * b ∣ c\nha : a = 0\n⊢ b ∣ c / a",
"tactic": "simp [ha]"
},
{
"state_after": "no goals",
"state_before": "a✝ b✝ m n k a b c : ℕ\nh : a * b ∣ c\nha✝ : ¬a = 0\nha : 0 < a\nh1 : ∃ d, c = a * b * d\nd : ℕ\nhd : c = a * b ... | [
186,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.exists_mk | [] | [
507,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | isClosedMap_mul_left | [] | [
93,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/Filter.lean | Filter.tendsto_nhds | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.5011\nα : Type u_1\nβ : Type u_2\nX : Type ?u.5020\nY : Type ?u.5023\nla : Filter α\nlb : Filter β\nf : α → Filter β\n⊢ Tendsto f la (𝓝 lb) ↔ ∀ (s : Set β), s ∈ lb → ∀ᶠ (a : α) in la, s ∈ f a",
"tactic": "simp only [nhds_eq', tendsto_lift', mem_... | [
89,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
11
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.hasSum_norm | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < ENNReal.toReal p\nf : { x // x ∈ lp E p }\n⊢ HasSum (fun i => ‖↑f i‖ ^ ENNReal.toReal p) (∑' (i : α), ‖↑f i‖ ^ ENNReal.toReal p)",
"state_before": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ni... | [
430,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.cos_angle_sub_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x (-y) = 0\n⊢ Real.cos (angle x (x - y)) = ‖x‖ / ‖x - y‖",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ Real.cos (ang... | [
285,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjUnion_empty | [] | [
1018,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul | [
{
"state_after": "Ω : Type u_2\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf g : Ω → ℝ≥0∞\nX✝ Y✝ : Ω → ℝ\nβ : Type u_1\ninst✝² : MeasurableSpace β\nX Y : Ω → β\ninst✝¹ : NormedDivisionRing β\ninst✝ : BorelSpace β\nhXY : IndepFun X Y\nh'XY : Integrable (X * Y)\nhX : AEStronglyMeasurable X μ\nhY : AEStr... | [
199,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Std/Data/Int/DivMod.lean | Int.sub_emod | [
{
"state_after": "a b n : Int\n⊢ (a - b + b) % n = (a % n - b % n + b) % n",
"state_before": "a b n : Int\n⊢ (a - b) % n = (a % n - b % n) % n",
"tactic": "apply (emod_add_cancel_right b).mp"
},
{
"state_after": "no goals",
"state_before": "a b n : Int\n⊢ (a - b + b) % n = (a % n - b % n + b... | [
499,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
497,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.cosh_lt_cosh | [] | [
736,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.mul_apply | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.map_add_left_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ map ((fun x x_1 => x + x_1) c) (Icc a b) = Icc (c + a) (c + b)",
"tactic": "classical rw [Icc, Icc, ← Finset.image_add_left_Icc, Finset.... | [
291,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.divInt_neg_den | [] | [
169,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | Ideal.IsMaximal.closure_eq | [] | [
265,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essInf_const' | [] | [
72,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.mul_right_injective | [] | [
794,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
11
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.HD_lipschitz_aux1 | [
{
"state_after": "case intro\nX : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf✝ : GromovHausdorff.ProdSpaceFun X Y\nx y z t : X ⊕ Y\nf g : GromovHausdorff.Cb X Y\ncg : ℝ\nhcg : cg ∈ lowerBounds (r... | [
377,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
9
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_sup_u | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nκ : ι → Sort ?u.37330\na✝ a₁ a₂ : α\nb✝ b₁ b₂ : β\nl : α → β\nu : β → α\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\ngi : GaloisInsertion l u\na b : β\n⊢ l (u a) ⊔ l (u b) = a ⊔ b",
"tactic": "simp onl... | [
537,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_of_empty | [] | [
1336,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
1
] |
Mathlib/Order/Cover.lean | toDual_wcovby_toDual_iff | [] | [
139,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/Perfect.lean | Perfect.exists_nat_bool_injection | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\ninst✝¹ : MetricSpace α\nC : Set α\nhC : Perfect C\nε : ℝ≥0∞\nhnonempty : Set.Nonempty C\ninst✝ : CompleteSpace α\nu : ℕ → ℝ≥0∞\nupos' : ∀ (n : ℕ), u n ∈ Ioo 0 1\nhu : Tendsto u atTop (𝓝 0)\n⊢ ∃ f, range f ⊆ C ∧ Continuous f ∧ Injective f",
"state_befo... | [
317,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.infsep_lt_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.59186\ninst✝ : PseudoMetricSpace α\nx y z : α\ns t : Set α\nd : ℝ\nhs : Set.Nontrivial s\n⊢ ¬infsep s < d ↔ ¬∃ x x_1 y x_2 _hxy, dist x y < d",
"state_before": "α : Type u_1\nβ : Type ?u.59186\ninst✝ : PseudoMetricSpace α\nx y z : α\ns t : Set α\nd : ℝ\nhs : Set.N... | [
408,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Order/Ring/Canonical.lean | mul_add_mul_le_mul_add_mul' | [
{
"state_after": "α : Type u\nβ : Type ?u.5132\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\ninst✝ : ExistsAddOfLE α\nhba : b ≤ a\nhdc : d ≤ c\n⊢ b • c + a • d ≤ b • d + a • c",
"state_before": "α : Type u\nβ : Type ?u.5132\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\ninst✝ : ExistsAddOfLE α\nhba : b ≤... | [
66,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.exists_ne_map_eq_of_mapsTo | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nf : α → β\nhs : Set.Infinite s\nhf : MapsTo f s t\nht : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → x ≠ y → f x ≠ f y\n⊢ ¬Set.Finite t",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nf ... | [
1369,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.proj_symm_apply | [] | [
395,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.add_rat_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p (x + ↑r)\n⊢ LiouvilleWith p x",
"tactic": "simpa using h.add_rat (-r)"
}
] | [
203,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
src/lean/Init/Data/Array/BasicAux.lean | List.of_toArrayAux_eq_toArrayAux | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nas bs : List α\ncs ds : Array α\nh : toArrayAux as cs = toArrayAux bs ds\nhlen : Array.size cs = Array.size ds\n⊢ as = bs ∧ cs = ds",
"tactic": "match as, bs with\n| [], [] => simp [toArrayAux] at h; simp [h]\n| a::as, [] => simp [toArrayAux... | [
33,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
22,
9
] |
Mathlib/SetTheory/Lists.lean | Lists'.cons_subset | [
{
"state_after": "α : Type u_1\na : Lists α\nl₁ l₂ : Lists' α true\nh : cons a l₁ ⊆ l₂\n⊢ a ∈ l₂ ∧ l₁ ⊆ l₂",
"state_before": "α : Type u_1\na : Lists α\nl₁ l₂ : Lists' α true\n⊢ cons a l₁ ⊆ l₂ ↔ a ∈ l₂ ∧ l₁ ⊆ l₂",
"tactic": "refine' ⟨fun h => _, fun ⟨⟨a', m, e⟩, s⟩ => Subset.cons e m s⟩"
},
{
"s... | [
174,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_atTop | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∃ v, v ∈ atTop ∧ ∀ (y : ℝ), y ∈ v → HasDerivAt f (f' y) y\nhgg' : ∃ v, v ∈ atTop ∧ ∀ (y : ℝ), y ∈ v → HasDerivAt g (g' y) y\nhg' : ∃ v, v ∈ atTop ∧ ∀ (y : ℝ), y ∈ v → g' y ≠ 0\nhftop : Tendsto f atTop (𝓝 0)\nhgtop : Tendsto g atTop... | [
357,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | iUnion_Iic_eq_Iio_of_lt_of_tendsto | [] | [
450,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.apply_eq_of_lt_firstDiff | [
{
"state_after": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\nhn : n < if h : x ≠ y then Nat.find (_ : ∃ a, x a ≠ y a) else 0\n⊢ x n = y n",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\nhn : n < firstDiff x y\n⊢ x n = y n",
"tactic": "rw [firstDiff_def] at hn"
},
{
"state_aft... | [
87,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_sub_const_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) ⁻¹' Ioi b = Ioi (b + a)",
"tactic": "simp [sub_eq_add_neg]"
}
] | [
182,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.