file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.IsClosable.closure_mono | [
{
"state_after": "R : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module R E\ninst✝⁷ : Module R F\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : ContinuousAdd E\ninst✝³ : ContinuousAdd F\ninst✝² : TopologicalSpace R... | [
141,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/PUnitInstances.lean | PUnit.lcm_eq | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Int/Basic.lean | Int.coe_pred_of_pos | [
{
"state_after": "case zero\nh : 0 < zero\n⊢ ↑(zero - 1) = ↑zero - 1\n\ncase succ\nn✝ : ℕ\nh : 0 < Nat.succ n✝\n⊢ ↑(Nat.succ n✝ - 1) = ↑(Nat.succ n✝) - 1",
"state_before": "n : ℕ\nh : 0 < n\n⊢ ↑(n - 1) = ↑n - 1",
"tactic": "cases n"
},
{
"state_after": "case succ\nn✝ : ℕ\nh : 0 < Nat.succ n✝\n⊢ ... | [
181,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
14
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_epi_zero | [] | [
320,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Topology/Basic.lean | Filter.lift'_closure_eq_bot | [
{
"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\nl : Filter α\nh : l = ⊥\n⊢ Filter.lift' ⊥ closure = ⊥",
"tactic": "rw [lift'_bot (monotone_closure _), closure_empty, principal_empty]"
}
] | [
596,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_prod | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nh : Set.Infinite (s ×ˢ t)\n⊢ Set.Infinite s ∧ Set.Nonempty t ∨ Set.Infinite t ∧ Set.Nonempty s\n\ncase refine'_2\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\n⊢ Set.Infinite s ∧ Set.N... | [
941,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
11
] |
Mathlib/Data/TypeVec.lean | TypeVec.lastFun_appendFun | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.prodMk | [] | [
385,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
8
] |
Mathlib/Topology/Constructions.lean | mem_nhds_prod_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.36228\nδ : Type ?u.36231\nε : Type ?u.36234\nζ : Type ?u.36237\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
558,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/Int/Log.lean | Int.neg_clog_inv_eq_log | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr : R\n⊢ -clog b r⁻¹ = log b r",
"tactic": "rw [clog_inv, neg_neg]"
}
] | [
230,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
src/lean/Init/Control/Lawful.lean | ReaderT.run_seq | [] | [
204,
59
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
203,
9
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_subset_Icc | [] | [
240,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.nonempty_of_neBot | [] | [
700,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.out_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\na b : Associates α\nx✝¹ x✝ : α\n⊢ Associates.out (Quotient.mk (Associated.setoid α) x✝¹ * Quotient.mk (Associated.setoid α) x✝) =\n Associates.out (Quotient.mk (Associated.setoi... | [
233,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset_union | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.474148\nγ : Type ?u.474151\ninst✝ : DecidableEq α\nl✝ l'✝ : List α\na : α\nl l' : List α\na✝ : α\n⊢ a✝ ∈ toFinset (l ∪ l') ↔ a✝ ∈ toFinset l ∪ toFinset l'",
"state_before": "α : Type u_1\nβ : Type ?u.474148\nγ : Type ?u.474151\ninst✝ : DecidableEq α\nl✝ l'... | [
3323,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3321,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | isClosed_omegaLimit | [] | [
93,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/Convex/Jensen.lean | ConcaveOn.exists_le_of_mem_convexHull | [] | [
145,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/Dual.lean | TensorProduct.dualDistrib_apply | [] | [
1563,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measure_eq_measure_preimage_add_measure_tsum_Ico_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1709267\nγ : Type ?u.1709270\nγ₂ : Type ?u.1709273\nδ : Type ?u.1709276\nι : Sort y\ns✝ t✝ u : Set α\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\ns : Set α\nhs : MeasurableSet s\nt : ℝ≥0\nht ... | [
1511,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Deprecated/Submonoid.lean | Monoid.exists_list_of_mem_closure | [
{
"state_after": "case basic\nM : Type u_1\ninst✝¹ : Monoid M\ns✝ : Set M\nA : Type ?u.66965\ninst✝ : AddMonoid A\nt : Set A\ns : Set M\na a✝¹ : M\na✝ : a✝¹ ∈ s\n⊢ ∃ l, (∀ (x : M), x ∈ l → x ∈ s) ∧ List.prod l = a✝¹\n\ncase one\nM : Type u_1\ninst✝¹ : Monoid M\ns✝ : Set M\nA : Type ?u.66965\ninst✝ : AddMonoid A... | [
384,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Finsupp/Fin.lean | Finsupp.cons_tail | [
{
"state_after": "case h\nn : ℕ\ni : Fin n\nM : Type u_1\ninst✝ : Zero M\ny : M\nt : Fin (n + 1) →₀ M\ns : Fin n →₀ M\na : Fin (n + 1)\n⊢ ↑(cons (↑t 0) (tail t)) a = ↑t a",
"state_before": "n : ℕ\ni : Fin n\nM : Type u_1\ninst✝ : Zero M\ny : M\nt : Fin (n + 1) →₀ M\ns : Fin n →₀ M\n⊢ cons (↑t 0) (tail t) = ... | [
67,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_sub_self | [
{
"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\na b : α\n⊢ toIocMod hp a b - b = -toIocDiv hp a b • p",
"tactic": "rw [toIocMod, sub_sub_cancel_left, neg_smul]"
}
] | [
141,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.congr_trans | [] | [
693,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.ext_iff | [] | [
143,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.exists_zpow_eq | [] | [
307,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.mul_const | [] | [
132,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mul_left_mono | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nI J J' : FractionalIdeal S P\nh : J ≤ J'\n⊢ (fun x x_1 => x * x_1) I J ≤ (fun x x_1 => x * x_1) I J'",
"state_before": "R : Type u_1\ninst✝² : CommRing R\nS... | [
569,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_ne_zero | [] | [
276,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_sup | [] | [
249,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Computability/NFA.lean | NFA.eval_append_singleton | [] | [
105,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Std/Data/List/Lemmas.lean | List.set_nil | [] | [
817,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
817,
9
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_left_cancel'' | [] | [
297,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.coe_copy | [] | [
757,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.bddAbove | [] | [
157,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.fst_prod | [
{
"state_after": "case h\nR : Type u_1\nA : Type u_2\nB : Type u_3\nC : Type u_4\ninst✝⁹ : CommSemiring R\ninst✝⁸ : Semiring A\ninst✝⁷ : Algebra R A\ninst✝⁶ : Star A\ninst✝⁵ : Semiring B\ninst✝⁴ : Algebra R B\ninst✝³ : Star B\ninst✝² : Semiring C\ninst✝¹ : Algebra R C\ninst✝ : Star C\nf : A →⋆ₐ[R] B\ng : A →⋆ₐ[... | [
631,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Order/BooleanAlgebra.lean | inf_sdiff_distrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.40407\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\na b c : α\n⊢ a \\ b ⊓ c = (a ⊓ c) \\ (b ⊓ c)",
"tactic": "simp_rw [@inf_comm _ _ _ c, inf_sdiff_distrib_left]"
}
] | [
458,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Logic/Basic.lean | And.exists | [] | [
834,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Order/Closure.lean | closureOperator_gi_self | [
{
"state_after": "case a.h\nα : Type u_1\nι : Sort ?u.34522\nκ : ι → Sort ?u.34527\nβ : Type ?u.34530\ninst✝ : PartialOrder α\nc : ClosureOperator α\nx : α\n⊢ ↑(GaloisConnection.closureOperator (_ : GaloisConnection (ClosureOperator.toClosed c) Subtype.val)).toOrderHom x =\n ↑c.toOrderHom x",
"state_befo... | [
573,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_add_right | [
{
"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\na b : α\n⊢ toIocDiv hp a (b + p) = toIocDiv hp a b + 1",
"tactic": "simpa only [one_zsmul] using toIocDiv_add_zsmul hp a b 1"
}
] | [
310,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.nonempty_coe | [] | [
137,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_coe_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nf✝ : α → β → γ\na✝ : Option α\nb✝ : Option β\nc : Option γ\nf : α → β → γ\na : Option α\nb : β\n⊢ map₂ f a (some b) = Option.map (fun a => f a b) a",
"tactic": "cases a <;> rfl"
}
] | [
76,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/LinearAlgebra/Matrix/DotProduct.lean | Matrix.dotProduct_eq_zero | [] | [
69,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.prod_trans | [
{
"state_after": "case hs.h.mk\nα : Type u_3\nβ : Type u_4\nγ : Type u_5\nδ : Type u_6\ne✝ : LocalEquiv α β\ne'✝ : LocalEquiv β γ\nη : Type u_1\nε : Type u_2\ne : LocalEquiv α β\nf : LocalEquiv β γ\ne' : LocalEquiv δ η\nf' : LocalEquiv η ε\nx : α\ny : δ\n⊢ (x ∈ e.source ∧ y ∈ e'.source) ∧ ↑e x ∈ f.source ∧ ↑e' ... | [
978,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_hom_snd | [
{
"state_after": "case mk\nC : Type u\n𝒞 : Category C\ninst✝⁴ : MonoidalCategory C\nC₁ : Type u₁\ninst✝³ : Category C₁\ninst✝² : MonoidalCategory C₁\nC₂ : Type u₂\ninst✝¹ : Category C₂\ninst✝ : MonoidalCategory C₂\nfst✝ : C₁\nsnd✝ : C₂\n⊢ (ρ_ (fst✝, snd✝)).hom.snd = (ρ_ (fst✝, snd✝).snd).hom",
"state_befor... | [
663,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_pos_iff | [] | [
324,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_le_of_forall_fin_meas_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1832179\nγ : Type ?u.1832182\nδ : Type ?u.1832185\nm m0 : MeasurableSpace α\nE : Type ?u.1832194\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : MeasurableSpace E\ninst✝² : OpensMeasurableSpace E\ninst✝¹ : MeasurableSpace α\nμ : Measure α\nins... | [
2029,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2026,
1
] |
Mathlib/Data/List/Sigma.lean | List.not_mem_keys_kerase | [
{
"state_after": "case nil\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nnd : NodupKeys []\n⊢ ¬a ∈ keys (kerase a [])\n\ncase cons\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nhead✝ : Sigma β\ntail✝ : List (Sigma β)\ntail_ih✝ : Nodup... | [
495,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_eq_span_vsub_set_left_ne | [
{
"state_after": "k : Type u_3\nV : Type u_2\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.258427\ns : Set P\np : P\nhp : p ∈ s\n⊢ Submodule.span k (insert ((fun x x_1 => x -ᵥ x_1) p p) ((fun x x_1 => x -ᵥ x_1) p '' (s \\ {p}))) =\n Submodu... | [
1059,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_sdiff | [] | [
2158,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2157,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_two | [
{
"state_after": "x : ℝ≥0∞\n⊢ x ^ 2 = x ^ ↑2",
"state_before": "x : ℝ≥0∞\n⊢ x ^ 2 = x ^ 2",
"tactic": "rw [← rpow_nat_cast]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ≥0∞\n⊢ x ^ 2 = x ^ ↑2",
"tactic": "simp only [Nat.cast_ofNat]"
}
] | [
480,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Real.borel_eq_generateFrom_Ioo_rat | [] | [
1682,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_smul_eq_of_isUnit | [
{
"state_after": "case a\nR : Type u_2\nR₂ : Type ?u.69448\nK : Type ?u.69451\nM : Type u_1\nM₂ : Type ?u.69457\nV : Type ?u.69460\nS : Type ?u.69463\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\... | [
293,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_nat_eval_succ | [
{
"state_after": "case pos\nS : Type ?u.31829\ninst✝ : Semiring S\nr✝ n r : ℕ\nh : r = 0\n⊢ 0 * eval (0 + 1) (pochhammer ℕ r) = (0 + r) * eval 0 (pochhammer ℕ r)\n\ncase neg\nS : Type ?u.31829\ninst✝ : Semiring S\nr✝ n r : ℕ\nh : ¬r = 0\n⊢ 0 * eval (0 + 1) (pochhammer ℕ r) = (0 + r) * eval 0 (pochhammer ℕ r)",
... | [
207,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_range | [] | [
1102,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.add_mem_iff_left | [] | [
567,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
11
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.fold_eq_foldTR | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : Nat → α → α\nn✝ : Nat\ninit : α\nn : Nat\n⊢ foldTR.loop f (0 + n) 0 (fold f n init) = fold f (0 + n) init",
"tactic": "simp [foldTR.loop]"
},
{
"state_after": "α : Type u_1\nf : Nat → α → α\nn✝ : Nat\ninit : α\nm n : Nat\n⊢ foldTR.l... | [
740,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
735,
10
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_mul_right_unit | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\na✝ b : α\ninst✝ : CommSemiring α\nI : Ideal α\na : α\nh2 : IsUnit a\nx : α\n⊢ span {x * a} = span {x}",
"tactic": "rw [mul_comm, span_singleton_mul_left_unit h2]"
}
] | [
518,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Order/WellFoundedSet.lean | Finset.isWf | [] | [
555,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
11
] |
Mathlib/Data/Finset/Image.lean | Finset.image_id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.77099\nγ : Type ?u.77102\ninst✝¹ : DecidableEq β\nf g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\ninst✝ : DecidableEq α\nx✝ : α\n⊢ x✝ ∈ image id s ↔ x✝ ∈ s",
"tactic": "simp only [mem_image, exists_prop, id, exists_eq_right... | [
413,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.mem_affineSpan_iff | [
{
"state_after": "case mp\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : Nontrivial k\np : ι → P\nha : AffineIndependent k p\ni : ι\ns : Set ι\n⊢ p i ∈ affineSpan k (p '' s) → i ∈ s\n\ncase mpr\nk : Type u... | [
458,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
11
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_comp_toList | [] | [
78,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.div_left | [
{
"state_after": "α : Type ?u.2754\nM₀ : Type ?u.2757\nG₀ : Type u_1\nM₀' : Type ?u.2763\nG₀' : Type ?u.2766\nF : Type ?u.2769\nF' : Type ?u.2772\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na b c : G₀\nhac : Commute a c\nhbc : Commute b c\n⊢ Commute (a * b⁻¹) c",
"state_before": "α : Type ?u.2754... | [
92,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.ext_iff | [] | [
157,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
11
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.finrank_add_finrank_orthogonal | [
{
"state_after": "case h.e'_2\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1005430\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK✝ : Submodule 𝕜 E\ninst✝ : FiniteDimensional 𝕜 E\nK : Submodule 𝕜 E\n⊢ finrank �... | [
1112,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | MeasureTheory.IntegrableOn.intervalIntegrable | [] | [
119,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_lt_add_left | [] | [
396,
73
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
395,
11
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_pi_le_of_le | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.307283\ninst✝² : PseudoEMetricSpace α\nx✝ y✝ z : α\nε ε₁ ε₂ : ℝ≥0∞\ns✝ t : Set α\nπ : β → Type u_1\ninst✝¹ : Fintype β\ninst✝ : (b : β) → PseudoEMetricSpace (π b)\ns : (b : β) → Set (π b)\nc : ℝ≥0∞\nh : ∀ (b : β), diam (s b) ≤ c\nx : (i : β) → π i\nhx : x ∈ ... | [
987,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_pos_iff | [
{
"state_after": "β : Type ?u.274493\nA : Type ?u.274496\nG : Type ?u.274499\nM : Type u_1\nR : Type ?u.274505\ninst✝¹ : LinearOrderedCommMonoidWithZero M\ninst✝ : NoZeroDivisors M\na : M\nn : ℕ\nhn : 0 < n\n⊢ a ^ n ≠ 0 ↔ a ≠ 0",
"state_before": "β : Type ?u.274493\nA : Type ?u.274496\nG : Type ?u.274499\nM... | [
775,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.eqvGen_eq | [] | [
210,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.differentiableAt | [] | [
49,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_one | [] | [
262,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.extension_coe_to_fun | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_of_one_le_of_le | [] | [
884,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.jb_transform | [
{
"state_after": "no goals",
"state_before": "n : Type ?u.156835\np : Type ?u.156838\nq : Type ?u.156841\nl : Type u_1\nR : Type u₂\ninst✝⁷ : DecidableEq n\ninst✝⁶ : DecidableEq p\ninst✝⁵ : DecidableEq q\ninst✝⁴ : DecidableEq l\ninst✝³ : CommRing R\ninst✝² : Fintype p\ninst✝¹ : Fintype q\ninst✝ : Fintype l\... | [
359,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.coeff_zero_eq_aeval_zero' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\nA' : Type ?u.1127963\nB' : Type ?u.1127966\na b : R\nn : ℕ\ninst✝⁶ : CommSemiring A'\ninst✝⁵ : Semiring B'\ninst✝⁴ : CommSemiring R\np✝ q : R[X]\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nB : Type ?u.1128179\ninst... | [
325,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.singleMapHomologicalComplex_hom_app_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.156859\nV : Type u\ninst✝⁶ : Category V\ninst✝⁵ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh k : D ⟶ E\ni : ι\ninst✝⁴ : HasZeroObject V\nW : Type ?u.157228\ninst✝³ : Category W\ninst✝² : Preadditive W\ninst✝¹ : ... | [
318,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderivWithin_neg | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.431682\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.431777\... | [
461,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | mem_exposedPoints_iff_exposed_singleton | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : OrderedRing 𝕜\ninst✝² : AddCommMonoid E\ninst✝¹ : TopologicalSpace E\ninst✝ : Module 𝕜 E\nl : E →L[𝕜] 𝕜\nA B C : Set E\nX : Finset E\nx : E\n⊢ IsExposed 𝕜 A {x} → x ∈ exposedPoints 𝕜 A",
"state_before": "𝕜 : Type u_... | [
233,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_bot | [] | [
521,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PushoutCocone.unop_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nJ : Type u₂\ninst✝ : Category J\nX✝ : Type v₂\nX Y Z : Cᵒᵖ\nf : X ⟶ Y\ng : X ⟶ Z\nc : PushoutCocone f g\n⊢ PullbackCone.snd (unop c) = (inr c).unop",
"tactic": "aesop_cat"
}
] | [
487,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
src/lean/Init/Data/List/Basic.lean | List.append_eq | [] | [
101,
81
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
101,
9
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | pairwise_coprime_iff_coprime_prod | [
{
"state_after": "case refine'_1\nR : Type u\nI : Type v\ninst✝¹ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\ninst✝ : DecidableEq I\nhp : Pairwise (IsCoprime on fun i => s ↑i)\ni : I\nhi : i ∈ t\nj : I\nhj : j ∈ t \\ {i}\n⊢ IsCoprime (s i) (s j)\n\ncase refine'_2\nR : Type u\nI : Type v\ninst✝¹ : CommS... | [
187,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.measurePreserving_finTwoArrow_vec | [] | [
811,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
src/lean/Init/Data/Nat/Gcd.lean | Nat.gcd_succ | [] | [
24,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
23,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelHom.ext | [] | [
132,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.pow_snd | [] | [
327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_mul | [] | [
133,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arctan_mem_Ioo | [] | [
128,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_lt | [
{
"state_after": "case zero\ninst✝ : NeZero Nat.zero\na : ZMod Nat.zero\n⊢ val a < Nat.zero\n\ncase succ\nn✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\na : ZMod (Nat.succ n✝)\n⊢ val a < Nat.succ n✝",
"state_before": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ val a < n",
"tactic": "cases n"
},
{
"state_afte... | [
58,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/Order/Kleene.lean | Pi.kstar_def | [] | [
348,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/PrimeIdeal.lean | Order.Ideal.PrimePair.I_isProper | [
{
"state_after": "case intro\nP : Type u_1\ninst✝ : Preorder P\nIF : PrimePair P\nw : P\nh : w ∈ ↑IF.F\n⊢ IsProper IF.I",
"state_before": "P : Type u_1\ninst✝ : Preorder P\nIF : PrimePair P\n⊢ IsProper IF.I",
"tactic": "cases' IF.F.nonempty with w h"
},
{
"state_after": "P : Type u_1\ninst✝ : Pr... | [
73,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | Antitone.quasiconvexOn | [] | [
221,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.singleton_eq_cons_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.26091\nγ : Type ?u.26094\na b : α\nm : Multiset α\n⊢ (a = b ∧ 0 = m ∨ a ≠ b ∧ ∃ cs, 0 = b ::ₘ cs ∧ m = a ::ₘ cs) ↔ a = b ∧ m = 0",
"state_before": "α : Type u_1\nβ : Type ?u.26091\nγ : Type ?u.26094\na b : α\nm : Multiset α\n⊢ {a} = b ::ₘ m ↔ a = b ∧ m = 0",
"... | [
361,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.take_succ' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\nn : ℕ\n⊢ take (n + 1 + 1) s = take (n + 1) s ++ [nth s (n + 1)]",
"tactic": "rw [take_succ, take_succ' n, ← List.cons_append, ← take_succ, nth_tail]"
}
] | [
585,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt_dvd | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\n⊢ a = 0 ∨ padicValInt p a ≤ padicValInt p a",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\n⊢ ↑p ^ padicValInt p a ∣ a",
"tactic": "rw [padicValInt_dvd_iff]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (... | [
523,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | Set.Subsingleton.measure_zero | [] | [
3286,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3284,
1
] |
Mathlib/Data/List/Basic.lean | List.attach_map_val' | [] | [
3122,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3121,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.dist_mk | [] | [
103,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | exists_prime_addOrderOf_dvd_card | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.713413\ninst✝³ : Fintype α\nG✝ : Type ?u.713419\ninst✝² : Group G✝\nn : ℕ\nG : Type u_1\ninst✝¹ : AddGroup G\ninst✝ : Fintype G\np : ℕ\nhp : Fact (Nat.Prime p)\nhdvd : p ∣ Fintype.card G\n⊢ p ∣ Fintype.card (Multiplicative G)",
"tactic": "convert... | [
493,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | IsExposed.refl | [] | [
98,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
11
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.