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/Order/Lemmas.lean | Nat.dvd_iff_div_mul_eq | [] | [
168,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_zero_index | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.rotateR | [
{
"state_after": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : Sized l\nhr : Sized r\n⊢ Sized (Ordnode.rotateL (Ordnode.dual r) x (Ordnode.dual l))",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : Sized l\nhr : Sized r\n⊢ Sized (Ordnode.dual (Ordnode.rotateR l x r))",
... | [
419,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_mono_left' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.1201627\nF' : Type ?u.1201630\nG : Type ?u.1201633\n𝕜 : Type ?u.1201636\np : ℝ≥0∞\ninst✝¹⁵ : NormedAddCommGroup E\ninst✝¹⁴ : NormedSpace ℝ E\ninst✝¹³ : NormedAddCommGroup F\ninst✝¹² : NormedSpace ℝ F\ninst✝¹¹ : NormedAddC... | [
1178,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1166,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_dvd_mul_iff_right | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\nhc : 0 < c\nd : ℕ\n⊢ b * c = a * c * d ↔ b = a * d",
"tactic": "rw [mul_right_comm, mul_left_inj' hc.ne']"
}
] | [
738,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
11
] |
Mathlib/Order/Interval.lean | NonemptyInterval.snd_sup | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.mod_le | [
{
"state_after": "m k : ℕ+\n⊢ ↑(mod m k) ≤ ↑m ∧ ↑(mod m k) ≤ ↑k",
"state_before": "m k : ℕ+\n⊢ mod m k ≤ m ∧ mod m k ≤ k",
"tactic": "change (mod m k : ℕ) ≤ (m : ℕ) ∧ (mod m k : ℕ) ≤ (k : ℕ)"
},
{
"state_after": "m k : ℕ+\n⊢ (if ↑m % ↑k = 0 then ↑k else ↑m % ↑k) ≤ ↑m ∧ (if ↑m % ↑k = 0 then ↑k el... | [
394,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.eq_bot_of_subsingleton | [
{
"state_after": "R : Type u_1\nS : Type ?u.48789\nM : Type u_2\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : Module S M\ninst✝² : SMul S R\ninst✝¹ : IsScalarTower S R M\np✝ q p : Submodule R M\ninst✝ : Subsingleton { x // x ∈ p }\n⊢ p ≤ ⊥",
"state_before... | [
134,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_single | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\na b : Γ\nr✝ : R\nΓ' : Type u_2\ninst✝ : PartialOrder Γ'\nf : Γ ↪o Γ'\ng : Γ\nr : R\ng' : Γ'\n⊢ coeff (embDomain f (↑(single g) r)) g' = coeff (↑(single (↑f g)) r) g'",
"state_before": "Γ : Type u_1\nR : Typ... | [
330,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.zero_apply | [] | [
628,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.mul_toInvSubmonoid | [] | [
79,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.prod_top | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.297763\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.297772\ninst✝² : AddGroup A\nH K✝ : Subgroup G\nk : Set G\nN : Type u_2\ninst✝¹ : Group N\nP : Type ?u.297799\ninst✝ : Group P\nK : Subgroup G\nx : G × N\n⊢ x ∈ prod K ⊤ ↔ x ∈ co... | [
1741,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1740,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_one | [] | [
231,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.coprod_inl_inr | [
{
"state_after": "no goals",
"state_before": "R : 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\nM₅ : Type ?u.73472\nM₆ : Type ?u.73475\nS : Type ?u.73478\ninst✝¹³ : Semiring R\ninst✝¹² : Semiring S\ninst✝¹¹ : AddCommMonoid M\nins... | [
236,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_const | [] | [
328,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.hasSum_orthogonalProjection | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\n𝕜 : Type u_1\ninst✝⁵ : IsROrC 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type ?u.879353\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G... | [
532,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
11
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_sq | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : 0 ≤ x\n⊢ sqrt (x ^ 2) = x",
"tactic": "rw [sq, sqrt_mul_self h]"
}
] | [
239,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_filter_of_le_const | [
{
"state_after": "Ω : Type u_2\ninst✝³ : MeasurableSpace Ω\ninst✝² : TopologicalSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nι : Type u_1\nL : Filter ι\ninst✝ : IsCountablyGenerated L\nμ : FiniteMeasure Ω\nfs : ι → Ω →ᵇ ℝ≥0\nc : ℝ≥0\nfs_le_const : ∀ᶠ (i : ι) in L, ∀ᵐ (ω : Ω) ∂↑μ, ↑(fs i) ω ≤ c\nf : Ω →ᵇ ℝ≥0\nfs_li... | [
628,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_iff_le | [] | [
75,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.condition | [] | [
611,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.infty_coeFn_one | [] | [
901,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_comm | [
{
"state_after": "case a\nα : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns s₁ s₂ t t₁ t₂ u : Finset α\na b c a✝ : α\n⊢ a✝ ∈ s ○ t ↔ a✝ ∈ t ○ s",
"state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : Or... | [
527,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_pos | [
{
"state_after": "p : ℝ\nx : ℝ≥0\nhx_pos : 0 < x\nrpow_pos_of_nonneg : ∀ {p : ℝ}, 0 < p → 0 < x ^ p\n⊢ 0 < x ^ p",
"state_before": "p : ℝ\nx : ℝ≥0\nhx_pos : 0 < x\n⊢ 0 < x ^ p",
"tactic": "have rpow_pos_of_nonneg : ∀ {p : ℝ}, 0 < p → 0 < x ^ p := by\n intro p hp_pos\n rw [← zero_rpow hp_pos.ne']\n ex... | [
197,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.denseEmbedding_coe | [] | [
397,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.le_of_dvd | [
{
"state_after": "m n : ℕ+\n⊢ mod n m = m → m ≤ n",
"state_before": "m n : ℕ+\n⊢ m ∣ n → m ≤ n",
"tactic": "rw [dvd_iff']"
},
{
"state_after": "m n : ℕ+\nh : mod n m = m\n⊢ m ≤ n",
"state_before": "m n : ℕ+\n⊢ mod n m = m → m ≤ n",
"tactic": "intro h"
},
{
"state_after": "m n : ℕ... | [
429,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_carrier | [] | [
114,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mk_initialSeg | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.106108\nβ : Type ?u.106111\nγ : Type ?u.106114\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ (#↑{o' | o' < o}) = Cardinal.lift (card o)",
"tactic": "rw [lift_card, ← type_subrel_lt, card_type]"
}
] | [
390,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_lt_add_right | [] | [
399,
64
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
398,
11
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_mk | [] | [
330,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_mul | [] | [
305,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_subset_Iic_union_Icc | [] | [
1451,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.31212\nγ : Type ?u.31215\nι : Type ?u.31218\nM : Type u_2\nM' : Type ?u.31224\nN : Type ?u.31227\nP : Type ?u.31230\nG : Type ?u.31233\nH : Type ?u.31236\nR : Type ?u.31239\nS : Type ?u.31242\ninst✝¹ : Zero M\na a' : α\nb : M\ninst✝ : D... | [
313,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.is_le | [] | [
277,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.totallyBounded_iff | [] | [
859,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Topology/Inseparable.lean | specializes_TFAE | [
{
"state_after": "case tfae_1_to_2\nX : Type u_1\nY : Type ?u.7977\nZ : Type ?u.7980\nα : Type ?u.7983\nι : Type ?u.7986\nπ : ι → Type ?u.7991\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx✝ y✝ z : X\ns : Set X\nf : X → Y\nx y ... | [
98,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_monomial_succ | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ coeff (↑(monomial (n + 1)) a) 0 = 0",
"tactic": "simp [coeff_monomial]"
}
] | [
700,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.mul_def | [] | [
843,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | Set.exists_isOpen_lt_of_lt | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.8664\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace α\nμ : Measure α\ninst✝ : OuterRegular μ\nA : Set α\nr : ℝ≥0∞\nhr : ↑↑μ A < r\nU : Set α\nhAU : U ⊇ toMeasurable μ A\nhUo : IsOpen U\nhU : ↑↑?m.8932 U < r\n⊢ ∃ U, U ⊇ A ∧ IsOpen U ∧ ↑↑... | [
250,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.subsingleton_of_normal | [
{
"state_after": "case allEq\nG : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Finite (Sylow p G)\nP : Sylow p G\nh : Normal ↑P\n⊢ ∀ (a b : Sylow p G), a = b",
"state_before": "G : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\np : ℕ\ninst✝¹ : Fact (Nat.Pr... | [
706,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.res_length | [
{
"state_after": "no goals",
"state_before": "E : ℕ → Type ?u.20551\nα : Type u_1\nx : ℕ → α\nn : ℕ\n⊢ length (res x n) = n",
"tactic": "induction n <;> simp [*]"
}
] | [
221,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.traverse_eq | [] | [
262,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.toCocone_pt | [] | [
1024,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.aeval_repr | [] | [
407,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | integralClosure_map_algEquiv | [
{
"state_after": "case h\nR : Type u_1\nA : Type u_2\nB : Type u_3\nS : Type ?u.725847\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf✝ : R →+* S\nf : A ≃ₐ[R] B\ny : B\n⊢ y ∈ Subalgebra.map (↑f) (integralClosure R A) ↔ y ∈ integra... | [
598,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.isGreatest_iff_eq | [] | [
1085,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_inf | [] | [
201,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.update_data | [] | [
22,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
21,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.mul_coeff_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ r p q : R[X]\n⊢ coeff (p * q) 0 = coeff p 0 * coeff q 0",
"tactic": "simp [coeff_mul]"
}
] | [
130,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_le_smul_left | [] | [
1043,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_ne_zero_iff | [
{
"state_after": "case inl\n\n⊢ ↑Λ 1 ≠ 0 ↔ IsPrimePow 1\n\ncase inr\nn : ℕ\nhn : n ≠ 1\n⊢ ↑Λ n ≠ 0 ↔ IsPrimePow n",
"state_before": "n : ℕ\n⊢ ↑Λ n ≠ 0 ↔ IsPrimePow n",
"tactic": "rcases eq_or_ne n 1 with (rfl | hn)"
},
{
"state_after": "no goals",
"state_before": "case inr\nn : ℕ\nhn : n ≠ 1... | [
99,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Topology/Semicontinuous.lean | continuousOn_iff_lower_upperSemicontinuousOn | [
{
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1114,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.mk.inj_left | [
{
"state_after": "α✝ : Type ?u.2199\nβ✝ : Type ?u.2202\nγ : Type ?u.2205\nδ : Type ?u.2208\nα : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\nh : (a, b₁) = (a, b₂)\n⊢ b₁ = b₂",
"state_before": "α✝ : Type ?u.2199\nβ✝ : Type ?u.2202\nγ : Type ?u.2205\nδ : Type ?u.2208\nα : Type u_1\nβ : Type u_2\na : α\n⊢ Functio... | [
106,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Logic/Basic.lean | Ne.dite_ne_right_iff | [] | [
1197,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
11
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toLinearMap₂'Aux_toMatrix₂Aux | [
{
"state_after": "R : Type u_2\nR₁ : Type u_1\nR₂ : Type u_4\nM : Type ?u.119507\nM₁ : Type ?u.119510\nM₂ : Type ?u.119513\nM₁' : Type ?u.119516\nM₂' : Type ?u.119519\nn : Type u_3\nm : Type u_5\nn' : Type ?u.119528\nm' : Type ?u.119531\nι : Type ?u.119534\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing R₁\ninst✝⁸ : C... | [
132,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.induction_on | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.79966\ninst✝¹³ : Monoid R'\nR'' : Type ?u.79972\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type ?u.79984\nQ : Type ?u.79987\nS : Type ?u.79990\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoid P\nins... | [
130,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
11
] |
Mathlib/Computability/Partrec.lean | Computable.decode | [] | [
407,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
11
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.div'_to_nat | [] | [
1630,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1629,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | exists_deriv_eq_slope | [] | [
784,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_pos_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.133631\nα : Type u_1\nβ : Type ?u.133637\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\n⊢ 0 < a / b ↔ 0 < a ∧ 0 < b ∨ a < 0 ∧ b < 0",
"tactic": "simp only [division_def, mul_pos_iff, inv_pos, inv_lt_zero]"
}
] | [
681,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Order/Filter/IndicatorFunction.lean | Filter.EventuallyEq.indicator_zero | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nM : Type ?u.7467\nE : Type ?u.7470\ninst✝ : Zero β\nl : Filter α\nf : α → β\ns : Set α\nhf : f =ᶠ[l] 0\n⊢ Set.indicator s 0 =ᶠ[l] 0",
"state_before": "α : Type u_2\nβ : Type u_1\nM : Type ?u.7467\nE : Type ?u.7470\ninst✝ : Zero β\nl : Filter α\nf : α → β\ns : Se... | [
116,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_sub_sub_succ | [
{
"state_after": "no goals",
"state_before": "n m k : Nat\n⊢ succ n - m - succ k = n - m - k",
"tactic": "rw [Nat.sub_sub, Nat.sub_sub, add_succ, succ_sub_succ]"
}
] | [
412,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
411,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.length_toList | [
{
"state_after": "no goals",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\n⊢ List.length (toList s) = s.length + 1",
"tactic": "rw [toList, List.length_ofFn]"
}
] | [
220,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mem_direction_iff_eq_vsub | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\nh : Set.Nonempty ↑s\nv : V\n⊢ v ∈ ↑s -ᵥ ↑s ↔ ∃ p1, p1 ∈ s ∧ ∃ p2, p2 ∈ s ∧ v = p1 -ᵥ p2",
"state_before": "k : Type u_1\nV : Type u_2\nP... | [
256,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Logic/Small/Basic.lean | small_of_injective | [] | [
94,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_symm_real | [
{
"state_after": "no goals",
"state_before": "r s : ℝ\n⊢ IsSt (↑r) s ↔ IsSt (↑s) r",
"tactic": "rw [isSt_real_iff_eq, isSt_real_iff_eq, eq_comm]"
}
] | [
376,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_conj' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁹ : CommRing R\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nN : Type u_3\ninst✝⁶ : AddCommGroup N\ninst✝⁵ : Module R N\nι : Type ?u.740490\ninst✝⁴ : Module.Free R M\ninst✝³ : Module.Finite R M\ninst✝² : Module.Free R N\ninst✝¹ ... | [
290,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.hom_as_subtype | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/Constructions.lean | Continuous.sigma_map | [] | [
1545,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.pointReflection_self | [] | [
791,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.IntegrableOn.continuousOn_smul | [
{
"state_after": "X : Type u_1\nY : Type ?u.2484781\nE : Type u_3\nR : Type ?u.2484787\ninst✝⁹ : MeasurableSpace X\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : MeasurableSpace Y\ninst✝⁶ : TopologicalSpace Y\ninst✝⁵ : NormedAddCommGroup E\nf✝ : X → E\nμ : Measure X\ns : Set X\ninst✝⁴ : OpensMeasurableSpace X\nA K : Se... | [
435,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.val_rat_smul | [] | [
417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_deriv_of_nonpos | [
{
"state_after": "E : Type ?u.162446\nf f' : ℝ → E\ng g' : ℝ → ℝ\na b l : ℝ\nm : E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nhcont : ContinuousOn g (Ici a)\nhderiv : ∀ (x : ℝ), x ∈ Ioi a → HasDerivAt g (g' x) x\ng'neg : ∀ (x : ℝ), x ∈ Ioi a → g' x ≤ 0\nhg : Tendsto g atT... | [
764,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Order/Atoms.lean | GaloisCoinsertion.isAtom_of_image | [] | [
788,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.size_eq | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\nn a✝³ : Nat\na✝² : α\na✝¹ : HeapNode α\na✝ : Heap α\nleft✝ : n ≤ a✝³\nh₁ : HeapNode.WellFormed le a✝² a✝¹ a✝³\nh₂ : WellFormed le (a✝³ + 1) a✝\n⊢ 2 ^ a✝³ + realSize a✝ = HeapNode.realSize a✝¹ + 1 + realSize a✝",
"state_before": "α : Type u_1\nle : α → α → B... | [
445,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
440,
9
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.subset | [] | [
118,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.join_cons_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nS : Seq (Seq1 α)\n⊢ destruct (join (cons (a, nil) S)) = some (a, join S)",
"tactic": "simp [join]"
}
] | [
758,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_iInter_eq_right | [] | [
745,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.coe_zero | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
11
] |
Mathlib/CategoryTheory/Monoidal/Types/Basic.lean | CategoryTheory.associator_inv_apply | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_of_disjoint_append_right_left | [] | [
1402,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1401,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.toFun_eq_coe | [] | [
263,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Std/Data/List/Lemmas.lean | List.length_range' | [] | [
1811,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1809,
9
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_le_snorm'_of_exponent_le | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.4184586\nG : Type ?u.4184589\nm✝ m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq✝ : ℝ\nμ✝ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\nm : MeasurableSpace α\np q : ℝ\nhp0_lt : 0 < p\nhpq : p ≤ q\nμ : Me... | [
1100,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Data/Finsupp/Pointwise.lean | Finsupp.coe_pointwise_smul | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_ofAdd | [] | [
3211,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3211,
9
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.map_id | [] | [
1217,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedField β\nt u v w : α → β\nl : Filter α\nhtu : t ~[l] u\nhvw : v ~[l] w\n⊢ (fun x => t x / v x) ~[l] fun x => u x / w x",
"tactic": "simpa only [div_eq_mul_inv] using htu.mul hvw.inv"
}
] | [
301,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Topology/Basic.lean | isOpen_biInter | [] | [
171,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_def | [] | [
317,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_eq | [
{
"state_after": "case h.e'_2.h.e'_1\nx y z : ℂ\n⊢ z = ↑z.re + ↑z.im * I",
"state_before": "x y z : ℂ\n⊢ cos z = cos ↑z.re * cosh ↑z.im - sin ↑z.re * sinh ↑z.im * I",
"tactic": "convert cos_add_mul_I z.re z.im"
},
{
"state_after": "no goals",
"state_before": "case h.e'_2.h.e'_1\nx y z : ℂ\n⊢... | [
891,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_op | [] | [
1367,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_sSup_of_mem | [] | [
1053,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongEpi_of_epi | [] | [
221,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.lift₂_mk | [] | [
587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_left_cancel_iff | [] | [
186,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_mul_iff | [] | [
271,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/PFun.lean | PFun.dom_eq | [] | [
92,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/Order/Basic.lean | continuous_max | [] | [
698,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | continuous_of_linear_of_boundₛₗ | [] | [
87,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\n⊢ eval₂ f x X = x",
"tactic": "simp [eval₂_eq_sum]"
}
] | [
77,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
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