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/Fin/Basic.lean | Fin.cast_natAdd_right | [
{
"state_after": "case h\nn✝ m✝ n n' m : ℕ\ni : Fin n'\nh : m + n' = m + n\n⊢ ↑(↑(cast h) (↑(natAdd m) i)) = ↑(↑(natAdd m) (↑(cast (_ : n' = n)) i))",
"state_before": "n✝ m✝ n n' m : ℕ\ni : Fin n'\nh : m + n' = m + n\n⊢ ↑(cast h) (↑(natAdd m) i) = ↑(natAdd m) (↑(cast (_ : n' = n)) i)",
"tactic": "ext"
... | [
1425,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.mem_nhds_iff | [] | [
920,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
11
] |
Mathlib/Data/Part.lean | Part.subsingleton | [] | [
159,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_smulRightₗ | [] | [
1643,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1642,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.divOf_add_modOf | [
{
"state_after": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\ng g' : G\n⊢ ↑(of' k G g * (x /ᵒᶠ g) + x %ᵒᶠ g) g' = ↑x g'",
"state_before": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\ng... | [
189,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurableSet_preimage | [] | [
314,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofNat_mul_re | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6340432\ninst✝¹ : IsROrC K\nn : ℕ\ninst✝ : Nat.AtLeastTwo n\nz : K\n⊢ ↑re (OfNat.ofNat n * z) = OfNat.ofNat n * ↑re z",
"tactic": "rw [← ofReal_ofNat, ofReal_mul_re]"
}
] | [
657,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_inf_const_le | [] | [
403,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_self_left | [] | [
292,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.onFun_apply | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_closure_iff_infDist_zero | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.65322\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : Set.Nonempty s\n⊢ x ∈ closure s ↔ infDist x s = 0",
"tactic": "simp [mem_closure_iff_infEdist_zero, infDist, ENNReal.... | [
594,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Init/Logic.lean | iff_false_iff | [] | [
198,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_set_pairwise | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.517618\nf : α → β\nr : β → β → Prop\nm : Multiset α\nh : Set.Pairwise {a | a ∈ m} fun a₁ a₂ => r (f a₁) (f a₂)\na₁ : α\nH₁ : a₁ ∈ m\nh₁ : f a₁ ∈ {b | b ∈ map f m}\na₂ : α\nH₂ : a₂ ∈ m\nh₂ : f a₂ ∈ {b | b ∈ map f m}\nhn : f a... | [
3020,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3016,
1
] |
Std/Tactic/Ext.lean | Std.Tactic.Ext.$extIffName | [] | [
89,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
86,
15
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.mem_support_cycleOf_iff | [
{
"state_after": "case pos\nι : Type ?u.2515226\nα : Type u_1\nβ : Type ?u.2515232\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\nhx : ↑f x = x\n⊢ y ∈ support (cycleOf f x) ↔ SameCycle f x y ∧ x ∈ support f\n\ncase neg\nι : Type ?u.2515226\nα : Type u_1\nβ : Type ?u.2515232\ninst✝¹ : Decidab... | [
1156,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.DominatedFinMeasAdditive.of_measure_le_smul | [] | [
274,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_quotient_lift_on' | [] | [
986,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_invOf | [
{
"state_after": "R✝ : Type u\nR : Type u_1\ninst✝³ : Monoid R\ninst✝² : StarSemigroup R\nr : R\ninst✝¹ : Invertible r\ninst✝ : Invertible (star r)\nthis : star ⅟r = star ⅟r * (star r * ⅟(star r))\n⊢ star ⅟r = ⅟(star r)",
"state_before": "R✝ : Type u\nR : Type u_1\ninst✝³ : Monoid R\ninst✝² : StarSemigroup ... | [
587,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Std/Data/List/Lemmas.lean | List.get_of_eq | [
{
"state_after": "case refl\nα : Type u_1\nl : List α\ni : Fin (length l)\n⊢ get l i = get l { val := i.val, isLt := (_ : i.val < length l) }",
"state_before": "α : Type u_1\nl l' : List α\nh : l = l'\ni : Fin (length l)\n⊢ get l i = get l' { val := i.val, isLt := (_ : i.val < length l') }",
"tactic": "... | [
582,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
581,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.ext_iff₂ | [] | [
127,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.leComap_id_iff | [] | [
299,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/Rat/BigOperators.lean | Rat.cast_multiset_sum | [] | [
34,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.of_union | [
{
"state_after": "case hf₁\nα : Type u_1\nβ : Type ?u.20634\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\nv : VectorMeasure α M\nf : ℕ → Set α\nA B : Set α\nh : Disjoint A B\nhA : MeasurableSet A\nhB : MeasurableSet B\n⊢ ∀ (i : Bool), MeasurableS... | [
191,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.toHamming_symm_eq | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiff.ccos | [] | [
351,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Algebra/Order/Module.lean | lowerBounds_smul_of_neg | [] | [
230,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_id | [] | [
1548,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1547,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_erase | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.8691\nα : Type u_1\nβ : Type ?u.8697\nγ : Type ?u.8700\ninst✝¹ : CommMonoid α\ns t : Multiset α\na : α\nm : Multiset ι\nf g : ι → α\ninst✝ : DecidableEq α\nh : a ∈ s\n⊢ a * prod (erase s a) = prod s",
"tactic": "rw [← s.coe_toList, coe_erase, coe... | [
93,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.head_empty | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.lift_comp_of | [] | [
131,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.inf_sq_eq_mul_div_abs_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\n⊢ (a ⊓ b) ^ 2 = a * b / abs (b / a)",
"tactic": "rw [← inf_mul_sup a b, ← sup_div_inf_eq_abs_div, div_eq_mul_inv, div_eq_mu... | [
410,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_le_one_of_subsingleton | [
{
"state_after": "V : Type u\nG✝ : SimpleGraph V\nα : Type v\nC : Coloring G✝ α\nG : SimpleGraph V\ninst✝ : Subsingleton V\n⊢ sInf {n | Colorable G n} ≤ 1",
"state_before": "V : Type u\nG✝ : SimpleGraph V\nα : Type v\nC : Coloring G✝ α\nG : SimpleGraph V\ninst✝ : Subsingleton V\n⊢ chromaticNumber G ≤ 1",
... | [
287,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.property_of_mem_map_subtype | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.135235\nγ : Type ?u.135238\np : α → Prop\ns : Finset { x // p x }\nx : { x // p x }\nleft✝ : x ∈ s\nh : ↑(Embedding.subtype fun x => p x) x ∈ map (Embedding.subtype fun x => p x) s\n⊢ p (↑(Embedding.subtype fun x => p x) x)",
"state_before": "α :... | [
699,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_left_cancel | [] | [
435,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.eventually_eq_or_eq_zero_of_isLocalMin_norm | [
{
"state_after": "E : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℂ E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℂ F\ninst✝ : StrictConvexSpace ℝ F\nf : E → ℂ\nc : E\nhf : ∀ᶠ (z : E) in 𝓝 c, DifferentiableAt ℂ f z\nhc : IsLocalMin (norm ∘ f) c\nh : ¬f c = 0\n⊢ ∀ᶠ (z : E) i... | [
354,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Std/Data/List/Lemmas.lean | List.prefix_append | [] | [
1559,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1559,
9
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_fin_succ_eq_det_submatrix | [
{
"state_after": "m : Type u\nn✝ : Type v\nα : Type w\ninst✝⁴ : DecidableEq n✝\ninst✝³ : Fintype n✝\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nn : ℕ\nA : Matrix (Fin (Nat.succ n)) (Fin (Nat.succ n)) α\ni j : Fin (Nat.succ n)\n⊢ ∑ x : Fin (Nat.succ n), (-1) ^ (↑j + ↑x) * Pi.single i 1 x * d... | [
429,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate_mod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ rotate l (n % length l) = rotate l n",
"tactic": "simp [rotate]"
}
] | [
38,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieModule.mem_maxTrivSubmodule | [] | [
132,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_norm_smul | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.160196\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns t : Set E\na : ℝ\ninst✝² : IsROrC 𝕜\ninst✝¹ : Module 𝕜 E\ninst✝ : IsScalarTower ℝ 𝕜 E\nhs : Balanced 𝕜 s\nr : 𝕜\nx : E\n⊢ sInf {r_1 | 0 < r_1 ∧ ‖r‖ • x ∈ r_1 • s} = sInf {r_1 | 0 < r_1 ∧ r • x... | [
319,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.eqOn_closure | [] | [
885,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_succ_le | [
{
"state_after": "S : Set Ordinal\na b : Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\nha : a ∈ S\nhb : enumOrd S b < a\n⊢ sInf (S ∩ {b_1 | ∀ (c : Ordinal), c < succ b → enumOrd S c < b_1}) ≤ a",
"state_before": "S : Set Ordinal\na b : Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\nha : a ∈ S\nhb : e... | [
2236,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2232,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.K'.elim_update_rev | [
{
"state_after": "case h\na b c d b' : List Γ'\nx : K'\n⊢ update (elim a b c d) rev b' x = elim a b' c d x",
"state_before": "a b c d b' : List Γ'\n⊢ update (elim a b c d) rev b' = elim a b' c d",
"tactic": "funext x"
},
{
"state_after": "no goals",
"state_before": "case h\na b c d b' : List... | [
1288,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1287,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.dense_image | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2172\nδ : Type ?u.2175\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ni : α → β\ndi✝ di : DenseInducing i\ns : Set α\nH : Dense (i '' s)\nx : α\n⊢ x ∈ closure s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2172\nδ : Type ?u.2... | [
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10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Topology/Sober.lean | IsGenericPoint.def | [] | [
47,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Analysis/Calculus/ParametricIntervalIntegral.lean | intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : IsROrC 𝕜\nμ : MeasureTheory.Measure ℝ\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : CompleteSpace E\nH : Type u_2\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\na b ε : ℝ\nbound : ℝ → ℝ\nF : H → ℝ... | [
51,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
8
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_smul_deriv | [] | [
1431,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1428,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.extraction_forall_of_frequently | [
{
"state_after": "ι : Type ?u.59096\nι' : Type ?u.59099\nα : Type ?u.59102\nβ : Type ?u.59105\nγ : Type ?u.59108\nP : ℕ → ℕ → Prop\nh : ∀ (n a : ℕ), ∃ b, b > a ∧ P n b\n⊢ ∃ φ, StrictMono φ ∧ ∀ (n : ℕ), P n (φ n)",
"state_before": "ι : Type ?u.59096\nι' : Type ?u.59099\nα : Type ?u.59102\nβ : Type ?u.59105\n... | [
488,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_of_mem_insert_of_ne | [] | [
1125,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | inv_pow_sub_of_lt | [
{
"state_after": "no goals",
"state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na✝ : G₀\nm n : ℕ\na : G₀\nh : n < m\n⊢ a⁻¹ ^ (m - n) = (a ^ m)⁻¹ * a ^ n",
"tactic": "rw [pow_sub_of_lt a⁻¹ h, inv_pow, inv_pow, inv_inv]"
}
] | [
49,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.local_hom_TFAE | [
{
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319,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_differentiableOn_iff | [] | [
312,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
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Mathlib/Algebra/Opposites.lean | MulOpposite.unop_surjective | [] | [
171,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.isSupFiniteCompact_iff_isSupClosedCompact | [] | [
285,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mem_Iio_self_add | [] | [
1289,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1289,
1
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Mathlib/Data/Set/Basic.lean | Set.nontrivial_iff_pair_subset | [] | [
2481,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2478,
1
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Mathlib/Order/Concept.lean | extentClosure_Union₂ | [] | [
134,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.edist_iterate_succ_le_geometric | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf✝ : α → β\nx✝ y : α\nr : ℝ≥0∞\nf : α → α\nhf : LipschitzWith K f\nx : α\nn : ℕ\n⊢ edist ((f^[n]) x) ((f^[n] ∘ f) x) ≤ ↑K ^ n * edist x (f x)",
... | [
280,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.coe_mk' | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.homIso_hom | [] | [
298,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Order/RelClasses.lean | of_eq | [] | [
32,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Data/Fintype/Quotient.lean | Quotient.finChoice_eq | [
{
"state_after": "ι : Type u_1\ninst✝² : DecidableEq ι\ninst✝¹ : Fintype ι\nα : ι → Type u_2\ninst✝ : (i : ι) → Setoid (α i)\nf : (i : ι) → α i\n⊢ Quotient.liftOn\n (Quotient.recOn Finset.univ.val (fun l => finChoiceAux l fun i x => Quotient.mk (inst✝ i) (f i))\n (_ :\n ∀ (a b : List ι) (h ... | [
87,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_fdiv_cancel_left | [] | [
217,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
216,
9
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_self | [
{
"state_after": "no goals",
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"tactic": "simpa only [mul_one] using mul_div_cancel 1 h"
}
] | [
967,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_of_larger_base_of_injective | [
{
"state_after": "no goals",
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232,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_add_lt | [] | [
187,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Data/Real/Basic.lean | Real.sSup_nonneg | [
{
"state_after": "case inl\nx y : ℝ\nhS : ∀ (x : ℝ), x ∈ ∅ → 0 ≤ x\n⊢ 0 ≤ sSup ∅\n\ncase inr.intro\nx y✝ : ℝ\nS : Set ℝ\nhS : ∀ (x : ℝ), x ∈ S → 0 ≤ x\ny : ℝ\nhy : y ∈ S\n⊢ 0 ≤ sSup S",
"state_before": "x y : ℝ\nS : Set ℝ\nhS : ∀ (x : ℝ), x ∈ S → 0 ≤ x\n⊢ 0 ≤ sSup S",
"tactic": "rcases S.eq_empty_or_non... | [
860,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_congr | [] | [
164,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_add | [] | [
167,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.eq_mul_inv_iff_mul_eq | [] | [
2169,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2167,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_transpose_row_self | [
{
"state_after": "case h\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\nb : n → α\ni j : n\n⊢ ↑(cramer Aᵀ) (A i) j = Pi.single i (det A) j",
"state_before": "m : Type u\nn : Type v\nα : Type w... | [
120,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_simple_isCompactElement | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα x : E\n⊢ ∀ (s : Set (IntermediateField F E)),\n Set.Nonempty s → DirectedOn (fun x x_1 => x ≤ x_1) s → F⟮x⟯ ≤ sSup s → ∃ x_1, x_1 ∈ s ∧ F⟮x⟯ ≤ x_1",
"state_before": "F : Type u_2\ninst✝² : ... | [
608,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.succ_nth_stream_eq_some_iff | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nifp_succ_n : IntFractPair K\n⊢ IntFractPair.stream v (n + 1) = some ifp_succ_n ↔\n ∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧ ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_... | [
95,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.map_div₂ | [] | [
175,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_sub_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ (fun x => x - a) ⁻¹' [[b, c]] = [[b + a, c + a]]",
"tactic": "simp [sub_eq_add_neg]"
}
] | [
446,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Equalizer.Sieve.compatible_iff | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP : Cᵒᵖ ⥤ Type (max v₁ u₁)\nX : C\nR : Presieve X\nS : Sieve X\nx : FirstObj P S.arrows\n⊢ Presieve.FamilyOfElements.SieveCompatible ((firstObjEqFamily P S.arrows).hom x) ↔ firstMap P S x = secondMap P S x",
"state_before": "C : Type u₁\ninst✝ : Category C\... | [
907,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.natDegree_basis | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nv : ι → F\ni j : ι\nhvs : Set.InjOn v ↑s\nhi : i ∈ s\nH : ∀ (j : ι), j ∈ Finset.erase s i → basisDivisor (v i) (v j) ≠ 0\n⊢ natDegree (Lagrange.basis s v i) = card s - 1",
"state_before": "F : Type u_2\ninst... | [
249,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.card_toFinset | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\ninst✝ : Fintype ↑s\nh : Set.Finite s\n⊢ Fintype.card { x // x ∈ Finite.toFinset h } = Fintype.card ↑s",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\ninst✝ : Fintype ↑s\nh : Set.Finite s\n⊢ Finset.card... | [
1261,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/Data/Finmap.lean | Multiset.coe_keys | [] | [
36,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Std/Data/Rat/Basic.lean | Rat.sub.aux | [
{
"state_after": "a b : Rat\ng ad bd : Nat\nhg : g = Nat.gcd a.den b.den\nhad : ad = a.den / g\nhbd : bd = b.den / g\nthis :\n let den := ad * (-b).den;\n let num := a.num * ↑bd + (-b).num * ↑ad;\n Nat.gcd (Int.natAbs num) g = Nat.gcd (Int.natAbs num) den\n⊢ let den := ad * b.den;\n let num := a.num * ↑bd -... | [
242,
13
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
236,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinian.wellFounded_submodule_lt | [] | [
69,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | cauchy_map_of_uniformCauchySeqOn_fderiv | [
{
"state_after": "ι : Type u_3\nl : Filter ι\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\n𝕜 : Type u_4\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E → E →L[𝕜] G\nx✝ : E\ns : Set ... | [
256,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.eq_empty | [
{
"state_after": "x : ZFSet\n⊢ (∀ (z : ZFSet), z ∈ x ↔ z ∈ ∅) ↔ ∀ (y : ZFSet), ¬y ∈ x",
"state_before": "x : ZFSet\n⊢ x = ∅ ↔ ∀ (y : ZFSet), ¬y ∈ x",
"tactic": "rw [ext_iff]"
},
{
"state_after": "no goals",
"state_before": "x : ZFSet\n⊢ (∀ (z : ZFSet), z ∈ x ↔ z ∈ ∅) ↔ ∀ (y : ZFSet), ¬y ∈ x"... | [
854,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_mul_eq_mul_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.40092\nG : Type ?u.40095\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / b * c = a * c / b",
"tactic": "simp"
}
] | [
565,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Logic/Basic.lean | ite_eq_left_iff | [] | [
1154,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
9
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_fst | [] | [
1612,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1610,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.append | [] | [
227,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.range_one | [] | [
3000,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2999,
1
] |
Mathlib/Data/List/Basic.lean | List.pmap_append | [
{
"state_after": "case nil\nι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ : List α\np : ι → Prop\nf : (a : ι) → p a → α\nl₁ l₂ : List ι\nh✝ : ∀ (a : ι), a ∈ l₁ ++ l₂ → p a\nh : ∀ (a : ι), a ∈ [] ++ l₂ → p a\n⊢ pmap f ([] ++ l₂) h = pmap f [] (_ : ∀ (a : ι), a ∈ [] → p a) ++ pmap f l₂ (_ ... | [
3219,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3211,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_inf | [] | [
1237,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.map_X | [
{
"state_after": "case h\nR : Type u_2\ninst✝² : Semiring R\nS : Type u_1\nT : Type ?u.2938579\ninst✝¹ : Semiring S\ninst✝ : Semiring T\nf : R →+* S\ng : S →+* T\nn✝ : ℕ\n⊢ ↑(coeff S n✝) (↑(map f) X) = ↑(coeff S n✝) X",
"state_before": "R : Type u_2\ninst✝² : Semiring R\nS : Type u_1\nT : Type ?u.2938579\ni... | [
1702,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1700,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_zero | [] | [
1053,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Mathlib/Data/Int/Log.lean | Int.clog_one_right | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\n⊢ clog b 1 = 0",
"tactic": "rw [clog_of_one_le_right _ le_rfl, Nat.ceil_one, Nat.clog_one_right, Int.ofNat_zero]"
}
] | [
267,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.exists_large_model_of_infinite_model | [
{
"state_after": "case intro\nL : Language\nT✝ : Theory L\nα : Type w\nn : ℕ\nT' T : Theory L\nκ : Cardinal\nM : Type w'\ninst✝² : Structure L M\ninst✝¹ : M ⊨ T\ninst✝ : Infinite M\nN : ModelType (LHom.onTheory (lhomWithConstants L (Quotient.out κ)) T ∪ distinctConstantsTheory L Set.univ)\n⊢ ∃ N, lift κ ≤ (#↑N)... | [
189,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul_inv_cancel | [
{
"state_after": "case c\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : Nontrivial R\ninst✝¹ : OreSet R⁰\ninst✝ : NoZeroDivisors R\nx : OreLocalization R R⁰\nh✝ : x ≠ 0\nr : R\ns : { x // x ∈ R⁰ }\nh : r /ₒ s ≠ 0\n⊢ r /ₒ s * (r /ₒ s)⁻¹ = 1",
"state_before": "R : Type u_1\ninst✝³ : Ring R\ninst✝² : Nontrivial R\ni... | [
928,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
11
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.fg_iff | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\ninst✝ : Structure L M\n⊢ FG L M ↔ ∃ S, Set.Finite S ∧ LowerAdjoint.toFun (closure L) S = ⊤",
"tactic": "rw [fg_def, Substructure.fg_def]"
}
] | [
214,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Topology/Sequences.lean | isSeqClosed_iff_isClosed | [] | [
202,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/PFun.lean | PFun.preimage_subset_core | [] | [
510,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.284395\nγ : Type ?u.284398\nδ : Type ?u.284401\nι : Type ?u.284404\nR : Type ?u.284407\nR' : Type ?u.284410\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
1586,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1580,
1
] |
src/lean/Init/Control/Lawful.lean | bind_pure_unit | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m PUnit\n⊢ (do\n x\n pure PUnit.unit) =\n x",
"tactic": "rw [bind_pure]"
}
] | [
72,
17
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
71,
9
] |
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