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/LocalExtr.lean | isLocalExtr_const | [] | [
211,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.preimage_emetric_closedBall | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.688882\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nh : α ≃ᵢ β\nx : β\nr : ℝ≥0∞\n⊢ ↑h ⁻¹' EMetric.closedBall x r = EMetric.closedBall (↑(IsometryEquiv.symm h) x) r",
... | [
487,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.functor_obj_map_obj | [
{
"state_after": "case h.h\nX Y : TopCat\nf : X ⟶ Y\nhf : IsOpenMap ((forget TopCat).map f)\nU : Opens ↑Y\nx✝ : ↑Y\n⊢ x✝ ∈ ↑((IsOpenMap.functor hf).obj ((map f).obj U)) ↔ x✝ ∈ ↑((IsOpenMap.functor hf).obj ⊤ ⊓ U)",
"state_before": "X Y : TopCat\nf : X ⟶ Y\nhf : IsOpenMap ((forget TopCat).map f)\nU : Opens ↑Y... | [
372,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.toProd_mul | [] | [
177,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prodComparison_fst | [] | [
1260,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "n m : Nat\n⊢ n * m ≠ 0 ↔ n ≠ 0 ∧ m ≠ 0",
"tactic": "simp [mul_eq_zero, not_or]"
}
] | [
332,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
332,
11
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.isHomeomorphicTrivialFiberBundle_im | [] | [
53,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.append_stream_head_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\n⊢ [head s] ++ₛ tail s = s",
"tactic": "rw [cons_append_stream, nil_append_stream, Stream'.eta]"
}
] | [
552,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.toZNum_inj | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.446714\nm n : Num\nh : toZNum m = toZNum n\n⊢ m = n",
"tactic": "cases m <;> cases n <;> cases h <;> rfl"
}
] | [
782,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Init/Algebra/Classes.lean | incomp_iff_eq | [
{
"state_after": "α : Type u\nlt : α → α → Prop\ninst✝¹ : IsTrichotomous α lt\ninst✝ : IsIrrefl α lt\na b : α\nhab : a = b\n⊢ ¬lt b b ∧ ¬lt b b",
"state_before": "α : Type u\nlt : α → α → Prop\ninst✝¹ : IsTrichotomous α lt\ninst✝ : IsIrrefl α lt\na b : α\nhab : a = b\n⊢ ¬lt a b ∧ ¬lt b a",
"tactic": "rw... | [
424,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.min_eq_zero_iff | [
{
"state_after": "case mp\nm n k l : ℕ\n⊢ min m n = 0 → m = 0 ∨ n = 0\n\ncase mpr\nm n k l : ℕ\n⊢ m = 0 ∨ n = 0 → min m n = 0",
"state_before": "m n k l : ℕ\n⊢ min m n = 0 ↔ m = 0 ∨ n = 0",
"tactic": "constructor"
},
{
"state_after": "case mp\nm n k l : ℕ\nh : min m n = 0\n⊢ m = 0 ∨ n = 0",
... | [
124,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.isProj_iff_idempotent | [
{
"state_after": "case mp\nR : Type ?u.424574\ninst✝⁹ : Ring R\nE : Type ?u.424580\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.425139\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.425655\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type u_1\ninst✝² : Semiri... | [
398,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Algebra/Opposites.lean | AddOpposite.op_div | [] | [
424,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/Category/Ring/Constructions.lean | CommRingCat.subsingleton_of_isTerminal | [
{
"state_after": "no goals",
"state_before": "X : CommRingCat\nhX : IsTerminal X\n⊢ Subsingleton PUnit",
"tactic": "infer_instance"
}
] | [
174,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.σ_comp_σ | [
{
"state_after": "case a.h.h.mk.h\nn : ℕ\ni j : Fin (n + 1)\nH : i ≤ j\nk : ℕ\nhk : k < len [n + 1 + 1] + 1\n⊢ ↑(↑(Hom.toOrderHom (σ (↑Fin.castSucc i) ≫ σ j)) { val := k, isLt := hk }) =\n ↑(↑(Hom.toOrderHom (σ (Fin.succ j) ≫ σ i)) { val := k, isLt := hk })",
"state_before": "n : ℕ\ni j : Fin (n + 1)\nH ... | [
348,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_Ici | [] | [
1087,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1086,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.id_comp | [] | [
971,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
9
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.val_ratCast | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.add_lt_add | [
{
"state_after": "case inl\ny z t : EReal\nh2 : z < t\nh1 : ⊥ < y\n⊢ ⊥ + z < y + t\n\ncase inr\nx y z t : EReal\nh1 : x < y\nh2 : z < t\nhx : x ≠ ⊥\n⊢ x + z < y + t",
"state_before": "x y z t : EReal\nh1 : x < y\nh2 : z < t\n⊢ x + z < y + t",
"tactic": "rcases eq_or_ne x ⊥ with (rfl | hx)"
},
{
... | [
701,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Data/Set/Function.lean | Function.antitoneOn_of_rightInvOn_of_mapsTo | [] | [
1709,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/Algebra/BigOperators/NatAntidiagonal.lean | Finset.Nat.prod_antidiagonal_succ' | [
{
"state_after": "M : Type u_1\nN : Type ?u.4907\ninst✝¹ : CommMonoid M\ninst✝ : AddCommMonoid N\nn : ℕ\nf : ℕ × ℕ → M\n⊢ f (Prod.swap (0, n + 1)) * ∏ p in antidiagonal n, f (Prod.swap ((Prod.swap p).fst + 1, (Prod.swap p).snd)) =\n f (n + 1, 0) * ∏ p in antidiagonal n, f (p.fst, p.snd + 1)",
"state_befo... | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | pos_of_mul_pos_left | [] | [
400,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_def | [] | [
1436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Path.eq_cast_iff_heq | [] | [
130,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_map_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\n⊢ Disjoint (map f s) (map g t) ↔ ∀ (a : α), a ∈ s → ∀ (b : β), b ∈ t → f a ≠ g b",
"tactic": "simp [Disjoint, @eq_comm _ (f _) (g _)]"
}
] | [
2992,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2990,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.mk_π_app_left | [] | [
586,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.smul_eq_of_normal | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nG : Type u_1\ninst✝ : Group G\ng : G\nP : Sylow p G\nh : Normal ↑P\n⊢ g • P = P",
"tactic": "simp only [Sylow.smul_eq_iff_mem_normalizer, normalizer_eq_top.mpr h, mem_top]"
}
] | [
274,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_neg_iff_of_base_lt_one | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nh : 0 < x\n⊢ logb b x < 0 ↔ 1 < x",
"tactic": "rw [← @logb_one b, logb_lt_logb_iff_of_base_lt_one b_pos b_lt_one h zero_lt_one]"
}
] | [
298,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_inv_cancel | [
{
"state_after": "case intro.intro.intro\nR : Type ?u.613996\nA : Type u_1\nK : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : Algebra A K\ninst✝¹ : IsFractionRing A K\ninst✝ : IsDedekindDomain A\nI : FractionalIdeal A⁰ K\nhne : I ≠ 0\na : A\nJ : Ideal A\nha ... | [
548,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
11
] |
Mathlib/Algebra/Algebra/Basic.lean | LinearMap.map_algebraMap_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Semiring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : A →ₗ[R] B\na : A\nr : R\n⊢ ↑f (↑(algebraMap R A) r * a) = ↑(algebraMap R B) r * ↑f a",
"tactic": "rw [... | [
699,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Ioc_left | [] | [
187,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_le_iff_le_log | [] | [
336,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Data/Vector3.lean | Vector3.cons_head_tail | [] | [
112,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_of_image | [
{
"state_after": "case a\nR : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³... | [
875,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.contDiffAt_tan | [
{
"state_after": "no goals",
"state_before": "n : ℕ∞\nx : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"tactic": "exact_mod_cast h"
}
] | [
74,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/List/Zip.lean | List.nthLe_zip | [] | [
427,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.map_comp_ofLE | [] | [
362,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Order/UpperLower/Hom.lean | UpperSet.iciSupHom_apply | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.coeff_eq_zero_of_trailingDegree_lt | [] | [
266,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_add | [
{
"state_after": "case a.h\nl : Type ?u.926145\nm : Type u_1\nn : Type u_2\no : Type ?u.926154\nm' : o → Type ?u.926159\nn' : o → Type ?u.926164\nR : Type ?u.926167\nS : Type ?u.926170\nα : Type v\nβ : Type w\nγ : Type ?u.926177\ninst✝ : Add α\nM N : Matrix m n α\ni✝ : n\nx✝ : m\n⊢ (M + N)ᵀ i✝ x✝ = (Mᵀ + Nᵀ) i✝... | [
1990,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1988,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_mono_left | [] | [
158,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.ext | [] | [
146,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_smul_self_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.3140024\nE : Type ?u.3140027\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : F\nr : ℝ\n⊢ inner (r • x) x = r ... | [
1543,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1542,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurableSet_pi_of_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.147740\nβ : Type ?u.147743\nγ : Type ?u.147746\nδ : Type u_1\nδ' : Type ?u.147752\nι : Sort uι\ns✝ t✝ u : Set α\nπ : δ → Type u_2\ninst✝² : MeasurableSpace α\ninst✝¹ : (a : δ) → MeasurableSpace (π a)\ninst✝ : MeasurableSpace γ\ns : Set δ\nt : (i : δ)... | [
894,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Init/Function.lean | Function.rightInverse_of_injective_of_leftInverse | [] | [
107,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.mapsTo | [] | [
495,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
11
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_empty | [] | [
518,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.optionSubtype_symm_apply_apply_some | [] | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Pi/Algebra.lean | Function.surjective_pi_map | [] | [
413,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_left_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.147536\nγ : Type ?u.147539\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u✝ v : Finset α\na b : α\ns t u : Finset α\nx✝ : α\n⊢ x✝ ∈ s ∪ (t ∪ u) ↔ x✝ ∈ t ∪ (s ∪ u)",
"tactic": "simp only [mem_union, or_left_comm]"
}
] | [
1424,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | Commute.orderOf_mul_dvd_mul_orderOf | [] | [
404,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Std/Data/List/Init/Lemmas.lean | List.tailD_nil | [] | [
32,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
32,
14
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_iInter_eq_or_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.94856\nι : Sort ?u.94859\nι' : Sort ?u.94862\nι₂ : Sort ?u.94865\nκ : ι → Sort ?u.94870\nκ₁ : ι → Sort ?u.94875\nκ₂ : ι → Sort ?u.94880\nκ' : ι' → Sort ?u.94885\nb : β\np : β → Prop\ns : (x : β) → x = b ∨ p x → Set α\n⊢ (⋂... | [
845,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.repr_symm_single | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.771553\n𝕜 : Type u_2\ninst✝¹⁰ : IsROrC 𝕜\nE : Type u_3\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : InnerProductSpace 𝕜 E\nE' : Type ?u.771582\ninst✝⁷ : NormedAddCommGroup E'\ninst✝⁶ : InnerProductSpace 𝕜 E'\nF : Type ?u.771600\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ ... | [
387,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
11
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.id_apply | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.esymm_isSymmetric | [
{
"state_after": "σ : Type u_1\nR : Type u_2\nτ : Type ?u.175098\nS : Type ?u.175101\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S\ninst✝¹ : Fintype σ\ninst✝ : Fintype τ\nn : ℕ\ne✝ : Perm σ\n⊢ ↑(rename ↑e✝) (esymm σ R n) = esymm σ R n",
"state_before": "σ : Type u_1\nR : Type u_2\nτ : Type ?u.175098\nS ... | [
216,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.coe_ne_zero | [] | [
151,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Sigma/Lex.lean | Sigma.Lex.mono_right | [] | [
81,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.univ_le_of_forall_fin_meas_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1823883\nγ : Type ?u.1823886\nδ : Type ?u.1823889\nm m0 : MeasurableSpace α\nE : Type ?u.1823898\ninst✝³ : NormedAddCommGroup E\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\nμ : Measure α\nhm : m ≤ m0\ninst✝ : SigmaFinite (Measure.trim μ hm)\nC : ℝ≥0∞\... | [
1963,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1952,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.prime_def_le_sqrt | [
{
"state_after": "case inl\np : ℕ\np2 : 2 ≤ p\na : ∀ (m : ℕ), 2 ≤ m → m ≤ sqrt p → ¬m ∣ p\nthis : ∀ {m k : ℕ}, m ≤ k → 1 < m → p ≠ m * k\nm : ℕ\nm2 : 2 ≤ m\nl : m < p\nx✝ : m ∣ p\nk : ℕ\ne : p = m * k\nmk : m ≤ k\n⊢ False\n\ncase inr\np : ℕ\np2 : 2 ≤ p\na : ∀ (m : ℕ), 2 ≤ m → m ≤ sqrt p → ¬m ∣ p\nthis : ∀ {m k ... | [
146,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_le_sqrt | [
{
"state_after": "x y : ℝ\nh : x ≤ y\n⊢ toNNReal x ≤ toNNReal y",
"state_before": "x y : ℝ\nh : x ≤ y\n⊢ sqrt x ≤ sqrt y",
"tactic": "rw [sqrt, sqrt, NNReal.coe_le_coe, NNReal.sqrt_le_sqrt_iff]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : x ≤ y\n⊢ toNNReal x ≤ toNNReal y",
... | [
277,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Std/Data/List/Lemmas.lean | List.reverse_suffix | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ : List α✝\nx✝ : reverse l₁ <:+ reverse l₂\nr : List α✝\ne : r ++ reverse l₁ = reverse l₂\n⊢ l₁ ++ reverse r = l₂",
"tactic": "rw [← reverse_reverse l₁, ← reverse_append, e, reverse_reverse]"
},
{
"state_after": "no goals",
"s... | [
1620,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1618,
9
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.pow_smul_mem_closure_smul | [
{
"state_after": "case refine'_1\nα : Type ?u.11742\nG : Type ?u.11745\nM : Type u_2\nR : Type ?u.11751\nA : Type ?u.11754\ninst✝⁴ : Monoid M\ninst✝³ : AddMonoid A\ns✝ t u : Set M\nN : Type u_1\ninst✝² : CommMonoid N\ninst✝¹ : MulAction M N\ninst✝ : IsScalarTower M N N\nr : M\ns : Set N\nx : N\nhx : x ∈ closure... | [
111,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_lt_div_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.155109\nα : Type u_1\nβ : Type ?u.155115\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhb : b < 0\n⊢ 1 < a / b ↔ a < b",
"tactic": "rw [lt_div_iff_of_neg hb, one_mul]"
}
] | [
813,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Data/List/Perm.lean | List.erase_cons_subperm_cons_erase | [
{
"state_after": "case pos\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : a = b\n⊢ List.erase (a :: l) b <+~ a :: List.erase l b\n\ncase neg\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : ¬a = b\n⊢ List.erase (a :: l) b <+~ ... | [
819,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_lt_true | [] | [
677,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_diff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.42374\ninst✝ : PartialOrder α\na b c x : α\n⊢ x ∈ Iic a \\ {a} ↔ x ∈ Iio a",
"tactic": "simp [lt_iff_le_and_ne]"
}
] | [
806,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | Commute.list_sum_left | [] | [
42,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_one | [
{
"state_after": "ι : Type ?u.450637\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\n⊢ ∏ k in {0}, f k = f 0",
"state_before": "ι : Type ?u.450637\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β... | [
1268,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.comp_assoc | [] | [
805,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Orientation.map_neg | [] | [
126,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/Algebra/BigOperators/Fin.lean | finPiFinEquiv_apply | [] | [
433,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Part.lean | Part.none_ne_some | [] | [
201,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.canonicalEquiv_coeIdeal | [
{
"state_after": "case a\nR : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_3\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type u_2\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.1004372\ninst✝¹ : CommRing P''\ninst✝ : Algebra R... | [
947,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/GroupTheory/Torsion.lean | IsTorsionFree.prod | [] | [
416,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/Ring/Units.lean | Units.coe_neg_one | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
11
] |
Mathlib/Data/Finset/Finsupp.lean | Finsupp.mem_pi | [] | [
99,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.463074\nr : R\ne : ℕ\nn✝ m : σ\ns✝ : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\ninst✝ : Nontrivial R\ns : σ\nn : ℕ\n⊢ totalDegree (X s ^ n) = n",
"tactic": "simp [X_pow_eq_monomial, one_ne_zero]... | [
723,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_ret_comp | [] | [
1142,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.C_injective | [] | [
754,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_compl | [] | [
1823,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1822,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.card_sigma | [] | [
357,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofMul_one | [] | [
219,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_one | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ yn a1 1 = 1",
"tactic": "simp"
}
] | [
156,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | mul_cancel_left_mem_nonZeroDivisors | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.17057\nM' : Type ?u.17060\nM₁ : Type ?u.17063\nR : Type ?u.17066\nR' : Type u_1\nF : Type ?u.17072\ninst✝⁴ : MonoidWithZero M\ninst✝³ : MonoidWithZero M'\ninst✝² : CommMonoidWithZero M₁\ninst✝¹ : Ring R\ninst✝ : CommRing R'\nx y r : R'\nhr : r ∈ R'⁰\... | [
79,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.tendsto_log_comp_add_sub_log | [
{
"state_after": "case this\ny : ℝ\n⊢ Tendsto (fun x => 1 + y / x) atTop (𝓝 (1 + 0))\n\ny : ℝ\nthis : Tendsto (fun x => 1 + y / x) atTop (𝓝 (1 + 0))\n⊢ Tendsto (fun x => log (x + y) - log x) atTop (𝓝 0)",
"state_before": "y : ℝ\n⊢ Tendsto (fun x => log (x + y) - log x) atTop (𝓝 0)",
"tactic": "have ... | [
421,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.preimage_floor_zero | [] | [
261,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.IsLimit.lift_ι | [] | [
432,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/NumberTheory/FrobeniusNumber.lean | frobeniusNumber_pair | [
{
"state_after": "m n : ℕ\ncop : coprime m n\nhm : 1 < m\nhn : 1 < n\n⊢ IsGreatest {k | ¬∃ m_1 n_1, m_1 • m + n_1 • n = k} (m * n - m - n)",
"state_before": "m n : ℕ\ncop : coprime m n\nhm : 1 < m\nhn : 1 < n\n⊢ FrobeniusNumber (m * n - m - n) {m, n}",
"tactic": "simp_rw [FrobeniusNumber, AddSubmonoid.m... | [
86,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_annihilator | [] | [
56,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
src/lean/Init/Control/Lawful.lean | ReaderT.run_seqLeft | [] | [
210,
57
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
209,
9
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_preimage_of_injective_of_subset_range_lift | [] | [
2187,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2185,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_map' | [] | [
1834,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1833,
1
] |
Mathlib/Algebra/Bounds.lean | isGLB_inv' | [] | [
84,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.associator_naturality | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX Y : C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX₁ X₂ X₃ Y₁ Y₂ Y₃ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₂\nf₃ : X₃ ⟶ Y₃\n⊢ IsLimit.lift (ℬ (tensorObj ℬ Y₁ Y₂) Y₃).isLimit\n (BinaryFan.mk\n (BinaryFan.fst (ℬ (tensorObj ℬ X... | [
331,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_le_of_le_sub | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\nhle : b ≤ c\nh : a ≤ c - b\n⊢ a + b ≤ c",
"tactic": "match le.dest h with\n| ⟨d, hd⟩ =>\n apply @le.intro _ _ d\n rw [Nat.eq_add_of_sub_eq hle hd.symm]\n simp [Nat.add_comm, Nat.add_assoc, Nat.add_left_comm]"
},
{
"state_after": "a b ... | [
658,
58
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
653,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.Injective.iterate | [] | [
94,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.recOn_cons | [] | [
211,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasStrictFDerivAt.sum | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.296313\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.296408\... | [
338,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.center_le_radical | [] | [
294,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
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