file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.mem_polar_iff | [] | [
196,
10
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195,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.map_sub | [] | [
2279,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2278,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_prod | [] | [
1561,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1559,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.smulRight_one_one | [
{
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1182,
49
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Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.mul_aux | [
{
"state_after": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA B C : Finset α\nhA : Finset.Nonempty A\nhAB : A ⊆ B\nh : ∀ (A' : Finset α), A' ∈ erase (powerset B) ∅ → ↑(card (A * C)) / ↑(card A) ≤ ↑(card (A' * C)) / ↑(card A')\nA' : Finset α\nhAA' : A' ⊆ A\n⊢ card (A * C) * card A' ≤ card (A' * ... | [
137,
87
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Mathlib/Data/Complex/Exponential.lean | Complex.tanh_conj | [
{
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"tactic": "rw [tanh, sinh_conj, cosh_conj, ← map_div₀, tanh]"
}
] | [
705,
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Mathlib/Order/WithBot.lean | WithBot.some_le_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7924\nγ : Type ?u.7927\nδ : Type ?u.7930\na b : α\ninst✝ : LE α\n⊢ Option.some a ≤ Option.some b ↔ a ≤ b",
"tactic": "simp [LE.le]"
}
] | [
203,
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Mathlib/Order/CompleteLattice.lean | Prod.fst_iInf | [] | [
1858,
39
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.singularPart_sub | [
{
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1127,
74
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.exists_eq_pow_mul_and_not_dvd | [] | [
578,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.gc_set | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nideal_gc : GaloisConnection Ideal.span SetLike.coe\n⊢ GaloisConnection (fun s => zeroLocus 𝒜 s) fun t => ↑(vanishingIdeal t)",
"state_before": ... | [
145,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/Data/Ordmap/Ordset.lean | Ordset.pos_size_of_mem | [
{
"state_after": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nt : Ordset α\nh_mem : Ordnode.mem x ↑t = true\n⊢ 0 < size t",
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Mathlib/Order/Bounds/Basic.lean | upperBounds_empty | [
{
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"tactic": "simp only [upperBounds, eq_univ_iff_forall, mem_setOf_eq, ball_empty_iff, forall_true_iff]"
}
] | [
865,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.mul_diagonal | [
{
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_pos_iff | [] | [
2076,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2075,
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.as_sum | [
{
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"state_bef... | [
58,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_apply_fintype | [] | [
233,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.mem_uniformity' | [
{
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150,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.eq_iff_forall_dual_eq | [
{
"state_after": "𝕜 : Type v\ninst✝² : IsROrC 𝕜\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx y : E\n⊢ (∀ (g : Dual 𝕜 E), ↑g (x - y) = 0) ↔ ∀ (g : Dual 𝕜 E), ↑g x = ↑g y",
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161,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/Algebra/Squarefree.lean | Squarefree.gcd_right | [] | [
96,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.aemeasurable | [] | [
457,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
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Mathlib/Topology/Homotopy/Contractible.lean | ContinuousMap.Nullhomotopic.comp_right | [
{
"state_after": "case intro\nX : Type u_1\nY : Type u_2\nZ : Type u_3\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : C(X, Y)\ng : C(Y, Z)\ny : Y\nhy : Homotopic f (const X y)\n⊢ Nullhomotopic (comp g f)",
"state_before": "X : Type u_1\nY : Type u_2\nZ : Type u_3\... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Max.lean | IsTop.mono | [] | [
304,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.mul_kroneckerTMul_mul | [] | [
553,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
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Mathlib/Order/ModularLattice.lean | covby_sup_of_inf_covby_left | [] | [
150,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | quasiconvexOn_iff_le_max | [] | [
131,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Dynamics/PeriodicPts.lean | Function.Commute.minimalPeriod_of_comp_dvd_mul | [] | [
435,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_subset_iff_left | [] | [
1850,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1849,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.exists_of_le | [] | [
225,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/Order/Filter/Lift.lean | Filter.lift'_mono | [] | [
283,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
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Mathlib/LinearAlgebra/Dual.lean | Submodule.dualPairing_apply | [] | [
1237,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.nontrivial_iff | [] | [
1226,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
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Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.finish_v | [
{
"state_after": "u : XgcdType\nhr : r u = 0\nha : r u + ↑(b u) * q u = ↑(a u) := rq_eq u\n⊢ v (finish u) = v u",
"state_before": "u : XgcdType\nhr : r u = 0\n⊢ v (finish u) = v u",
"tactic": "let ha : u.r + u.b * u.q = u.a := u.rq_eq"
},
{
"state_after": "u : XgcdType\nhr : r u = 0\nha : ↑(b u)... | [
299,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ext_ring | [] | [
527,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
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Mathlib/Data/Part.lean | Part.bind_le | [
{
"state_after": "case mp\nα✝ : Type ?u.51205\nβ : Type u_1\nγ : Type ?u.51211\nα : Type u_1\nx : Part α\nf : α → Part β\ny : Part β\nh : x >>= f ≤ y\n⊢ ∀ (a : α), a ∈ x → f a ≤ y\n\ncase mpr\nα✝ : Type ?u.51205\nβ : Type u_1\nγ : Type ?u.51211\nα : Type u_1\nx : Part α\nf : α → Part β\ny : Part β\nh : ∀ (a : α... | [
631,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/RingTheory/Ideal/Cotangent.lean | Ideal.toCotangent_surjective | [] | [
87,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.divInt_zero | [] | [
126,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
126,
9
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_inv_cancel_left₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.14933\nM₀ : Type ?u.14936\nG₀ : Type u_1\nM₀' : Type ?u.14942\nG₀' : Type ?u.14945\nF : Type ?u.14948\nF' : Type ?u.14951\ninst✝ : GroupWithZero G₀\na b✝ c g h✝ x : G₀\nh : a ≠ 0\nb : G₀\n⊢ a * a⁻¹ * b = b",
"tactic": "simp [h]"
}
] | [
249,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderiv_sub | [] | [
524,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
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] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.map_eq_desc'_lift_left | [
{
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257,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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Mathlib/Data/Finmap.lean | Finmap.empty_union | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ : Finmap β\ns₁ : AList β\n⊢ ⟦∅⟧ ∪ ⟦s₁⟧ = ⟦s₁⟧",
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"tactic": "rw [← empty_toFinmap]"
},
{
"state_after": "no... | [
626,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Floor.lean | Int.fract_eq_iff | [
{
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"state_before": "F : Type ?u.161626\nα : Type u_1\nβ : Type ?u.161632\ninst✝¹ : LinearOrderedRi... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_zero | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mul_mem_cancel_left | [] | [
621,
24
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620,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_filter | [
{
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Mathlib/Analysis/Convex/Cone/Dual.lean | innerDualCone_singleton | [] | [
92,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | ne_one_of_nnnorm_ne_zero | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Lemmas.lean | Nat.add_div_left | [
{
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"tactic": "rw [Nat.add_comm, add_div_right x H]"
}
] | [
568,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_nodal_at_node | [
{
"state_after": "F : Type u_2\ninst✝ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\nhi : i ∈ s\n⊢ ∃ a, a ∈ s ∧ v i - v a = 0",
"state_before": "F : Type u_2\ninst✝ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\nhi : i ∈ s\n⊢ eval (v i) (nodal s v) = 0... | [
510,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_neg | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type ?u.43288\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nv₁ v₂ v₃ : V\n⊢ ∠ (-v₁) (-v₂) (-v₃) = ∠ v₁ v₂ v₃",
"tactic": "simpa only [zero_sub] using angle_const_sub 0 v... | [
124,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrOn.inter | [] | [
305,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_involutive | [] | [
579,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isPwo_iff_exists_monotone_subseq | [] | [
415,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.mem_of_frequently_of_tendsto | [] | [
1449,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.coe_toNat_eq_self | [
{
"state_after": "no goals",
"state_before": "m n : ℕ∞\n⊢ ↑(↑toNat ⊤) = ⊤ ↔ ⊤ ≠ ⊤",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ∞\nx✝ : ℕ\n⊢ ↑(↑toNat ↑x✝) = ↑x✝ ↔ ↑x✝ ≠ ⊤",
"tactic": "simp [toNat_coe]"
}
] | [
157,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.div_def | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableOn.norm | [] | [
282,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.ofNat'_one | [
{
"state_after": "α : Type ?u.179670\n⊢ (match (motive := Bool → Num → Num) true with\n | true => Num.bit1\n | false => Num.bit0)\n 0 =\n 1",
"state_before": "α : Type ?u.179670\n⊢ ofNat' 1 = 1",
"tactic": "erw [ofNat'_bit true 0, cond, ofNat'_zero]"
},
{
"state_after": "no goa... | [
246,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Combinatorics/Derangements/Basic.lean | derangements.Equiv.RemoveNone.mem_fiber | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.70902\ninst✝ : DecidableEq α\na : Option α\nf : Perm α\n⊢ f ∈ fiber a ↔ ∃ F, F ∈ derangements (Option α) ∧ ↑F none = a ∧ removeNone F = f",
"tactic": "simp [RemoveNone.fiber, derangements]"
}
] | [
129,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.ptendsto_iff_rtendsto | [] | [
236,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanCompIso_hom_app_zero | [] | [
364,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.tr_reaches₁ | [
{
"state_after": "case single\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂ → Prop\nH : Respects f₁ f₂ tr\na₁ : σ₁\na₂ : σ₂\naa : tr a₁ a₂\nb₁ c₁ : σ₁\nac : c₁ ∈ f₁ a₁\n⊢ ∃ b₂, tr c₁ b₂ ∧ Reaches₁ f₂ a₂ b₂\n\ncase tail\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf... | [
895,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.refl_apply | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type w'\ninst✝³ : Structure L M\ninst✝² : Structure L N\nP : Type ?u.257731\ninst✝¹ : Structure L P\nQ : Type ?u.257739\ninst✝ : Structure L Q\nx : M\n⊢ ↑(mk (_root_.Equiv.refl M)) x = x",
"state_before": "L : Language\nL' : Language\nM : Type w... | [
869,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.IsSymmetric.coe_toSelfAdjoint | [] | [
349,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.left_cancel_inv | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : Rack R\nx y y' : R\n⊢ x ◃⁻¹ y = x ◃⁻¹ y' → y = y'\n\ncase mpr\nR : Type u_1\ninst✝ : Rack R\nx y y' : R\n⊢ y = y' → x ◃⁻¹ y = x ◃⁻¹ y'",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y y' : R\n⊢ x ◃⁻¹ y = x ◃⁻¹ y' ↔ y = y'",
"tactic": "constructor"
}... | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/CategoryTheory/Subterminal.lean | CategoryTheory.IsSubterminal.mono_terminal_from | [] | [
67,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.norm_setToL1_le | [] | [
1243,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_succ_eq_succ_sum | [
{
"state_after": "case zero\n\n⊢ fib (zero + 1) = ∑ k in Finset.range zero, fib k + 1\n\ncase succ\nn : ℕ\nih : fib (n + 1) = ∑ k in Finset.range n, fib k + 1\n⊢ fib (succ n + 1) = ∑ k in Finset.range (succ n), fib k + 1",
"state_before": "n : ℕ\n⊢ fib (n + 1) = ∑ k in Finset.range n, fib k + 1",
"tacti... | [
305,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Topology/PathConnected.lean | JoinedIn.joined_subtype | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.563745\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.563760\nF : Set X\nh : JoinedIn F x y\n⊢ Continuous fun t => { val := ↑(somePath h) t, property := (_ : ↑(somePath h) t ∈ F) }",
"tactic": "cont... | [
850,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.mul_pos | [] | [
699,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.id | [] | [
2447,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2446,
11
] |
Mathlib/Order/Grade.lean | grade_ne_grade_iff | [] | [
194,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Order/Cover.lean | Wcovby.Ioo_eq | [] | [
109,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSets_piiUnionInter_of_disjoint | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nΩ : Type u_1\nι : Type u_2\nm0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsProbabilityMeasure μ\ns : ι → Set (Set Ω)\nS T : Set ι\nh_indep : iIndepSets s\nhST : Disjoint S T\nt1 t2 : Set Ω\np1 : Finset ι\nhp1 : ↑p1 ⊆ S\nf1 :... | [
425,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | BooleanRing.sup_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12720\nγ : Type ?u.12723\ninst✝² : BooleanRing α\ninst✝¹ : BooleanRing β\ninst✝ : BooleanRing γ\na b : α\n⊢ a + b + a * b = b + a + b * a",
"tactic": "ring"
}
] | [
200,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
src/lean/Init/Data/List/Basic.lean | List.cons_getElem_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nas : List α\nh : 0 < length (a :: as)\n⊢ getElem (a :: as) 0 h = a",
"tactic": "rfl"
}
] | [
22,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
21,
9
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_multiset_prod_of_monic | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : CommSemiring R\np : R[X]\nt : Multiset ι\nf : ι → R[X]\n⊢ (∀ (i : ι), i ∈ t → Monic (f i)) → Monic (Multiset.prod (Multiset.map f t))",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : CommSemiring ... | [
271,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/List/AList.lean | AList.mem_of_perm | [] | [
102,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.rank_lt_aleph0 | [
{
"state_after": "R : Type u\nM : Type v\nN : Type w\ninst✝⁷ : Ring R\ninst✝⁶ : StrongRankCondition R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : Module.Finite R M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : Module.Finite R N\n⊢ (⨆ (ι : { s // LinearIndependent R Subtype.val }), #↑↑ι) < ℵ... | [
68,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_of_lt | [
{
"state_after": "case intro\nn b x : ℕ\nhx : succ x ≠ 0\nhxb : succ x < b\n⊢ digits b (succ x) = [succ x]",
"state_before": "n b x : ℕ\nhx : x ≠ 0\nhxb : x < b\n⊢ digits b x = [x]",
"tactic": "rcases exists_eq_succ_of_ne_zero hx with ⟨x, rfl⟩"
},
{
"state_after": "case intro.intro\nn x : ℕ\nhx ... | [
135,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/RingTheory/Localization/Ideal.lean | IsLocalization.map_comap | [
{
"state_after": "case intro.intro\nR : Type u_2\ninst✝³ : CommSemiring R\nM : Submonoid R\nS : Type u_1\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : IsLocalization M S\nJ : Ideal S\nx : S\nhJ : x ∈ J\nr : R\ns : { x // x ∈ M }\nhx : mk' S r s = x\n⊢ x ∈ Ideal.map (algebraMap R S) (Ideal.comap (algeb... | [
78,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_lt_wf | [] | [
58,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_const_mul_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.59587\nE : Type ?u.59590\nF : Type u_3\nG : Type ?u.59596\nE' : Type ?u.59599\nF' : Type ?u.59602\nG' : Type ?u.59605\nE'' : Type ?u.59608\nF'' : Type ?u.59611\nG'' : Type ?u.59614\nR : Type ?u.59617\nR' : Type ?u.59620\n𝕜 : Type u_1\n... | [
301,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_pow | [] | [
381,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | AddSubgroup.normedMk.apply | [] | [
290,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | max_le_mul_of_one_le | [] | [
153,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mapEmbedding_apply | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_left_comm | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ a * (b * c) = b * (a * c)",
"tactic": "rw [← Int.mul_assoc, ← Int.mul_assoc, Int.mul_comm a]"
}
] | [
401,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
400,
11
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | Subsemiring.topologicalClosure_minimal | [] | [
127,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithZero.inv_zero | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Init/Algebra/Classes.lean | refl | [] | [
261,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.reindex_symm | [] | [
520,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_mono | [] | [
181,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | LocalHomeomorph.isBigO_congr | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\nE : Type u_3\ninst✝¹ : Norm E\nF : Type u_4\ninst✝ : Norm F\ne : LocalHomeomorph α β\nb : β\nhb : b ∈ e.target\nf : β → E\ng : β → F\n⊢ (∃ c, IsBigOWith c (𝓝 b) f g) ↔ ∃ c, IsBigOWith c (𝓝 (↑(LocalHomeomorp... | [
2196,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2193,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.mul_natDegree_lt_iff | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : Monic p\nq : R[X]\nhq : q = 0\n⊢ natDegree (p * q) < natDegree p ↔ p ≠ 1 ∧ q = 0\n\ncase neg\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : Monic p\nq : R... | [
463,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.BlankRel.trans | [
{
"state_after": "case inl.inl\nΓ : Type u_1\ninst✝ : Inhabited Γ\nl₁ l₂ l₃ : List Γ\nh₁ : BlankExtends l₁ l₂\nh₂ : BlankExtends l₂ l₃\n⊢ BlankRel l₁ l₃\n\ncase inl.inr\nΓ : Type u_1\ninst✝ : Inhabited Γ\nl₁ l₂ l₃ : List Γ\nh₁ : BlankExtends l₁ l₂\nh₂ : BlankExtends l₃ l₂\n⊢ BlankRel l₁ l₃\n\ncase inr.inl\nΓ : ... | [
145,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min_empty | [] | [
1248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/Data/PFun.lean | PFun.core_restrict | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.48707\nδ : Type ?u.48710\nε : Type ?u.48713\nι : Type ?u.48716\nf✝ : α →. β\nf : α → β\ns : Set β\nx : α\n⊢ x ∈ core (↑f) s ↔ x ∈ f ⁻¹' s",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.48707\nδ : Type ?u.48710\nε : Type ?u.48713\n... | [
504,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Std/Data/Option/Lemmas.lean | Option.mem_unique | [] | [
41,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
40,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.circulant_apply | [] | [
55,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
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