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/MeasureTheory/Function/SpecialFunctions/Basic.lean | Real.measurable_sinh | [] | [
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29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffWithinAt.rpow | [] | [
503,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.coe_fill | [] | [
532,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
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Mathlib/Order/Compare.lean | Ordering.compares_swap | [
{
"state_after": "case lt\nα : Type u_1\nβ : Type ?u.6152\ninst✝ : LT α\na b : α\n⊢ Compares (swap lt) a b ↔ Compares lt b a\n\ncase eq\nα : Type u_1\nβ : Type ?u.6152\ninst✝ : LT α\na b : α\n⊢ Compares (swap eq) a b ↔ Compares eq b a\n\ncase gt\nα : Type u_1\nβ : Type ?u.6152\ninst✝ : LT α\na b : α\n⊢ Compares... | [
74,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Topology/Order/Basic.lean | isOpen_lt' | [] | [
904,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_one_div | [
{
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1204,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
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Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean | CategoryTheory.Idempotents.app_p_comm | [] | [
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25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Commute.lean | Commute.units_of_val | [] | [
253,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.gcd_eq_one_iff_coprime | [
{
"state_after": "case mp\na b : ℤ\n⊢ gcd a b = 1 → IsCoprime a b\n\ncase mpr\na b : ℤ\n⊢ IsCoprime a b → gcd a b = 1",
"state_before": "a b : ℤ\n⊢ gcd a b = 1 ↔ IsCoprime a b",
"tactic": "constructor"
},
{
"state_after": "case mp\na b : ℤ\nhg : gcd a b = 1\n⊢ IsCoprime a b",
"state_before":... | [
202,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Tactic/Linarith/Lemmas.lean | le_zero_of_zero_ge | [] | [
79,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.norm_set_integral_le_of_norm_le_const | [] | [
549,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
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Mathlib/Algebra/Hom/Group.lean | Monoid.coe_one | [] | [
1333,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjoint_id | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.826219\nG : Type ?u.826222\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : Comp... | [
185,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_le_tsub_iff_right | [
{
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"ta... | [
47,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.factorThruImage_preComp | [
{
"state_after": "no goals",
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"tactic": "simp [image.preComp]"
}
] | [
558,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean | SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty' | [] | [
65,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
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Mathlib/Control/Traversable/Instances.lean | List.traverse_append | [
{
"state_after": "no goals",
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"tactic": ... | [
133,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | leftInverse_expMapCircle_arg | [] | [
77,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | Units.inv_pos | [] | [
950,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.biproductComparison_π | [] | [
241,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.unop_op | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/RingTheory/Finiteness.lean | RingHom.Finite.of_comp_finite | [
{
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"state_before": "A : Type u_1\nB : Type u_2\nC : Type u_3\ninst✝² : CommRing A\ni... | [
707,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux | [
{
"state_after": "case refine'_1\nm : Type ?u.1709668\nn✝ : Type ?u.1709671\ninst✝⁴ : DecidableEq n✝\ninst✝³ : Fintype n✝\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nn : ℕ\nk : Fin (n + 1)\nc : Fin n → R\nhc : ∀ (i : Fin n), 0 < Fin.succ i → c i = 0\nM N : Matrix (Fin (Nat.succ ... | [
551,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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] |
Std/Data/List/Lemmas.lean | List.sublist_or_mem_of_sublist | [
{
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"tactic": "induction l₁ generalizing l with\n| nil => match h with\n | .cons _ h => exact .inl h\n | .cons₂ _ h => exact .inr (.head ..)\n| cons b l₁ IH ... | [
381,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
373,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_add | [] | [
1752,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1751,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_empty_type_iff | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.74821\nR : Type u_2\nK : Type ?u.74827\nA : Type u_3\nA' : Type ?u.74833\nA'' : Type ?u.74836\nV : Type u\nV' : Type ?u.74841\nx : ι → A\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing A'\ninst✝⁴ : CommRing A''\ninst✝³ : Algebra R A\ninst✝² : Algebra R A... | [
103,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAt.continuousAt | [] | [
724,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
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Mathlib/Data/List/Cycle.lean | List.next_prev | [
{
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"state_before": "α : Type u_1\ninst✝ : DecidableEq α\... | [
398,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_add_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.106815\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group G\na : G\nn : ℕ\n⊢ a ^ (↑n + 1) = a ^ ↑n * a",
"tactic": "simp only [← Int.ofNat_succ, zpow_ofNat, pow_succ']"
},
{
"s... | [
203,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | GroupWithZero.mul_left_injective | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.18039\nM₀ : Type ?u.18042\nG₀ : Type u_1\nM₀' : Type ?u.18048\nG₀' : Type ?u.18051\nF : Type ?u.18054\nF' : Type ?u.18057\ninst✝ : GroupWithZero G₀\na b c g h✝ x : G₀\nh : x ≠ 0\ny y' : G₀\nw : (fun y => x * y) y = (fun y => x * y) y'\n⊢ y = y'",
... | [
270,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.subset_smul_finset_iff | [
{
"state_after": "F : Type ?u.841640\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.841649\ninst✝² : DecidableEq β\ninst✝¹ : Group α\ninst✝ : MulAction α β\ns t : Finset β\na : α\nb : β\n⊢ ↑s ⊆ ↑(a • t) ↔ ↑(a⁻¹ • s) ⊆ ↑t",
"state_before": "F : Type ?u.841640\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.841649\ninst✝²... | [
1986,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1983,
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] |
Mathlib/Data/Set/Lattice.lean | sInf_sUnion | [] | [
2251,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2250,
1
] |
Mathlib/Data/ZMod/Quotient.lean | order_eq_card_zpowers' | [
{
"state_after": "n : ℕ\nA : Type ?u.322503\nR : Type ?u.322506\ninst✝² : AddGroup A\ninst✝¹ : Ring R\nα : Type u_1\ninst✝ : Group α\na : α\nthis :\n Nat.card ↑(MulAction.orbit { x // x ∈ zpowers a } 1) =\n Nat.card (ZMod (Function.minimalPeriod ((fun x x_1 => x • x_1) a) 1))\n⊢ orderOf a = Nat.card { x // ... | [
197,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.modEq_iff_add_fac | [
{
"state_after": "m n✝ a✝ b✝ c d a b n : ℤ\n⊢ n ∣ b - a ↔ ∃ t, b = a + n * t",
"state_before": "m n✝ a✝ b✝ c d a b n : ℤ\n⊢ a ≡ b [ZMOD n] ↔ ∃ t, b = a + n * t",
"tactic": "rw [modEq_iff_dvd]"
},
{
"state_after": "no goals",
"state_before": "m n✝ a✝ b✝ c d a b n : ℤ\n⊢ n ∣ b - a ↔ ∃ t, b = a... | [
104,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/ULift.lean | PLift.up_surjective | [] | [
49,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.le_mul_iff_one_le_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.88130\ninst✝² : LE α\ninst✝¹ : CommMonoid α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\nha : MulLECancellable a\n⊢ a ≤ b * a ↔ 1 ≤ b",
"tactic": "rw [mul_comm, ha.le_mul_iff_one_le_right]"
}
] | [
1665,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1663,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.Lifts.exists_max_two | [
{
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1013,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_compl_iff | [] | [
803,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.noSibling_deleteMin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nle : α → α → Bool\na : α\ns' s : Heap α\neq : deleteMin le s = some (a, s')\n⊢ NoSibling s'",
"tactic": "cases s with cases eq | node a c => exact noSibling_combine _ _"
},
{
"state_after": "no goals",
"state_before": "case node.ref... | [
106,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
104,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.closure_setOf_lt_im | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ closure {z | a < z.im} = {z | a ≤ z.im}",
"tactic": "simpa only [closure_Ioi] using closure_preimage_im (Ioi a)"
}
] | [
133,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.ne_bot_of_dvd_card | [
{
"state_after": "G : Type u\nα : Type v\nβ : Type w\ninst✝¹ : Group G\ninst✝ : Fintype G\np : ℕ\nhp : Fact (Nat.Prime p)\nP : Sylow p G\nhdvd : p ∣ Fintype.card G\nh : ↑P = ⊥\n⊢ p ∣ 1",
"state_before": "G : Type u\nα : Type v\nβ : Type w\ninst✝¹ : Group G\ninst✝ : Fintype G\np : ℕ\nhp : Fact (Nat.Prime p)\... | [
686,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
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Std/Logic.lean | exists₃_congr | [] | [
395,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
393,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.bit1 | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.36077\ninst✝¹ : Semiring R\ninst✝ : StarRing R\nx : R\nhx : IsSelfAdjoint x\n⊢ IsSelfAdjoint (_root_.bit1 x)",
"tactic": "simp only [isSelfAdjoint_iff, star_bit1, hx.star_eq]"
}
] | [
198,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2621009\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑im (inner x y) =\n (‖x‖ * ‖x‖ - 2 * -↑im (inner x y) + ‖I • ... | [
1160,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.sec_snd_ne_zero | [] | [
1188,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_inter | [
{
"state_after": "x y : ZFSet\n⊢ toSet (ZFSet.sep (fun z => z ∈ y) x) = toSet x ∩ toSet y",
"state_before": "x y : ZFSet\n⊢ toSet (x ∩ y) = toSet x ∩ toSet y",
"tactic": "change (ZFSet.sep (fun z => z ∈ y) x).toSet = _"
},
{
"state_after": "case h\nx y x✝ : ZFSet\n⊢ x✝ ∈ toSet (ZFSet.sep (fun z ... | [
1156,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.zero_mul_subset | [
{
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"tactic": "simp [subset_def, mem_mul]"
}
] | [
1141,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
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Mathlib/Order/Grade.lean | isMin_grade_iff | [] | [
140,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.self_mem_periodicOrbit | [] | [
535,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | card_orderOf_eq_totient_aux₁ | [
{
"state_after": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhn : ∀ (n : ℕ), 0 < n → card (filter (fun a => a ^ n = 1) univ) ≤ n\nd : ℕ\nhd : d ∣ Fintype.card α\nhpos : 0 < card (filter (fun a => orderOf a = d) univ)\n⊢ card (filter (fun a => orderOf a = d) univ) = φ d",
... | [
363,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
9
] |
Mathlib/FieldTheory/Subfield.lean | RingHom.eq_of_eqOn_of_field_closure_eq_top | [] | [
891,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.prod_sup | [] | [
1582,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1581,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.restrictScalars_top | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_univ_iff_measure_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.646530\nγ : Type ?u.646533\nδ : Type ?u.646536\nι : Type ?u.646539\nR : Type ?u.646542\nR' : Type ?u.646545\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\ninst✝ : IsFiniteMeasure μ\nh... | [
3168,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3161,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_empty | [] | [
366,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Order/Heyting/Basic.lean | codisjoint_hnot_hnot_right_iff | [
{
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"tactic": "simp_rw [← hnot_le_iff_codisjoint_left, hnot_hnot_hnot]"
}
] | [
1102,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_isSpecial | [
{
"state_after": "u : XgcdType\n⊢ u.zp + u.wp + u.zp * u.wp = u.y * u.x ↔ u.wp + u.zp + u.wp * u.zp = u.x * u.y",
"state_before": "u : XgcdType\n⊢ IsSpecial (flip u) ↔ IsSpecial u",
"tactic": "dsimp [IsSpecial, flip]"
},
{
"state_after": "no goals",
"state_before": "u : XgcdType\n⊢ u.zp + u.... | [
227,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_congr_norm_ae | [] | [
372,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ici | [
{
"state_after": "no goals",
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"tactic": "simp [Pi.le_def]"
}
] | [
37,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_le_iff_le_add' | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\n⊢ a - b ≤ c ↔ a ≤ b + c",
"tactic": "rw [Nat.sub_le_iff_le_add, Nat.add_comm]"
}
] | [
471,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
470,
11
] |
Mathlib/CategoryTheory/Adjunction/Reflective.lean | CategoryTheory.unitCompPartialBijective_symm_apply | [
{
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149,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.symm_dual_id | [] | [
778,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.subtype_comp_rangeRestrict | [] | [
2639,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2638,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.inv_right_iff₀ | [] | [
77,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/BigOperators/Pi.lean | Pi.multiset_prod_apply | [] | [
38,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_curry | [
{
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1268,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Analysis/Convex/Cone/Dual.lean | innerDualCone_le_innerDualCone | [] | [
82,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.comp_right | [
{
"state_after": "no goals",
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"tactic": "simp only [comp_apply, h.eq, h'.... | [
53,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | MulAction.bijective | [] | [
148,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
11
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.preimageSingletonHomeomorph_apply | [] | [
505,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Algebra/Field/Basic.lean | div_add_div_same | [] | [
37,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.epi_iff_cancel_zero | [] | [
257,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | nhdsWithin_pos_comap_mul_left | [
{
"state_after": "𝕜 : Type u_1\nα : Type ?u.51715\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nx : 𝕜\nhx : 0 < x\n⊢ comap (fun x_1 => x * x_1) (𝓝 0) ⊓ 𝓟 (Ioi 0) = 𝓝 0 ⊓ 𝓟 (Ioi 0)",
"state_before": "𝕜 : Type u_1\nα : Type ?u.51715... | [
232,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_ne' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.415768\nβ : Type u_1\nγ : Type ?u.415774\np q : α → Prop\ninst✝³ : DecidablePred p\ninst✝² : DecidablePred q\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns : Finset β\nb x✝¹ : β\nx✝ : x✝¹ ∈ s\n⊢ x✝¹ ≠ b ↔ b ≠ x✝¹",
"tactic": "simp_rw [@ne_comm... | [
2946,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2945,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.rangeRestrict_surjective | [] | [
2645,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2644,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.toFun_eq_coe | [] | [
624,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Std/Data/String/Lemmas.lean | String.firstDiffPos_loop_eq | [
{
"state_after": "l₁ l₂ r₁ r₂ : List Char\nstop p : Nat\nhl₁ : p = utf8Len l₁\nhl₂ : p = utf8Len l₂\nhstop : stop = min (utf8Len l₁ + utf8Len r₁) (utf8Len l₂ + utf8Len r₂)\n⊢ firstDiffPos.loop { data := l₁ ++ r₁ } { data := l₂ ++ r₂ } { byteIdx := stop } { byteIdx := p } =\n {\n byteIdx :=\n p +\... | [
380,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
355,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_one | [] | [
568,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_ciSup | [] | [
786,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | IsOpen.measure_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.1584\ninst✝³ : TopologicalSpace X\nm : MeasurableSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\nμ ν : Measure X\ninst✝ : IsOpenPosMeasure μ\ns U : Set X\nx : X\nhU : IsOpen U\n⊢ ↑↑μ U = 0 ↔ U = ∅",
"tactic": "simpa only [... | [
58,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_nonneg | [] | [
135,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
8
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.image_source_inter_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.32210\nδ : Type ?u.32213\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ns : Set α\n⊢ ↑e '' (e.source ∩ s) = e.target ∩ ↑(LocalEquiv.symm e) ⁻¹' (e.source ∩ s)",
"tactic": "rw [inter_comm, e.leftInvOn.image_inter, image_sour... | [
491,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.supp_map | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nh : IsUniform\nα β : Type u\ng : α → β\nx : F α\n⊢ supp (g <$> abs (repr x)) = g '' supp (abs (repr x))",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nh : IsUniform\nα β : Type u\ng : α → β\nx : F α\n⊢ supp (g <$> x)... | [
702,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateColumn_reindex | [] | [
2918,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2915,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_projKerOfRightInverse_apply | [] | [
1457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/Order/Bounds/Basic.lean | bddBelow_Ico | [] | [
668,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_univ_iff | [] | [
2385,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2384,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_self_div_right | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.640245\n𝕜 : Type ?u.640248\nα : Type ?u.640251\nι : Type ?u.640254\nκ : Type ?u.640257\nE : Type u_1\nF : Type ?u.640263\nG : Type ?u.640266\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na✝ a₁ a₂ b✝ b₁ b₂ : E\nr r₁ r₂ : ℝ\na b : E... | [
1416,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_self_add_left | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ gcd (m + n) m = gcd n m",
"tactic": "rw [add_comm, gcd_add_self_left]"
}
] | [
86,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.a_mul_a | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.update_apply | [
{
"state_after": "case pos\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid M₂\ninst✝⁵ : Module R M₂\ninst✝⁴ : AddCommMonoid M₃\ninst✝³ : Module R M₃\nφ : ι → Type i\ninst✝²... | [
251,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.range_eq_iSup | [
{
"state_after": "ι : Type u_3\nM : ι → Type ?u.342946\ninst✝³ : (i : ι) → Monoid (M i)\nN✝ : Type ?u.342957\ninst✝² : Monoid N✝\nG : ι → Type u_2\ninst✝¹ : (i : ι) → Group (G i)\nN : Type u_1\ninst✝ : Group N\nf : (i : ι) → G i →* N\n⊢ (⨆ (i : ι), MonoidHom.range (f i)) ≤ MonoidHom.range (↑lift f)",
"state... | [
258,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasStrictFDerivAt_const | [
{
"state_after": "no goals",
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1060,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint_comm | [] | [
232,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.prod_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : CommMonoid β\ninst✝ : ContinuousMul β\nι : Type u_2\ns : Finset ι\nf : ι → C(α, β)\na : α\n⊢ ↑(∏ i in s, f i) a = ∏ i in s, ↑(f i) a",
"tactic": "simp"
}
] | [
388,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mul_mem | [] | [
576,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
11
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_nhdsWithin' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_2\nM : Type u_1\nH : Type u_4\nE' : Type ?u.212452\nM' : Type ?u.212455\nH' : Type ?u.212458\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : Topologi... | [
1173,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.inter_mem | [] | [
158,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/List/Basic.lean | List.sublist_cons_of_sublist | [] | [
1049,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_lt_31416 | [
{
"state_after": "no goals",
"state_before": "⊢ π < 3.1416",
"tactic": "pi_upper_bound\n [4756 / 3363, 101211 / 54775, 505534 / 257719, 83289 / 41846, 411278 / 205887,\n 438142 / 219137, 451504 / 225769, 265603 / 132804, 849938 / 424971]"
}
] | [
189,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
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