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/Nat/Choose/Basic.lean | Nat.choose_eq_descFactorial_div_factorial | [
{
"state_after": "n k : ℕ\n⊢ k ! * choose n k = k ! * (descFactorial n k / k !)",
"state_before": "n k : ℕ\n⊢ choose n k = descFactorial n k / k !",
"tactic": "apply mul_left_cancel₀ (factorial_ne_zero k)"
},
{
"state_after": "n k : ℕ\n⊢ descFactorial n k = k ! * (descFactorial n k / k !)",
... | [
273,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasFDerivAt | [] | [
723,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Topology/PathConnected.lean | JoinedIn.somePath_mem | [] | [
841,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
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Mathlib/Data/Nat/Interval.lean | Nat.Ico_succ_succ | [
{
"state_after": "case a\na b c x : ℕ\n⊢ x ∈ Ico (succ a) (succ b) ↔ x ∈ Ioc a b",
"state_before": "a b c : ℕ\n⊢ Ico (succ a) (succ b) = Ioc a b",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case a\na b c x : ℕ\n⊢ x ∈ Ico (succ a) (succ b) ↔ x ∈ Ioc a b",
"tactic":... | [
182,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.hasFDerivWithinAt | [] | [
373,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_add | [] | [
1191,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.symm_neg | [] | [
2284,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2283,
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.rowLens_ofRowLens_eq_self | [] | [
527,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_eq_one_iff_unique | [] | [
1773,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1772,
1
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Mathlib/RingTheory/WittVector/MulP.lean | WittVector.mulN_coeff | [
{
"state_after": "case zero\np : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nx : 𝕎 R\nk✝ k : ℕ\n⊢ coeff (x * ↑Nat.zero) k = ↑(aeval x.coeff) (wittMulN p Nat.zero k)\n\ncase succ\np : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nx : 𝕎 R\nk✝ n : ℕ\nih : ∀ (k : ℕ), coeff (x * ↑... | [
64,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
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Mathlib/Topology/GDelta.lean | mem_residual_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.16113\nγ : Type ?u.16116\nι : Type ?u.16119\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ (∃ S, S ⊆ {t | IsOpen t ∧ Dense t} ∧ Set.Countable S ∧ ⋂₀ S ⊆ s) ↔\n ∃ S, (∀ (t : Set α), t ∈ S → IsOpen t) ∧ (∀ (t : Set α), t ∈ S → Dense t) ∧ Se... | [
225,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.sup_eq_closure | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.19854\nG : Type u_1\nA : Type ?u.19860\nS : Type ?u.19863\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns : Set G\nH K : Subgroup G\n⊢ closure ↑H ⊔ closure ↑K ≤ H ⊔ K",
"tactic": "rw [closure_eq, closure_eq]"
}
] | [
155,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Algebra/Star/Order.lean | StarOrderedRing.nonneg_iff | [
{
"state_after": "no goals",
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"tactic": "simp only [le_iff, zero_add, exists_eq_right']"
}
] | [
147,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.toWord_eq_nil_iff | [] | [
1327,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1326,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_swap | [] | [
1578,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1577,
1
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Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicatorAux_zero | [
{
"state_after": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nδ_pos : 0 < δ\nE : Set α\nx : α\nx_out : ENNReal.ofReal δ ≤ infEdist x E\n⊢ thickenedIndicatorAux δ E x = 0",
"state_before": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nδ_pos : 0 < δ\nE : Set α\nx : α\nx_out : ¬x ∈ thickening δ E\... | [
105,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_prod_filter | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.196353\nι : Type ?u.196356\nG : Type ?u.196359\nM : Type u_2\nN : Type ?u.196365\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\nf : α → M\ns : Set α\ninst✝ : DecidablePred fun x => x ∈ s\nhf : Set.Finite (mulSupport f)\nx : α\n⊢ (x ∈ s ∩ mulSupport fun i => f ... | [
502,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.sub_int_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\n⊢ LiouvilleWith p (x - ↑m) ↔ LiouvilleWith p x",
"tactic": "rw [← Rat.cast_coe_int, sub_rat_iff]"
}
] | [
274,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Topology/Constructions.lean | CofiniteTopology.mem_nhds_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.18624\nδ : Type ?u.18627\nε : Type ?u.18630\nζ : Type ?u.18633\na : CofiniteTopology α\ns : Set (CofiniteTopology α)\n⊢ s ∈ 𝓝 a ↔ a ∈ s ∧ Set.Finite (sᶜ)",
"tactic": "simp [nhds_eq]"
}
] | [
305,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atBot_iInf | [] | [
174,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_ofBijective | [] | [
447,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
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] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Icc | [] | [
348,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
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] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.coe_single | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Associated.lean | Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.44629\nγ : Type ?u.44632\nδ : Type ?u.44635\ninst✝ : CancelCommMonoidWithZero α\np a b : α\nn : ℕ\nhp : Prime p\nhpow : p ^ Nat.succ n ∣ a ^ Nat.succ n * b ^ n\nhb : ¬p ^ 2 ∣ b\nH : p ∣ a ^ Nat.succ n\n⊢ p ∣ a\n\ncase inr\nα : Type u_1\nβ : Type ?u.44629\nγ ... | [
143,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_zero_right | [] | [
278,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.mem_supported | [
{
"state_after": "σ : Type u_1\nτ : Type ?u.120933\nR : Type u\nS : Type v\nr : R\ne : ℕ\nn m : σ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\ns t : Set σ\n⊢ (∃ x, ↑(rename Subtype.val) x = p) ↔ ↑(vars p) ⊆ s",
"state_before": "σ : Type u_1\nτ : Type ?u.120933\nR : Type u\nS : Type v\nr : R\ne : ℕ\nn m ... | [
86,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Star.lean | StarConvex.preimage_add_left | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.72281\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y z : E\ns : Set E\nhs : StarConvex 𝕜 (z + x) s\n⊢ StarConvex 𝕜 x ((fun x => x + z) ⁻¹' s)",
"state_before": "𝕜 :... | [
264,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tsum_geometric_of_lt_1 | [] | [
197,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_eq_bot_iff | [
{
"state_after": "α : Type u_2\nα' : Type ?u.22051\nβ : Type u_3\nβ' : Type ?u.22057\nγ : Type u_1\nγ' : Type ?u.22063\nδ : Type ?u.22066\nδ' : Type ?u.22069\nε : Type ?u.22072\nε' : Type ?u.22075\nm : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh h₁ h₂ : Filter γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : S... | [
124,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.foldl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl m r : List Char\nf : α → Char → α\ninit : α\n⊢ Substring.foldl f init\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len l },\n stopPos := { byteIdx := utf8Len l + utf8Len m } } =\n List.foldl f init m",
"tact... | [
923,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
922,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.coe_mul | [] | [
679,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Algebra/GroupPower/Identities.lean | sum_four_sq_mul_sum_four_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\na b x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ y₁ y₂ y₃ y₄ y₅ y₆ y₇ y₈ n : R\n⊢ (x₁ ^ 2 + x₂ ^ 2 + x₃ ^ 2 + x₄ ^ 2) * (y₁ ^ 2 + y₂ ^ 2 + y₃ ^ 2 + y₄ ^ 2) =\n (x₁ * y₁ - x₂ * y₂ - x₃ * y₃ - x₄ * y₄) ^ 2 + (x₁ * y₂ + x₂ * y₁ + x₃ * y₄ - x₄ * y₃) ... | [
63,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Ring/Basic.lean | AddMonoidHom.mulRight_apply | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Data/Fin/Basic.lean | Fin.cast_trans | [
{
"state_after": "case h\nn m k : ℕ\nh : n = m\nh' : m = k\ni : Fin n\n⊢ ↑(↑(cast h') (↑(cast h) i)) = ↑(↑(cast (_ : n = k)) i)",
"state_before": "n m k : ℕ\nh : n = m\nh' : m = k\ni : Fin n\n⊢ ↑(cast h') (↑(cast h) i) = ↑(cast (_ : n = k)) i",
"tactic": "ext"
},
{
"state_after": "no goals",
... | [
1095,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
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Mathlib/Analysis/Normed/MulAction.lean | nnnorm_smul | [] | [
103,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.Approx.agree_trival | [
{
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"state_before": "F : PFunctor\nx : CofixA F 0\ny : CofixA F 1\n⊢ Agree x y",
"tactic": "constructor"
}
] | [
89,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_reindexRange | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁹ : CommSemiring R\nl : Type ?u.1797707\nm : Type u_4\nn : Type u_5\ninst✝⁸ : Fintype n\ninst✝⁷ : Fintype m\ninst✝⁶ : DecidableEq n\nM₁ : Type u_1\nM₂ : Type u_2\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : Module R M₁\ninst... | [
641,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
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Mathlib/Topology/SubsetProperties.lean | IsIrreducible.isPreirreducible | [] | [
1699,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1698,
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_nat_cast_mul | [
{
"state_after": "no goals",
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"tactic": "induction' k with k ih generalizing f <;> simp [*]"
}
] | [
363,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.arrow_max | [
{
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195,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.interpolate_one | [
{
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"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Fin... | [
320,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_sum_val | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Order/UpperLower/Basic.lean | Set.monotone_mem | [] | [
267,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.aeval | [
{
"state_after": "A : Type u_2\nB : Type u_1\nB' : Type ?u.17400\ninst✝⁴ : CommRing A\ninst✝³ : Ring B\ninst✝² : Ring B'\ninst✝¹ : Algebra A B\ninst✝ : Algebra A B'\nx : B\n⊢ ↑(Polynomial.aeval x)\n (if hx : IsIntegral A x then\n WellFounded.min (_ : WellFounded fun p q => degree p < degree q)\n ... | [
91,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | norm_abs_sub_abs | [] | [
187,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.uniformContinuous_extension₂ | [] | [
698,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.map_id | [
{
"state_after": "case a.h\nl : Type ?u.6402\nm : Type u_1\nn : Type u_2\no : Type ?u.6411\nm' : o → Type ?u.6416\nn' : o → Type ?u.6421\nR : Type ?u.6424\nS : Type ?u.6427\nα : Type v\nβ : Type w\nγ : Type ?u.6434\nM : Matrix m n α\ni✝ : m\nx✝ : n\n⊢ map M id i✝ x✝ = M i✝ x✝",
"state_before": "l : Type ?u.... | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Algebra/GroupPower/Order.lean | abs_le_of_sq_le_sq | [
{
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"tactic": "rwa [← abs_of_nonneg hy, ← sq_le_sq]"
}
] | [
718,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_pow | [] | [
1222,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some | [
{
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464,
39
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459,
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Mathlib/Algebra/Order/Kleene.lean | kstar_zero | [] | [
257,
29
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256,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_range | [] | [
460,
24
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458,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.neg_cons | [
{
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35
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.coprod | [] | [
956,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
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Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_foldr | [
{
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},
{
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119,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/Analysis/Convex/Function.lean | ConcaveOn.comp | [] | [
141,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.of_isUnit_or_isUnit_of_isUnit_add | [] | [
59,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.StructuredArrow.isCoseparating_proj_preimage | [
{
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367,
84
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364,
1
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Std/Data/Array/Lemmas.lean | Array.set_set | [
{
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},
{
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111,
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110,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.edist_toL1_toL1 | [
{
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33
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1405,
1
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Mathlib/Topology/Constructions.lean | isOpen_range_inl | [] | [
926,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.mersenne_int_pos | [
{
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"tactic": "exact_mod_cast Nat.one_lt_two_pow p hp"
}
] | [
101,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Data/Set/Intervals/Infinite.lean | Set.Ico_infinite | [] | [
52,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
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Mathlib/Data/Set/Basic.lean | Set.inter_compl_nonempty_iff | [
{
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}
] | [
1784,
71
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1783,
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Mathlib/RingTheory/Ideal/Basic.lean | Ring.ne_bot_of_isMaximal_of_not_isField | [
{
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800,
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794,
1
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Mathlib/Analysis/Calculus/Deriv/Add.lean | hasDerivAt_neg | [] | [
251,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.tail_congr | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns t : WSeq α\nh : s ... | [
1189,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
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Mathlib/Data/Int/Cast/Field.lean | Int.cast_neg_natCast | [
{
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}
] | [
38,
87
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38,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_single_apply_aux | [
{
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"tactic": "classical exact\n have A :\n ∀ a₁ b₁,\n ... | [
553,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
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Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_pow_atTop_nhds_0_of_norm_lt_1 | [
{
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"state_before": "α : Type ?u.130810\nβ : Type ?u.130813\nι : Type ?u.130816\nR : Type u_1\ninst✝ : NormedRing R\nx : R\nh : ‖x‖ < ... | [
271,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
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Mathlib/Data/Finset/Sups.lean | Finset.sups_assoc | [] | [
200,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
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Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_insert | [] | [
1649,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1648,
1
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.funInvIdAssoc_inv_app | [
{
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"state_before": "C : Type u₁\ninst✝² : ... | [
335,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
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Mathlib/LinearAlgebra/Matrix/Basis.lean | mul_basis_toMatrix | [
{
"state_after": "ι : Type u_1\nι' : Type u_2\nκ : Type u_5\nκ' : Type ?u.502195\nR : Type u_3\nM : Type u_4\ninst✝¹³ : CommSemiring R\ninst✝¹² : AddCommMonoid M\ninst✝¹¹ : Module R M\nR₂ : Type ?u.502388\nM₂ : Type ?u.502391\ninst✝¹⁰ : CommRing R₂\ninst✝⁹ : AddCommGroup M₂\ninst✝⁸ : Module R₂ M₂\ne : Basis ι R... | [
213,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.ofSubtype_apply_of_mem | [] | [
450,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_inter_mul_prod_diff | [
{
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"state_before": "ι : Type ?u.772557\nβ : Type u\nα : Ty... | [
1547,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1544,
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Mathlib/Order/LiminfLimsup.lean | Filter.limsup_nat_add | [] | [
814,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.casesOn' | [
{
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118,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_left_injOn | [
{
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"state_before": "x✝ y z x : ℝ\nhx : x ≠ 0\n⊢ InjOn (fun y => y ^ x) {y | 0 ≤ y}",
"tactic": "rintro y hy z hz (hyz : y ^ x = z ^ x)"
},
{
"state_after": "no goal... | [
588,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_eq_biUnion | [
{
"state_after": "no goals",
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124,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_def' | [] | [
417,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.le_of_forall_pos_le_add | [
{
"state_after": "α : Type ?u.129734\nβ : Type ?u.129737\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : b < a\n⊢ ∃ ε, 0 < ε ∧ b < ⊤ ∧ b + ↑ε < a",
"state_before": "α : Type ?u.129734\nβ : Type ?u.129737\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : ∀ (ε : ℝ≥0), 0 < ε → b < ⊤ → a ≤ b + ↑ε\n⊢ a ≤ b",
"tactic": "contrapose! h"
}... | [
842,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_biInter | [] | [
1607,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1605,
1
] |
Mathlib/Data/List/Basic.lean | List.insert_neg | [] | [
255,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_subset_Ioo_union_Ici | [] | [
1258,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.modByMonic_eq_mod | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np✝ q p : R[X]\nhq : Monic q\n⊢ p %ₘ q = p %ₘ (q * ↑C (leadingCoeff q)⁻¹)",
"tactic": "simp only [Monic.def.1 hq, inv_one, mul_one, C_1]"
}
] | [
202,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.toOuterMeasure_bind_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.66368\np : Pmf α\nf : α → Pmf β\ng : β → Pmf γ\ns : Set β\n⊢ ↑(toOuterMeasure (bind p f)) s = ∑' (b : β), if b ∈ s then ∑' (a : α), ↑p a * ↑(f a) b else 0",
"tactic": "simp [toOuterMeasure_apply, Set.indicator_apply]"
... | [
184,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_Ioo_ae_eq_pi_Icc | [] | [
511,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | Real.Angle.expMapCircle_neg | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ expMapCircle (-↑x✝) = (expMapCircle ↑x✝)⁻¹",
"state_before": "θ : Angle\n⊢ expMapCircle (-θ) = (expMapCircle θ)⁻¹",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ expMapCircle (-↑x✝)... | [
138,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.ZeroAtFilter.smul | [
{
"state_after": "no goals",
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55,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/List/MinMax.lean | List.argmin_nil | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.exponent_eq_zero_of_infinite | [] | [
594,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_sdiff | [] | [
338,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
9
] |
Mathlib/LinearAlgebra/Finsupp.lean | mem_span_set | [
{
"state_after": "R : Type u_2\nM : Type u_1\nN : Type ?u.764012\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nm : M\ns : Set M\n⊢ m ∈ span R (_root_.id '' s) ↔ ∃ c, ↑c.support ⊆ s ∧ (Finsupp.sum c fun mi r => r • mi) = m",
"state_before":... | [
1192,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.AlgHom.fieldRange_eq_top | [] | [
286,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.smul_ae_eq_of_ae_eq | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.524934\nβ : Type ?u.524937\nγ : Type ?u.524940\nδ : Type ?u.524943\nι : Type ?u.524946\nR : Type ?u.524949\nR' : Type ?u.524952\nm0 : MeasurableSpace α✝\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α✝\ns✝... | [
2591,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2587,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.ext_iff_val | [
{
"state_after": "case h\nι : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁵ : AddCommMonoid ι\ninst✝⁴ : DecidableEq ι\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx : Submonoid A\ng : HomogeneousLocalization 𝒜 x\na✝ : NumDenSameDeg 𝒜 x\nh : ... | [
541,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.25404\nδ : Type ?u.25407\na : α\ns t : Multiset α\nf✝ g✝ f g : α → Multiset β\nm : Multiset α\n⊢ (∀ (a : α), a ∈ m → f a = g a) → bind m f = bind m g",
"tactic": "simp (config := { contextual := true }) [bind]"
}
] | [
152,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.strictMono_l | [] | [
840,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | injective_pow_p | [] | [
126,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
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