file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mem_incidence_iff_neighbor | [
{
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963,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.homOfLe_apply | [] | [
1063,
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Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.LeftSplit.shortExact | [] | [
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Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.tendsto_iff | [] | [
347,
94
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345,
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.card_cycleType_eq_one | [
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},
{
"state_a... | [
121,
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112,
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Mathlib/Algebra/Group/Defs.lean | mul_right_cancel | [] | [
215,
42
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214,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_norm_left | [
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753,
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Mathlib/Data/Prod/Basic.lean | Prod.lex_def | [
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"tactic": "cases h <;>... | [
232,
72
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Mathlib/Tactic/Group.lean | Mathlib.Tactic.Group.zpow_trick_one | [
{
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"tactic": "rw [mul_assoc, mul_self_zpow]"
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] | [
47,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_two | [] | [
711,
49
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Mathlib/Topology/Algebra/Group/Basic.lean | Filter.Tendsto.div' | [] | [
1087,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
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Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.div_closure | [
{
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"tactic": "simp_rw [div_eq_mul_inv, inv_closure, hs.mul_closure]"
}... | [
1385,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/GroupWithZero.lean | Continuous.comp_div_cases | [] | [
229,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
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Mathlib/Data/Complex/Basic.lean | Complex.conj_eq_iff_im | [] | [
557,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_biUnion_toMeasurable | [
{
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370,
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Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.map_vadd | [] | [
111,
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110,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two | [
{
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"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : Norm... | [
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Mathlib/Topology/Semicontinuous.lean | IsOpen.upperSemicontinuous_indicator | [] | [
740,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mod_le | [] | [
1032,
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Mathlib/Topology/Constructions.lean | IsOpenMap.sum_elim | [] | [
985,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Basic.lean | Filter.ext' | [] | [
1080,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Div.lean | Polynomial.rootMultiplicity_zero | [] | [
558,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendsto_comp_of_locally_uniform_limit | [
{
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_zsmul | [] | [
498,
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497,
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Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.Independent.dfinsupp_sumAddHom_injective | [
{
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.le_multiplicity_of_pow_dvd | [] | [
146,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
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Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.exists_nonsquare | [
{
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"state_before": "K : Type ?u.1094008\nR : Type ?u.1094011\nF : Type u_1\ninst✝¹ : Field F\ninst✝ : Finite F\nhF : ringChar F ≠... | [
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Mathlib/Topology/Algebra/Monoid.lean | continuousMul_of_comm_of_nhds_one | [
{
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302,
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297,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_smul | [] | [
533,
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532,
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Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.add_right | [] | [
151,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
11
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Mathlib/Computability/Primrec.lean | Primrec.list_headI | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | Multiset.Nat.nodup_antidiagonalTuple | [] | [
207,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
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Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.union | [] | [
436,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
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Mathlib/Data/Polynomial/Inductions.lean | Polynomial.divX_add | [
{
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"tactic": "simp"
}
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68,
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Mathlib/Analysis/NormedSpace/Basic.lean | rescale_to_shell_zpow | [] | [
408,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
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Mathlib/Algebra/Order/ToIntervalMod.lean | QuotientAddGroup.equivIcoMod_coe | [] | [
811,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.map_Q | [
{
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238,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_snorm_of_exponent_le | [
{
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Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atTop_iInf | [] | [
178,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Abelian/Transfer.lean | CategoryTheory.AbelianOfAdjunction.hasCokernels | [
{
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_eq_self_of_not_mem | [] | [
411,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
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Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.abs_circleTransformBoundingFunction_le | [
{
"state_after": "E : Type ?u.139500\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR✝ : ℝ\nz✝ w : ℂ\nR r : ℝ\nhr : r < R\nhr' : 0 ≤ r\nz : ℂ\ncts : ContinuousOn (↑abs ∘ fun t => circleTransformBoundingFunction R z t) (closedBall z r ×ˢ univ)\n⊢ ∃ x,\n ∀ (y : ↑(closedBall z r ×ˢ [[0, 2 * π]])),\n ... | [
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.diagonal_kroneckerTMul_diagonal | [] | [
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67
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.coe_inf | [] | [
297,
6
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296,
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Mathlib/Topology/Order/Basic.lean | Monotone.tendsto_nhdsWithin_Ioi | [] | [
2873,
67
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2870,
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Mathlib/Topology/Order.lean | generateFrom_iInter_of_generateFrom_eq_self | [] | [
991,
48
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src/lean/Init/Prelude.lean | Char.eq_of_val_eq | [] | [
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Mathlib/Topology/Order.lean | nhdsAdjoint_nhds | [
{
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"tactic": "letI := nhdsAdjoint a f"
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{
"state_aft... | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.domRestrict'_apply | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fst | [] | [
2178,
65
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Mathlib/Data/List/Nodup.lean | List.nodup_map_iff_inj_on | [] | [
264,
45
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262,
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Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_le_coe_ennreal_iff | [] | [
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35
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Mathlib/Data/List/Basic.lean | List.mem_takeWhile_imp | [
{
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1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_fuzzy_zero_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ -x ‖ 0 ↔ x ‖ 0",
"tactic": "rw [neg_fuzzy_iff, neg_zero]"
}
] | [
1400,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.linearProjOfIsCompl_idempotent | [] | [
200,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualPairing_eq | [
{
"state_after": "case h.h.h\nK : Type u\ninst✝⁴ : Field K\nV₁ : Type v'\nV₂ : Type v''\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nW : Subspace K V₁\nx✝¹ : Dual K V₁\nx✝ : { x // x ∈ W }\n⊢ ↑(↑(LinearMap.comp (Submodule.dualPairing W) (mkQ (dualAnnihilator W)... | [
1388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | finrank_vectorSpan_image_finset_le | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\nι : Type u_1\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\ns : Finset ι\nn : ℕ\nhc : Finset.card s = n + 1\nhn : Finset.Nonempty (Finset.image p s)\n⊢ finrank k { x // x ∈ vectorSpan k ↑(Fin... | [
154,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.const_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : α → Type ?u.91570\np q : ℝ≥0∞\ninst✝³ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type u_2\ninst✝² : NormedRing 𝕜\ninst✝¹ : (i : α) → Module 𝕜 (E i)\ninst✝ : ∀ (i : α), BoundedSMul 𝕜 (E i)\nf : α → 𝕜\nhf : Memℓp f p\nc : 𝕜\ni : α\n⊢ Bounded... | [
288,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/EqualizerProducts.lean | TopCat.Presheaf.SheafConditionEqualizerProducts.w | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\n⊢ ((Pi.lift fun i => F.map (leSupr U i).op) ≫\n Pi.lift fun p => Pi.π (fun i => F.obj (U i).op) p.fst ≫ F.map (infLELeft (U p.fst) (U p.snd)).op) =\n (Pi.lift fun i => F... | [
97,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/AssocList.lean | Std.AssocList.forM_eq | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝ : Monad m\nf : α → β → m PUnit\nl : AssocList α β\n⊢ forM f l =\n List.forM (toList l) fun x =>\n match x with\n | (a, b) => f a b",
"tactic": "induction l <;> simp [*, forM]"
}
] | [
78,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
76,
9
] |
Mathlib/Order/RelClasses.lean | transitive_ge | [] | [
909,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_mod | [
{
"state_after": "case h\nα : Type ?u.174271\nβ : Type ?u.174274\nγ : Type ?u.174277\nδ : Type ?u.174280\nσ : Type ?u.174283\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nm n : ℕ\n⊢ (m, n).fst = m % n + (m, n).snd * (fun x x_1 => x / x_1)... | [
837,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | nnnorm_pow | [] | [
553,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Std/Data/Int/DivMod.lean | Int.emod_sub_cancel_right | [] | [
448,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
447,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | LinearIsometry.map_orthogonalProjection' | [
{
"state_after": "case refine'_1\n𝕜 : Type u_3\nE✝ : Type ?u.533832\nF : Type ?u.533835\ninst✝¹⁰ : IsROrC 𝕜\ninst✝⁹ : NormedAddCommGroup E✝\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : InnerProductSpace 𝕜 E✝\ninst✝⁶ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E✝\ninst✝⁵ : CompleteSpace { x // x ∈ K }\nE : Type u_1... | [
547,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Init/Data/Int/Basic.lean | Int.natAbs_pos_of_ne_zero | [] | [
91,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.wrepr_wMk | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\na : (P F).A\nf' : MvPFunctor.B (MvPFunctor.drop (P F)) a ⟹ α\nf : PFunctor.B (MvPFunctor.last (P F)) a → MvPFunctor.W (P F) α\n⊢ (MvPFunctor.wMk' (P F) ∘ repr)\n (abs ((TypeVec.id ::: recF (MvPFunctor.wM... | [
146,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.map_sup | [] | [
831,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.colimit_isOpen_iff | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TopCatMax\nU : Set ↑(colimit F)\n⊢ IsOpen U ↔ ∀ (j : J), IsOpen ((forget TopCat).map (colimit.ι F j) ⁻¹' U)",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TopCatMax\nU : Set ↑(colimit F)\n⊢ IsOpen U ↔ ∀ (j : J), IsOpen ((forget ... | [
418,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.inv_hom_id_tensor | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V✝ W✝ X✝ Y✝ Z✝ V W X Y Z : C\nf : V ≅ W\ng : X ⟶ Y\nh : Y ⟶ Z\n⊢ (f.inv ⊗ g) ≫ (f.hom ⊗ h) = (𝟙 W ⊗ g) ≫ (𝟙 W ⊗ h)",
"tactic": "rw [... | [
362,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.subset_countable_closure_of_compact | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.280595\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε✝ ε₁ ε₂ : ℝ≥0∞\ns✝ t s : Set α\nhs : IsCompact s\nε : ℝ≥0∞\nhε : ε > 0\n⊢ ∃ t, Set.Countable t ∧ s ⊆ ⋃ (x : α) (_ : x ∈ t), closedBall x ε",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.280595\nin... | [
833,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.ext_iff | [] | [
112,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.flip | [] | [
667,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_pow_self | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np : α\nh0 : p ≠ 0\nhu : ¬IsUnit p\nn : ℕ\n⊢ p ^ n ∣ p ^ n ∧ ¬p ^ (n + 1) ∣ p ^ n",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np ... | [
619,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.div2_bit0 | [] | [
57,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_le_toMeasurable | [] | [
605,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/EqualizerProducts.lean | TopCat.Presheaf.SheafConditionEqualizerProducts.fork_pt | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Std/Data/Int/Lemmas.lean | Int.max_eq_left | [
{
"state_after": "a b : Int\nh : b ≤ a\n⊢ max b a = a",
"state_before": "a b : Int\nh : b ≤ a\n⊢ max a b = a",
"tactic": "rw [← Int.max_comm b a]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : b ≤ a\n⊢ max b a = a",
"tactic": "exact Int.max_eq_right h"
}
] | [
726,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
725,
11
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformEmbedding_subtype_val | [] | [
161,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coe_smul | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bitwise'_swap | [
{
"state_after": "case h.h\nf : Bool → Bool → Bool\nh : f false false = false\nm n : ℕ\n⊢ bitwise' (Function.swap f) m n = Function.swap (bitwise' f) m n",
"state_before": "f : Bool → Bool → Bool\nh : f false false = false\n⊢ bitwise' (Function.swap f) = Function.swap (bitwise' f)",
"tactic": "funext m ... | [
455,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.id_comp | [] | [
340,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.right_inv_eq_left_inv | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.261753\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B C : Matrix n n α\nh : A ⬝ B = 1\ng : C ⬝ A = 1\n⊢ B = C",
"tactic": "rw [← inv_eq_right_inv h, ← inv_eq_left_inv g]"
}
] | [
473,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | pairwise_disjoint_on | [] | [
60,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_subset_iff | [] | [
114,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_vsub_left | [] | [
636,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.one_le_iff_pos | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.179673\nβ : Type ?u.179676\nγ : Type ?u.179679\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ 1 ≤ o ↔ 0 < o",
"tactic": "rw [← succ_zero, succ_le_iff]"
}
] | [
1077,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean | SimpleGraph.FarFromTriangleFree.not_cliqueFree | [] | [
82,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13001\ninst✝¹ : OrderedSemiring α\ninst✝ : Nontrivial α\nn : ℕ\n⊢ 0 < ↑n ↔ 0 < n",
"tactic": "cases n <;> simp [cast_add_one_pos]"
}
] | [
113,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | EqualCharZero.to_not_mixedCharZero | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nh : ∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I)\np : ℕ\np_pos : p > 0\n⊢ ¬MixedCharZero R p",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nh : ∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I)\n⊢ ∀ (p : ℕ), p > 0 → ¬MixedCharZero R p",
"tactic": "intro p p... | [
275,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.neg | [] | [
1280,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.pow | [] | [
227,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_conj | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos (↑(starRingEnd ℂ) x) = ↑(starRingEnd ℂ) (cos x)",
"tactic": "rw [← cosh_mul_I, ← conj_neg_I, ← RingHom.map_mul, ← cosh_mul_I, cosh_conj, mul_neg, cosh_neg]"
}
] | [
951,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_comp_unsym | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_zero | [] | [
418,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_mul_left_add_left | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ coprime (n * k + m) n ↔ coprime m n",
"tactic": "rw [coprime, coprime, gcd_mul_left_add_left]"
}
] | [
189,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.support_restriction | [
{
"state_after": "case a\nR : Type u\nS : Type ?u.69179\ninst✝ : Ring R\np : R[X]\ni : ℕ\n⊢ i ∈ support (restriction p) ↔ i ∈ support p",
"state_before": "R : Type u\nS : Type ?u.69179\ninst✝ : Ring R\np : R[X]\n⊢ support (restriction p) = support p",
"tactic": "ext i"
},
{
"state_after": "case ... | [
296,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_lt_logb_of_base_lt_one | [
{
"state_after": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhxy : x < y\n⊢ log x < log y",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhxy : x < y\n⊢ logb b y < logb b x",
"tactic": "rw [logb, logb, div_lt_div_right_of_neg (log_neg b_pos b_lt_one)]"
},
{
... | [
262,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.coe_toHom | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
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