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/RingTheory/Ideal/Operations.lean | Submodule.mem_annihilator_span | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.12996\nG : Type ?u.12999\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI J : Ideal R\nN P : Submodule R M\ns : Set M\nr : R\n⊢ (∀ (n : M), n ∈ span R s → r • n = 0) ↔ ∀ (n : ↑s), r • ↑n = 0",
"state_before": "R : Type u\nM : Typ... | [
77,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_mul_cancel_right_of_invertible | [] | [
366,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.leAdd_apply | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_eq_coe_nnreal | [] | [
206,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.leftLim | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : ConditionallyCompleteLinearOrder β\ninst✝¹ : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\nhf : Monotone f\nx✝ y✝ x y : α\nh : x ≤ y\n⊢ leftLim f x ≤ leftLim f y",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : L... | [
132,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.ne_of_lt | [] | [
330,
46
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
329,
1
] |
Mathlib/Algebra/AddTorsor.lean | vsub_sub_vsub_cancel_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 p3 : P\n⊢ p1 -ᵥ p3 - (p2 -ᵥ p3) = p1 -ᵥ p2",
"tactic": "rw [← vsub_vadd_eq_vsub_sub, vsub_vadd]"
}
] | [
176,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Invertible.lean | one_sub_invOf_two | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Ring α\ninst✝ : Invertible 2\n⊢ 2 * (1 - ⅟2) = 2 * ⅟2",
"tactic": "rw [mul_sub, mul_invOf_self, mul_one, ← one_add_one_eq_two, add_sub_cancel]"
}
] | [
265,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/CategoryTheory/Limits/FullSubcategory.lean | CategoryTheory.Limits.hasColimit_of_closed_under_colimits | [] | [
140,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_div_div_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.8170\nM₀ : Type ?u.8173\nG₀ : Type u_1\nM₀' : Type ?u.8179\nG₀' : Type ?u.8182\nF : Type ?u.8185\nF' : Type ?u.8188\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\nhc : c ≠ 0\n⊢ a / c / (b / c) = a / b",
"tactic": "rw [div_d... | [
132,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.sq_add_sq | [
{
"state_after": "case inl\nK : Type ?u.822912\nR : Type ?u.822915\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ZMod p\nhp2 : p = 2\n⊢ ∃ a b, a ^ 2 + b ^ 2 = x\n\ncase inr\nK : Type ?u.822912\nR : Type ?u.822915\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ZMod p\nhp_odd : p % 2 = 1\n⊢ ∃ a b, a ^ 2 + b ^ 2 = x",
"state_bef... | [
324,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.interior_union_left | [] | [
1380,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1375,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.eq_one_of_lt_two | [
{
"state_after": "n : ℕ+\nh : n < 2\n⊢ n = 1",
"state_before": "n : ℕ+\n⊢ n < 2 → n = 1",
"tactic": "intro h"
},
{
"state_after": "case a\nn : ℕ+\nh : n < 2\n⊢ n ≤ 1\n\ncase a\nn : ℕ+\nh : n < 2\n⊢ 1 ≤ n",
"state_before": "n : ℕ+\nh : n < 2\n⊢ n = 1",
"tactic": "apply le_antisymm"
},
... | [
108,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_congr_perm | [
{
"state_after": "R : Type u_4\ninst✝¹⁶ : Semiring R\nM : Type u_3\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nN : Type ?u.482812\ninst✝¹³ : AddCommMonoid N\ninst✝¹² : Module R N\nP : Type ?u.482842\ninst✝¹¹ : AddCommMonoid P\ninst✝¹⁰ : Module R P\nM' : Type ?u.482872\ninst✝⁹ : AddCommGroup M'\ninst✝⁸ : M... | [
720,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.toSubalgebra_le_toSubalgebra | [] | [
595,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_image_sub_le' | [] | [
624,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | Differentiable.norm_sq | [] | [
248,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/Semicontinuous.lean | IsOpen.lowerSemicontinuousWithinAt_indicator | [] | [
224,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haarMeasure_self | [
{
"state_after": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : T2Space G\ninst✝² : TopologicalGroup G\ninst✝¹ : MeasurableSpace G\ninst✝ : BorelSpace G\nK₀ : PositiveCompacts G\nthis : LocallyCompactSpace G\n⊢ ↑↑(haarMeasure K₀) ↑K₀ = 1",
"state_before": "G : Type u_1\ninst✝⁵ : Grou... | [
640,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.self_sub_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.16691\ninst✝¹ : Semiring R✝\nf✝ : R✝[X]\nR : Type u_1\ninst✝ : Ring R\nf : R[X]\n⊢ f - ↑C (leadingCoeff f) * X ^ natDegree f = eraseLead f",
"tactic": "rw [C_mul_X_pow_eq_monomial, self_sub_monomial_natDegree_leadingCoeff]"
}
] | [
87,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.glueDist_triangle_inl_inr_inr | [
{
"state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝² : MetricSpace X\ninst✝¹ : MetricSpace Y\nΦ✝ : Z → X\nΨ✝ : Z → Y\nε✝ : ℝ\ninst✝ : Nonempty Z\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\nx : X\ny z : Y\n⊢ (⨅ (p : Z), dist x (Φ p) + dist z (Ψ p)) + ε ≤ (⨅ (p : Z), dist x (Φ p) + dist y (Ψ p)) + ε + dist y z",
"s... | [
124,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
9
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_isMinOn | [
{
"state_after": "case intro.intro.intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.35524\ninst✝⁴ : ConditionallyCompleteLinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ns : Set β\nhs : IsCompact s\nne_s : Set.Nonempty s\nf : β → α\nhf ... | [
245,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.coe_ne_infty | [] | [
100,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.smul_coe | [] | [
1079,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.zero_ne_one | [
{
"state_after": "a b c : ℚ\n⊢ 1 ≠ 0",
"state_before": "a b c : ℚ\n⊢ 0 ≠ 1",
"tactic": "rw [ne_comm, ← divInt_one_one, divInt_ne_zero one_ne_zero]"
},
{
"state_after": "no goals",
"state_before": "a b c : ℚ\n⊢ 1 ≠ 0",
"tactic": "exact one_ne_zero"
}
] | [
287,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
11
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.leftInv_eq_inv | [] | [
235,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.descFactorial_zero | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.eventually_ne | [] | [
99,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.15946\nδ : Type ?u.15949\ninst✝² : AddCommMonoid α\ninst✝¹ : TopologicalSpace α\nf g : β → α\na b : α\ns : Finset β\ninst✝ : IsEmpty β\n⊢ HasSum f 0",
"tactic": "convert @hasSum_zero α β _ _"
}
] | [
92,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.mk_le_mk | [] | [
319,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementarySubstructure.elementarilyEquivalent | [] | [
469,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/GroupTheory/Torsion.lean | CommMonoid.primaryComponent.disjoint | [
{
"state_after": "case intro.zero.intro\nG : Type u_1\nH : Type ?u.192353\ninst✝ : CommMonoid G\np : ℕ\nhp : Fact (Nat.Prime p)\np' : ℕ\nhp' : Fact (Nat.Prime p')\nhne : p ≠ p'\ng : G\nhn : orderOf g = p ^ Nat.zero\nn' : ℕ\nhn' : orderOf g = p' ^ n'\n⊢ g = 1\n\ncase intro.succ.intro\nG : Type u_1\nH : Type ?u.1... | [
256,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.diam_range | [] | [
202,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolRing_symmDiff | [] | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.fg_adjoin_finset | [] | [
924,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.ofFin_val | [
{
"state_after": "n : ℕ\ni : Fin (2 ^ n)\n⊢ ↑i < 2 ^ n",
"state_before": "n : ℕ\ni : Fin (2 ^ n)\n⊢ Bitvec.toNat (ofFin i) = ↑i",
"tactic": "rw [ofFin, toNat_ofNat, Nat.mod_eq_of_lt]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\ni : Fin (2 ^ n)\n⊢ ↑i < 2 ^ n",
"tactic": "apply... | [
82,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.VectorsProdEqOne.rotate_rotate | [] | [
447,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.mono_iff_kernel_ι_eq_zero | [] | [
271,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Logic/Equiv/Fin.lean | Fin.preimage_apply_01_prod' | [] | [
71,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_pure | [] | [
1992,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1991,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasFDerivAt.exp | [] | [
284,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Order/Atoms.lean | IsAtom.inf_eq_bot_of_ne | [] | [
211,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/CategoryTheory/Closed/FunctorCategory.lean | CategoryTheory.Functor.ihom_ev_app | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Order/Group/OrderIso.lean | le_inv' | [] | [
65,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/PathConnected.lean | Path.continuous_uncurry_extend_of_continuous_family | [
{
"state_after": "X✝ : Type ?u.327951\nY : Type ?u.327954\ninst✝³ : TopologicalSpace X✝\ninst✝² : TopologicalSpace Y\nx y z : X✝\nι✝ : Type ?u.327969\nγ✝ : Path x y\nX : Type u_1\nι : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace ι\na b : ι → X\nγ : (t : ι) → Path (a t) (b t)\nh : Continuous ↿... | [
503,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_zero | [
{
"state_after": "case inl\nl : Type ?u.265241\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nht : Subsingleton α\n⊢ 0⁻¹ = 0\n\ncase inr\nl : Type ?u.265241\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n... | [
498,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Energy.lean | Finpartition.coe_energy | [
{
"state_after": "α : Type u_2\ninst✝² : DecidableEq α\ns : Finset α\nP : Finpartition s\nG : SimpleGraph α\ninst✝¹ : DecidableRel G.Adj\n𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\n⊢ ↑((∑ uv in offDiag P.parts, SimpleGraph.edgeDensity G uv.fst uv.snd ^ 2) / ↑(card P.parts ^ 2)) =\n ↑(∑ uv in offDiag P.par... | [
68,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/Order.lean | nhds_true | [] | [
907,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.blockTriangular_blockDiagonal' | [
{
"state_after": "case mk.mk\nα : Type u_1\nβ : Type ?u.31715\nm : Type ?u.31718\nn : Type ?u.31721\no : Type ?u.31724\nm' : α → Type u_2\nn' : α → Type ?u.31734\nR : Type v\ninst✝² : CommRing R\nM N : Matrix m m R\nb : m → α\ninst✝¹ : Preorder α\ninst✝ : DecidableEq α\nd : (i : α) → Matrix (m' i) (m' i) R\ni :... | [
116,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/List/Range.lean | List.enumFrom_eq_zip_range' | [] | [
191,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_ord_compl | [
{
"state_after": "case inl\np : ℕ\n⊢ factorization (0 / p ^ ↑(factorization 0) p) = Finsupp.erase p (factorization 0)\n\ncase inr\nn p : ℕ\nhn : n ≠ 0\n⊢ factorization (n / p ^ ↑(factorization n) p) = Finsupp.erase p (factorization n)",
"state_before": "n p : ℕ\n⊢ factorization (n / p ^ ↑(factorization n) p... | [
555,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Algebra/Jordan/Basic.lean | two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_add | [
{
"state_after": "A : Type u_1\ninst✝¹ : NonUnitalNonAssocRing A\ninst✝ : IsCommJordan A\na b : A\n⊢ 2 • ⁅↑L a, ↑L (a * b)⁆ + 2 • ⁅↑L b, ↑L (b * a)⁆ + ⁅↑L b, ↑L (a * a)⁆ + ⁅↑L a, ↑L (b * b)⁆ = 0",
"state_before": "A : Type u_1\ninst✝¹ : NonUnitalNonAssocRing A\ninst✝ : IsCommJordan A\na b : A\n⊢ 2 • (⁅↑L a,... | [
183,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Algebra/Associated.lean | Associated.comm | [] | [
402,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
11
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_zero | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/MeasureTheory/Group/Pointwise.lean | MeasurableSet.const_smul_of_ne_zero | [
{
"state_after": "G₀ : Type u_1\nα : Type u_2\ninst✝⁴ : GroupWithZero G₀\ninst✝³ : MulAction G₀ α\ninst✝² : MeasurableSpace G₀\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSMul G₀ α\ns : Set α\nhs : MeasurableSet s\na : G₀\nha : a ≠ 0\n⊢ MeasurableSet ((fun x => a⁻¹ • x) ⁻¹' s)",
"state_before": "G₀ : Typ... | [
39,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Order/Chain.lean | IsChain.directed | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nr : α → α → Prop\nc✝ c₁ c₂ c₃ s t : Set α\na✝ b✝ x y : α\ninst✝ : IsRefl α r\nf : β → α\nc : Set β\nh : IsChain (f ⁻¹'o r) c\nx✝¹ x✝ : { a // a ∈ c }\na : β\nha : a ∈ c\nb : β\nhb : b ∈ c\nhab : a = b\n⊢ ∃ a, a ∈ c ∧ r (f b) (f a)",
"state_before": "α : Type u_2... | [
128,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
11
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.addVal_apply_of_ne | [] | [
1373,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.continuousOn | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
225,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/Instances/RatLemmas.lean | Rat.not_countably_generated_nhds_infty_opc | [
{
"state_after": "p q : ℚ\ns t : Set ℚ\na✝ : IsCountablyGenerated (𝓝 ∞)\n⊢ False",
"state_before": "p q : ℚ\ns t : Set ℚ\n⊢ ¬IsCountablyGenerated (𝓝 ∞)",
"tactic": "intro"
},
{
"state_after": "p q : ℚ\ns t : Set ℚ\na✝ : IsCountablyGenerated (𝓝 ∞)\nthis : IsCountablyGenerated (comap OnePoint.s... | [
72,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableAt.ccosh | [] | [
463,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_init_self | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (↑castSucc i)\ni : Fin n\ny : α (↑castSucc i)\nz : α (last n)\nj : Fin (n + 1)\n⊢ snoc (init q) (q (last n)) j = q j",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last... | [
552,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.aedisjoint_compl_right | [] | [
165,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Topology/Separation.lean | disjoint_nhdsSet_nhds | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : RegularSpace α\na : α\ns : Set α\nh : RegularSpace α ↔ ∀ (a : α) (s : Set α), Disjoint (𝓝ˢ s) (𝓝 a) ↔ ¬a ∈ closure s\n⊢ Disjoint (𝓝ˢ s) (𝓝 a) ↔ ¬a ∈ closure s",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpa... | [
1524,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/CategoryTheory/Category/Bipointed.lean | bipointedToPointedFst_comp_forget | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Aesop/BuiltinRules.lean | Aesop.BuiltinRules.not_intro | [] | [
43,
45
] | ca73109cc40837bc61df8024c9016da4b4f99d4c | https://github.com/JLimperg/aesop | [
43,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_injective | [] | [
325,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Logic/Equiv/Fintype.lean | Equiv.extendSubtype_apply_of_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.152201\ninst✝³ : Fintype α\ninst✝² : DecidableEq β\ne✝ : Perm α\nf : α ↪ β\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ne : { x // p x } ≃ { x // q x }\nx : α\nhx : p x\n⊢ ↑(subtypeCongr e (toCompl e)) x = ↑(↑e { val := x, property := hx })",
... | [
124,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_equiv_normalizer_eq | [
{
"state_after": "case h\nG : Type u_1\nG' : Type ?u.627985\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.627994\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ : G →* N\nH : Subgroup G\nf : G ≃* N\nx : N\n⊢ x ∈ map (MulEquiv.toMonoidHom f) (normalizer H) ↔ x ∈ normalizer (map (MulEquiv.toMonoidHom ... | [
3248,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3240,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.term_atom_pf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommMonoid α\nx x' : α\nh : x = x'\n⊢ x = term 1 x' 0",
"tactic": "simp [term, h]"
}
] | [
238,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.mul_nat | [] | [
173,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.ofList_nil | [] | [
1258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_id | [] | [
1399,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_lt_of_lt_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.293833\nβ : Type ?u.293836\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a < b * c\n⊢ a < c * b",
"tactic": "rwa [mul_comm]"
}
] | [
1623,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
1
] |
Mathlib/GroupTheory/GroupAction/Option.lean | Option.smul_some | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Finmap.lean | Finmap.insert_union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns₁ s₂ : Finmap β\na₁ a₂ : AList β\n⊢ insert a b (⟦a₁⟧ ∪ ⟦a₂⟧) = insert a b ⟦a₁⟧ ∪ ⟦a₂⟧",
"tactic": "simp [AList.insert_union]"
}
] | [
614,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_zero | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.nonzero | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nhq : q ≠ 0\n⊢ ↑p ^ (-padicValRat p q) ≠ 0",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nhq : q ≠ 0\n⊢ padicNorm p q ≠ 0",
"tactic": "rw [padicNorm.eq_zpow_of_nonzero hq]"
},
{
"state_after": "case ha\np : ℕ\nhp : Fact (Nat.Prim... | [
140,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
11
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Iic | [] | [
99,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivAt.cpow | [
{
"state_after": "no goals",
"state_before": "f g : ℂ → ℂ\ns : Set ℂ\nf' g' x c : ℂ\nhf : HasDerivAt f f' x\nhg : HasDerivAt g g' x\nh0 : 0 < (f x).re ∨ (f x).im ≠ 0\n⊢ HasDerivAt (fun x => f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x",
"tactic": "simpa only [aux] using... | [
180,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_sup | [] | [
326,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
9
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.homOfPair.val | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.left_distrib | [
{
"state_after": "no goals",
"state_before": "q : ℕ+\nx y z : X q\n⊢ x * (y + z) = x * y + x * z",
"tactic": "ext <;> dsimp <;> ring"
}
] | [
297,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Topology/Constructions.lean | closure_subtype | [] | [
1086,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_restrictVar | [
{
"state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.9538\nP : Type ?u.9541\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\ninst✝ : DecidableEq α\nt : Term L α\ns : Set α\nh✝ : ↑(varFinset t) ⊆ s\nv : α → M\n_a✝ : α\nh : ↑(varFinset ... | [
147,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_comp_of_one | [
{
"state_after": "case h\nα : Type u_3\nβ : Type ?u.22458\nι : Type ?u.22461\nM : Type u_2\nN : Type u_1\ninst✝¹ : One M\ninst✝ : One N\ns t : Set α\nf g✝ : α → M\na : α\ng : M → N\nhg : g 1 = 1\nx✝ : α\n⊢ mulIndicator s (g ∘ f) x✝ = (g ∘ mulIndicator s f) x✝",
"state_before": "α : Type u_3\nβ : Type ?u.224... | [
279,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_self | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\nK✝ K' : ChainComplex C ℕ\nf : K✝ ⟶ K'\nΔ Δ' Δ'' : SimplexCategory\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\nn : ℕ\n⊢ Splitting.ιSummand (Γ₀.splitting K) (Splitting.IndexSet.id [n].op) ≫ HomologicalComplex.Hom.f (P n) n =\n ... | [
365,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_smul | [
{
"state_after": "Ω : Type u_2\ninst✝¹⁰ : MeasurableSpace Ω\nR : Type u_1\ninst✝⁹ : SMul R ℝ≥0\ninst✝⁸ : SMul R ℝ≥0∞\ninst✝⁷ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝⁶ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝⁵ : TopologicalSpace Ω\ninst✝⁴ : OpensMeasurableSpace Ω\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0\ninst✝² : PseudoMetricSpace ... | [
399,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.nat_cast_mul_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\n⊢ comp (↑n * p) r = ↑n * comp p r",
"tactic": "rw [← C_eq_nat_cast, C_mul_comp, C_eq_nat_cast]"
}
] | [
625,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | LE.le.isOpenPosMeasure | [] | [
80,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Module/Projective.lean | Module.projective_def | [] | [
91,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.eq_reverse_iff | [
{
"state_after": "no goals",
"state_before": "U : Type ?u.1267\nV : Type u_1\nW : Type ?u.1273\ninst✝² : Quiver U\ninst✝¹ : Quiver V\ninst✝ : Quiver W\nh : HasInvolutiveReverse V\na b : V\nf : a ⟶ b\ng : b ⟶ a\n⊢ f = reverse g ↔ reverse f = g",
"tactic": "rw [←reverse_inj, reverse_reverse]"
}
] | [
82,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.card_bot | [] | [
127,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.pos_eq_zero | [
{
"state_after": "no goals",
"state_before": "l r : List Char\nit : Iterator\nh : ValidFor l r it\n⊢ it.i = 0 ↔ l = []",
"tactic": "simp [h.pos, Pos.ext_iff]"
}
] | [
539,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
538,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_subset_div_right | [] | [
650,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Logic/Relation.lean | Relation.church_rosser | [
{
"state_after": "case refl\nα : Type u_1\nβ : Type ?u.27200\nγ : Type ?u.27203\nδ : Type ?u.27206\nr : α → α → Prop\na b c d : α\nh : ∀ (a b c : α), r a b → r a c → ∃ d, ReflGen r b d ∧ ReflTransGen r c d\nhac : ReflTransGen r a c\n⊢ Join (ReflTransGen r) a c\n\ncase tail\nα : Type u_1\nβ : Type ?u.27200\nγ : ... | [
618,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.comap_subtype | [] | [
312,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Algebra/Ring/Defs.lean | neg_mul_eq_mul_neg | [] | [
309,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_principal | [] | [
171,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.hnot_hnot_sup_boundary | [
{
"state_after": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na✝ b a : α\n⊢ ￢￢a ≤ a",
"state_before": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na✝ b a : α\n⊢ ￢￢a ⊔ ∂ a = a",
"tactic": "rw [boundary, sup_inf_left, hnot_sup_self, inf_top_eq, sup_eq_right]"
},
{
"state_after": "no goals",
"state... | [
140,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Order/MinMax.lean | max_choice | [] | [
276,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.