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/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.ι_app_right | [] | [
791,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_mono_right | [] | [
198,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.const_mul_left | [] | [
1493,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1492,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.prod.unique | [] | [
920,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
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Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.deriv_log' | [] | [
78,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_inter_self_left | [] | [
2096,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2095,
1
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Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_range_cast_nat_sub | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nb : β\nf g : α → β\nR : Type u_1\ninst✝ : CommRing R\nn k : ℕ\n⊢ ∏ i in range k, (↑n - ↑i) = ∏ x in range k, ↑(n - x)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nb : β\nf g : α → β\nR : Typ... | [
235,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Std/Logic.lean | or_and_right | [
{
"state_after": "no goals",
"state_before": "a b c : Prop\n⊢ (a ∨ b) ∧ c ↔ a ∧ c ∨ b ∧ c",
"tactic": "simp [and_comm, and_or_left]"
}
] | [
326,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
325,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_injOn | [] | [
374,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | bernoulli'_three | [
{
"state_after": "A : Type ?u.186788\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\n⊢ 1 -\n (0 + ↑(Nat.choose 3 0) / (↑3 - ↑0 + 1) * bernoulli' 0 + ↑(Nat.choose 3 1) / (↑3 - ↑1 + 1) * bernoulli' 1 +\n ↑(Nat.choose 3 2) / (↑3 - ↑2 + 1) * bernoulli' 2) =\n 0",
"state_before": "A : Type ?u.186788\ni... | [
126,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/AlgebraicTopology/ExtraDegeneracy.lean | CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_succ | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\nf : Arrow C\ninst✝ : ∀ (n : ℕ), HasWidePullback f.right (fun x => f.left) fun x => f.hom\nS : SplitEpi f.hom\nn : ℕ\ni : Fin (n + 1)\n⊢ WidePullback.lift (WidePullback.base fun x => f.hom)\n (fun i =>\n if x : i = 0 then (WidePullback.base fun... | [
296,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_combineAux | [
{
"state_after": "no goals",
"state_before": "ctx : Context\nfuel : Nat\np₁ p₂ : Poly\n⊢ denote ctx (combineAux fuel p₁ p₂) = denote ctx p₁ + denote ctx p₂",
"tactic": "induction fuel generalizing p₁ p₂ with simp [combineAux]\n| succ fuel ih =>\n split <;> simp\n rename_i k₁ v₁ p₁ k₂ v₂ p₂\n by_cases... | [
518,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
510,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.fst_comp_inr | [] | [
530,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Data/Part.lean | Part.union_mem_union | [
{
"state_after": "α : Type u_1\nβ : Type ?u.88814\nγ : Type ?u.88817\ninst✝ : Union α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ∃ a_1, a_1 ∈ a ∧ ∃ a, a ∈ b ∧ a_1 ∪ a = ma ∪ mb",
"state_before": "α : Type u_1\nβ : Type ?u.88814\nγ : Type ?u.88817\ninst✝ : Union α\na b : Part α\nma mb : α\nha : ma... | [
844,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_of_le_one | [
{
"state_after": "case inl\no : Ordinal\nho : o ≠ 0\nhb : 0 ≤ 1\n⊢ CNF 0 o = [(0, o)]\n\ncase inr\no : Ordinal\nho : o ≠ 0\nhb : 1 ≤ 1\n⊢ CNF 1 o = [(0, o)]",
"state_before": "b o : Ordinal\nhb : b ≤ 1\nho : o ≠ 0\n⊢ CNF b o = [(0, o)]",
"tactic": "rcases le_one_iff.1 hb with (rfl | rfl)"
},
{
"... | [
107,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/Basic.lean | le_of_forall_le' | [] | [
533,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | tsum_coe_mul_geometric_of_norm_lt_1 | [] | [
370,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finRotate_last | [] | [
413,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_pair | [] | [
661,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.eq_of_lt_minimalPeriod_of_iterate_eq | [] | [
360,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_singleton | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.331505\nγ : Type ?u.331508\nδ : Type ?u.331511\nι : Type ?u.331514\nR : Type ?u.331517\nR' : Type ?u.331520\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✝ : Measurable... | [
2015,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2009,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_apply | [] | [
545,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Init/Function.lean | Function.comp.left_id | [] | [
56,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
9
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.inverseAssociator_obj_inl | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left | [
{
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476,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
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] |
Mathlib/Analysis/Calculus/LocalExtr.lean | Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ | [
{
"state_after": "case inl\np : ℝ[X]\nhp' : ↑derivative p = 0\n⊢ Finset.card (Multiset.toFinset (roots p)) ≤\n Finset.card (Multiset.toFinset (roots (↑derivative p)) \\ Multiset.toFinset (roots p)) + 1\n\ncase inr\np : ℝ[X]\nhp' : ↑derivative p ≠ 0\n⊢ Finset.card (Multiset.toFinset (roots p)) ≤\n Finset.c... | [
367,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Set/Image.lean | Prod.range_fst | [] | [
867,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.continuous_of_dominated_interval | [] | [
1116,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.eventually_filterAt_iff | [] | [
249,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.root_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\n⊢ IsRoot (p * q) a ↔ IsRoot p a ∨ IsRoot q a",
"tactic": "simp_rw [IsRoot, eval_mul, mul_eq_zero]"
}
] | [
339,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Logic/Small/Basic.lean | small_congr | [] | [
85,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/Computability/Halting.lean | Nat.Partrec'.map | [
{
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"state_before": "n : ℕ\nf : Vector ℕ n →. ℕ\ng : Vector ℕ (n + 1) → ℕ\nhf : Partrec' f\nhg : Partrec' ↑g\n⊢ Partrec' fun v => Pa... | [
336,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_pushoutAssoc_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nW X Y Z X₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝³ : HasPushout g₁ g₂\ninst✝² : HasPushout g₃ g₄\ninst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄\ninst✝ : HasPus... | [
2651,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2648,
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] |
Mathlib/Topology/ShrinkingLemma.lean | ShrinkingLemma.PartialRefinement.find_apply_of_mem | [] | [
141,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.exists_right_inv | [
{
"state_after": "case intro.mk\nα : Type u\nM : Type u_1\nN : Type ?u.56747\ninst✝ : Monoid M\na b : M\nhab : a * b = 1\ninv_val✝ : b * a = 1\n⊢ ∃ b_1, ↑{ val := a, inv := b, val_inv := hab, inv_val := inv_val✝ } * b_1 = 1",
"state_before": "α : Type u\nM : Type u_1\nN : Type ?u.56747\ninst✝ : Monoid M\na ... | [
637,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_le | [
{
"state_after": "α✝ : Type ?u.110770\nβ✝ : Type ?u.110773\nγ : Type ?u.110776\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\na b : Ordinal\nα : Type v\nr : α → α → Prop\nx✝¹ : IsWellOrder α r\nβ : Type v\ns : β → β → Prop\nx✝ : IsWellOrder β s\n⊢ lift (type r) ≤ lift (type s) ↔ type r ≤ type s",
... | [
768,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Init/Logic.lean | or_true_iff | [] | [
181,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_le_edist_add_infEdist | [
{
"state_after": "ι : Sort ?u.7435\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t : Set α\nΦ : α → β\n⊢ infEdist x s ≤ infEdist y s + edist x y",
"state_before": "ι : Sort ?u.7435\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetri... | [
116,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/Computability/Primrec.lean | Primrec.const | [
{
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"tactic... | [
255,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_eq_inv_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.48927\nβ : Type ?u.48930\nG : Type u_1\ninst✝ : Group G\na b c d : G\n⊢ a / b = b⁻¹ ↔ a = 1",
"tactic": "rw [div_eq_mul_inv, mul_left_eq_self]"
}
] | [
611,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_X | [] | [
704,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.div_congr | [
{
"state_after": "u : Lean.Level\nR✝ : Type ?u.398864\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : DivisionRing R\na' b' : R\n⊢ a' / b' = a' / b'",
"state_before": "u : Lean.Level\nR✝ : Type ?u.398864\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemir... | [
983,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_eq_top_iff_of_nonempty | [
{
"state_after": "case mp\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns : AffineSubspace k P\nh : Set.Nonempty ↑s\n⊢ direction s = ⊤ → s = ⊤\n\ncase mpr\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹... | [
882,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | derivWithin_ccosh | [] | [
253,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_inj | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c✝ : α\nn : ℤ\nc : α\n⊢ toIcoMod hp c a = toIcoMod hp c b ↔ a ≡ b [PMOD p]",
"tactic": "simp_rw [toIcoMod_eq_toIcoMod, modEq_iff_eq_add_zsmul, sub_eq_iff_eq_add']"
... | [
682,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_iUnion_eq_right | [] | [
757,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.add_factorial_le_factorial_add | [
{
"state_after": "case refl\nm n i : ℕ\n⊢ i + 1! ≤ (i + 1)!\n\ncase step\nm n i h : ℕ\na✝ : Nat.le 1 h\n⊢ i + (succ h)! ≤ (i + succ h)!",
"state_before": "m n✝ i n : ℕ\nn1 : 1 ≤ n\n⊢ i + n ! ≤ (i + n)!",
"tactic": "cases' n1 with h"
},
{
"state_after": "no goals",
"state_before": "case step\... | [
206,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.lift_add | [
{
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126,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.image_embedding_iff | [] | [
165,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le_of_add_le_add_left | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\nh : a + b ≤ a + c\n⊢ b ≤ c",
"tactic": "match le.dest h with\n| ⟨d, hd⟩ =>\n apply @le.intro _ _ d\n rw [Nat.add_assoc] at hd\n apply Nat.add_left_cancel hd"
},
{
"state_after": "a b c : Nat\nh : a + b ≤ a + c\nd : Nat\nhd : a + b + d... | [
415,
33
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
410,
11
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.subsemigroupMap_surjective | [
{
"state_after": "case mk.intro.intro\nM : Type u_1\nN : Type u_2\nP : Type ?u.76825\nσ : Type ?u.76828\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nS : Subsemigroup M\nf : M →ₙ* N\nM' : Subsemigroup M\nx : M\nhx : x ∈ ↑M'\n⊢ ∃ a, ↑(subsemigroupMap f M') a = { val := ↑f x, property := (_ : ∃ a, a ∈ ↑M' ∧ ↑f ... | [
899,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.toDual_max' | [
{
"state_after": "F : Type ?u.356766\nα : Type u_1\nβ : Type ?u.356772\nγ : Type ?u.356775\nι : Type ?u.356778\nκ : Type ?u.356781\ninst✝ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ns : Finset α\nhs : Finset.Nonempty s\n⊢ ↑(↑toDual (max' s hs)) = ↑(min' (image (↑toDual) s) (_ : Finset.Nonempt... | [
1460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1455,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.adjoin_range_X | [
{
"state_after": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nS : Subalgebra R (MvPolynomial σ R) := Algebra.adjoin R (range X)\n⊢ S = ⊤",
"state_before": "R : Type u\nS... | [
510,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | geometric_hahn_banach_closed_point | [] | [
195,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_one | [] | [
180,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_sub_edgeDensity_le_one_sub_mul | [
{
"state_after": "𝕜 : Type ?u.34819\nι : Type ?u.34822\nκ : Type ?u.34825\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns s₁ s₂ : Finset α\nt t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\nhs : s₂ ⊆ s₁\nht : t₂ ⊆ t₁\nhs₂ : Finset.Nonempty s₂\nht₂... | [
204,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Order/Interval.lean | Interval.one_mem_one | [] | [
141,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_sign | [] | [
202,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
201,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.neg_coe_abs_toReal_of_sign_nonpos | [
{
"state_after": "θ : Angle\nh : sign θ = -1 ∨ sign θ = 0\n⊢ -↑(abs (toReal θ)) = θ",
"state_before": "θ : Angle\nh : sign θ ≤ 0\n⊢ -↑(abs (toReal θ)) = θ",
"tactic": "rw [SignType.nonpos_iff] at h"
},
{
"state_after": "case inl\nθ : Angle\nh : sign θ = -1\n⊢ -↑(abs (toReal θ)) = θ\n\ncase inr\n... | [
941,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/RingTheory/WittVector/Teichmuller.lean | WittVector.ghostComponent_teichmullerFun | [
{
"state_after": "p : ℕ\nR : Type u_1\nS : Type ?u.10109\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nr : R\nn : ℕ\n⊢ coeff (teichmullerFun p r) 0 ^ p ^ n = r ^ p ^ n\n\ncase h₀\np : ℕ\nR : Type u_1\nS : Type ?u.10109\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nr : R... | [
76,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
9
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.addValuation.apply | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\nhx : x ≠ 0\n⊢ ↑addValuation x = ↑(valuation x)",
"tactic": "simp only [Padic.addValuation, AddValuation.of_apply, addValuationDef, if_neg hx]"
}
] | [
1156,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasFDerivAt_iff_hasDerivAt | [] | [
195,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.le_floor | [] | [
653,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_mul | [] | [
92,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | WfDvdMonoid.wellFounded_associates | [] | [
79,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_pos | [] | [
77,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Tactic/NormNum/NatFib.lean | Mathlib.Meta.NormNum.isFibAux_two_mul | [
{
"state_after": "no goals",
"state_before": "n a b n' a' b' : ℕ\nH : IsFibAux n a b\nhn : 2 * n = n'\nh1 : a * (2 * b - a) = a'\nh2 : a * a + b * b = b'\n⊢ fib n' = a'",
"tactic": "rw [← hn, fib_two_mul, H.1, H.2, ← h1]"
},
{
"state_after": "no goals",
"state_before": "n a b n' a' b' : ℕ\nH... | [
34,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.fst_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.5371212\nβ : Type u_2\nβ' : Type ?u.5371218\nγ : Type ?u.5371221\nE : Type ?u.5371224\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' :... | [
823,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.mk_add_moveRight_inl | [] | [
1518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1515,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforwardEq_hom_app | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nf g : X ⟶ Y\nh : f = g\nℱ : Presheaf C X\nU : (Opens ↑Y)ᵒᵖ\n⊢ ((Opens.map f).obj U.unop).op ⟶ ((Opens.map g).obj U.unop).op",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nf g : X ⟶ Y\nh : f = g\nℱ : Presheaf C X\nU : (Opens ↑Y... | [
175,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.exists_measurable_superset_forall_eq_trim | [
{
"state_after": "α : Type u_2\ninst✝¹ : MeasurableSpace α\nm : OuterMeasure α\nι : Sort u_1\ninst✝ : Countable ι\nμ : ι → OuterMeasure α\ns : Set α\nt : ι → Set α\nhst : ∀ (i : ι), s ⊆ t i\nht : ∀ (i : ι), MeasurableSet (t i)\nhμt : ∀ (i : ι), ↑(μ i) (t i) = ↑(trim (μ i)) s\n⊢ ∃ t, s ⊆ t ∧ MeasurableSet t ∧ ∀ ... | [
1732,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulActionHom.ext_iff | [] | [
130,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_div | [] | [
762,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.image_relEmbedding_iff | [] | [
146,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | IsExposed.isClosed | [
{
"state_after": "case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : TopologicalSpace 𝕜\ninst✝⁴ : OrderedRing 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : TopologicalSpace E\ninst✝¹ : Module 𝕜 E\nl : E →L[𝕜] 𝕜\nA✝ B C : Set E\nX : Finset E\nx : E\ninst✝ : OrderClosedTopology 𝕜\nA : Set E\nhA : IsClosed A\nhAB : IsE... | [
188,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
11
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotEquivQuotMap_symm_apply_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nI✝ : Ideal R\nf✝ f g : R[X]\nI : Ideal R\n⊢ ↑(AlgEquiv.symm (quotEquivQuotMap f I))\n (↑(Ideal.Quotient.mk (span {Polynomial.map (Ideal.Quotient.mk I) f})) (Polynomial.map (Ideal.Quotient.mk I) g)) =\n... | [
878,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.isHomogeneous_one | [] | [
151,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/Basic.lean | closure_nonempty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ Set.Nonempty (closure s) ↔ Set.Nonempty s",
"tactic": "simp only [nonempty_iff_ne_empty, Ne.def, closure_empty_iff]"
}
] | [
500,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.coe_top | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.single_div | [] | [
507,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.mem_diff_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁ l₂ : List α\nr : α → α → Prop\na b : α\ninst✝ : DecidableEq α\nhl₁ : Nodup l₁\n⊢ a ∈ List.diff l₁ l₂ ↔ a ∈ l₁ ∧ ¬a ∈ l₂",
"tactic": "rw [hl₁.diff_eq_filter, mem_filter, decide_eq_true_iff]"
}
] | [
400,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.add_apply | [] | [
689,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.algebraMap_eq_ofReal | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasStrictDerivAt.const_sub | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter �... | [
362,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.product | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.9045\nr : α → α → Prop\ns t✝ : Multiset α\na : α\nt : Multiset β\nl₁ : List α\nl₂ : List β\nd₁ : Nodup (Quotient.mk (isSetoid α) l₁)\nd₂ : Nodup (Quotient.mk (isSetoid β) l₂)\n⊢ Nodup (Quotient.mk (isSetoid α) l₁ ×ˢ Quotie... | [
191,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
11
] |
Mathlib/Order/Ideal.lean | Order.Ideal.lower | [] | [
129,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulActionHom.congr_fun | [] | [
134,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
11
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.countable_not_continuousAt | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝⁶ : LinearOrder α\ninst✝⁵ : ConditionallyCompleteLinearOrder β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : OrderTopology β\nf : α → β\nhf : Monotone f\nx y : α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : TopologicalSpace.SecondCountableTopology β... | [
291,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.map_boundedFormula | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\nN : Type u_4\nP : Type ?u.10715\nQ : Type ?u.10718\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\ninst✝ : Structure L Q\nf : M ↪ₑ[L] N\nα : Type u_5\nn : ℕ\nφ : BoundedFormula L α n\nv : α → M\nxs : Fin n → M... | [
104,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Order/Atoms.lean | sSup_atoms_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.19944\ninst✝¹ : CompleteLattice α\ninst✝ : IsAtomistic α\nx : α\n⊢ x ∈ {a | IsAtom a} ↔ x ∈ {a | IsAtom a ∧ a ≤ ⊤}",
"state_before": "α : Type u_1\nβ : Type ?u.19944\ninst✝¹ : CompleteLattice α\ninst✝ : IsAtomistic α\n⊢ sSup {a | IsAtom a} = ⊤",
"tactic": "ref... | [
396,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.run_seqRight | [
{
"state_after": "m : Type u_1 → Type u_2\nσ α β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : StateT σ m α\ny : StateT σ m β\ns : σ\n⊢ run\n (do\n let _ ← x\n y)\n s =\n do\n let p ← run x s\n run y p.snd",
"state_before": "m : Type u_1 → Type u_2\nσ α β : Type u... | [
282,
7
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
280,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ico_ae_eq_Icc' | [] | [
2992,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2991,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_div_of_lt_left | [] | [
404,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.ne_of_odd_add | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nh : Odd (m + n)\nhnot : m = n\n⊢ False",
"tactic": "simp [hnot] at h"
}
] | [
193,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_closure_toSubmonoid | [] | [
1305,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Data/Nat/WithBot.lean | Nat.WithBot.add_one_le_of_lt | [
{
"state_after": "case none\nm : WithBot ℕ\nh : none < m\n⊢ none + 1 ≤ m\n\ncase some\nm : WithBot ℕ\nval✝ : ℕ\nh : some val✝ < m\n⊢ some val✝ + 1 ≤ m",
"state_before": "n m : WithBot ℕ\nh : n < m\n⊢ n + 1 ≤ m",
"tactic": "cases n"
},
{
"state_after": "case some.none\nval✝ : ℕ\nh : some val✝ < n... | [
90,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_mul_eq_inter' | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t✝ : Set Ω\nhms : MeasurableSet s\nhcs : ↑↑μ s ≠ 0\nhcs' : ↑↑μ s ≠ ⊤\nt : Set Ω\n⊢ ↑↑(μ[|s]) t * ↑↑μ s = ↑↑μ (s ∩ t)",
"tactic": "rw [cond_apply μ hms t, mul_comm, ← mul_assoc, ENNReal.mul_i... | [
146,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | MulOpposite.dist_unop | [] | [
1657,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1657,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.mul_div_mod_by_monic_cancel_left | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q✝ p q : R[X]\nhmo : Monic q\n✝ : Nontrivial R\n⊢ q * p /ₘ q = p",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q✝ p q : R[X]\nhmo : Monic q\n⊢ ... | [
486,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.seq_def | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.258305\nι : Sort ?u.258308\nι' : Sort ?u.258311\nι₂ : Sort ?u.258314\nκ : ι → Sort ?u.258319\nκ₁ : ι → Sort ?u.258324\nκ₂ : ι → Sort ?u.258329\nκ' : ι' → Sort ?u.258334\ns : Set (α → β)\nt : Set α\n⊢ ∀ (x : β), x ∈ seq s t... | [
1951,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1950,
1
] |
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