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/MeasureTheory/Group/Integration.lean | MeasureTheory.integral_inv_eq_self | [
{
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Mathlib/Data/Set/Lattice.lean | Set.image_iUnion | [
{
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1656,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1652,
1
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Mathlib/Algebra/CharP/CharAndCard.lean | prime_dvd_char_iff_dvd_card | [
{
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"tacti... | [
77,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.of_mul_right_left | [
{
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},
{
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141,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.monic_of_d_eq_one | [
{
"state_after": "no goals",
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"tactic": "rw [Monic, leadingCoeff_of_c_eq_zero... | [
273,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.zero_eq_zero' | [] | [
231,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_one | [] | [
365,
6
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364,
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.hasBiproductsOfShape_of_equiv | [] | [
341,
71
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334,
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Mathlib/Data/ZMod/Basic.lean | ZMod.cast_zero | [
{
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"tactic": "delta ZMod.cast"
... | [
165,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.topologyOfClosureOperator_self | [
{
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319,
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Mathlib/Topology/Algebra/Group/Basic.lean | subset_interior_smul_right | [] | [
1234,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
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Mathlib/Deprecated/Subfield.lean | Field.closure_mono | [] | [
147,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Heyting/Basic.lean | himp_triangle | [
{
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464,
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Mathlib/Data/Finmap.lean | Finmap.insert_entries_of_neg | [
{
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"tactic": "simp [AList.insert_entries_of_neg (mt mem_toFinmap.1 h), -insert_ent... | [
492,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_le | [] | [
1596,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Hom/Basic.lean | WithTop.toDualBotEquiv_coe | [] | [
1285,
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1283,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.coe_rpow_of_nonneg | [
{
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{
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Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one | [
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_trans | [
{
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Mathlib/Order/Lattice.lean | inf_lt_left_or_right | [] | [
472,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_pos | [] | [
760,
34
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759,
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Mathlib/Data/Subtype.lean | Subtype.ext | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Sym/Sym2.lean | Sym2.inductionOn₂ | [
{
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Mathlib/Computability/Reduce.lean | ManyOneDegree.add_of | [] | [
487,
82
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480,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.inf_eq_inter | [] | [
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93
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Mathlib/Order/LiminfLimsup.lean | Filter.limsSup_le_of_le | [] | [
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16
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.Monic.comp_X_add_C | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.bounds_nonempty | [] | [
153,
25
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Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_bot_right | [
{
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Mathlib/Data/Bool/Basic.lean | Bool.and_or_distrib_left | [
{
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}
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183,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | AffineEquiv.pointReflection_midpoint_right | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.toSubtype_fromSubtype | [
{
"state_after": "case w\nJ : Type w\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nf : J → C\ninst✝² : HasBiproduct f\np : J → Prop\ninst✝¹ : HasBiproduct (Subtype.restrict p f)\ninst✝ : DecidablePred p\ni : J\n⊢ ι f i ≫ toSubtype f p ≫ fromSubtype f p = ι f i ≫ map fun j => if p j then 𝟙 (f j... | [
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Mathlib/Data/Matrix/Notation.lean | Matrix.cons_val' | [
{
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"tactic": "refine' Fin.cases _ _ i <;> simp"
}
] | [
122,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lift_mul | [] | [
701,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPushout_of_right_iso | [] | [
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46
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Mathlib/Topology/UniformSpace/Basic.lean | comp_le_uniformity3 | [] | [
576,
37
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574,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_false | [] | [
1024,
19
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_closure₁ | [
{
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}
] | [
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862,
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Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.mem_pointwise_smul_iff_inv_smul_mem | [] | [
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32
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111,
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Mathlib/Data/Finset/Option.lean | Finset.eraseNone_inter | [
{
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.eq_prime_pow_of_succ_lt_of_le | [
{
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_eq_zero | [
{
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"tactic": "simp [cycleType_def, cycleFactorsFinset_eq_empty_iff]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/List/Lemmas.lean | List.replicate_sublist_replicate | [
{
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48
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_union_le | [] | [
295,
29
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294,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | sInf_eq_argmin_on | [] | [
970,
77
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968,
1
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Std/Logic.lean | forall_eq | [] | [
448,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
447,
9
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_mono_right | [] | [
58,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.isOpen_b | [
{
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150,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Computability/Primrec.lean | Primrec.vector_ofFn' | [] | [
1333,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
1
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_epsilon | [] | [
719,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_natCast | [
{
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"tactic": "rw [← ofReal_natCast]"
},
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u... | [
698,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.to_subset | [] | [
363,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_iff_hasFDerivWithinAt | [] | [
180,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.refl_trans | [
{
"state_after": "case h.h\nF : Type ?u.82823\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.82832\nδ : Type ?u.82835\ninst✝² : LE α\ninst✝¹ : LE β\ninst✝ : LE γ\ne : α ≃o β\nx : α\n⊢ ↑(trans (refl α) e) x = ↑e x",
"state_before": "F : Type ?u.82823\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.82832\nδ : Type ?u.8283... | [
912,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
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Mathlib/Analysis/Normed/Field/Basic.lean | NNReal.norm_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.382178\nβ : Type ?u.382181\nγ : Type ?u.382184\nι : Type ?u.382187\nx : ℝ≥0\n⊢ ‖↑x‖ = ↑x",
"tactic": "rw [Real.norm_eq_abs, x.abs_eq]"
}
] | [
829,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | isometry_mul_left | [] | [
96,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_mul_const | [] | [
416,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_of_add_bdd_below_right' | [] | [
747,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.topEquiv_apply | [] | [
1284,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.forall_mem_single | [
{
"state_after": "no goals",
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"tactic":... | [
318,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.continuousAt_add_top_coe | [
{
"state_after": "α : Type ?u.18602\ninst✝ : TopologicalSpace α\na : ℝ\n⊢ ∀ (x : ℝ), ∀ᶠ (a : EReal × EReal) in 𝓝 (⊤, ↑a), ↑x < a.fst + a.snd",
"state_before": "α : Type ?u.18602\ninst✝ : TopologicalSpace α\na : ℝ\n⊢ ContinuousAt (fun p => p.fst + p.snd) (⊤, ↑a)",
"tactic": "simp only [ContinuousAt, ten... | [
189,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | MulOpposite.edist_unop | [] | [
423,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.succ_eq_iInf | [
{
"state_after": "α : Type u_1\ninst✝¹ : CompleteLattice α\ninst✝ : SuccOrder α\na : α\n⊢ (⨅ (b : α) (_ : a < b), b) ≤ succ a",
"state_before": "α : Type u_1\ninst✝¹ : CompleteLattice α\ninst✝ : SuccOrder α\na : α\n⊢ succ a = ⨅ (b : α) (_ : a < b), b",
"tactic": "refine' le_antisymm (le_iInf fun b => le... | [
582,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
src/lean/Init/Core.lean | Eq.propIntro | [] | [
1145,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1144,
1
] |
Mathlib/Algebra/Category/GroupCat/Colimits.lean | AddCommGroupCat.Colimits.quot_zero | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_inv_app_right | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_target | [] | [
727,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_add | [
{
"state_after": "x y : ℂ\n⊢ (exp x + exp (-x)) * (exp y + exp (-y)) + (exp x - exp (-x)) * (exp y - exp (-y)) =\n 2 * (exp x * exp y + exp (-x) * exp (-y))",
"state_before": "x y : ℂ\n⊢ cosh (x + y) = cosh x * cosh y + sinh x * sinh y",
"tactic": "rw [← mul_right_inj' (two_ne_zero' ℂ), two_cosh, exp... | [
633,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_bit1 | [] | [
221,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.coe_negPart | [] | [
501,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | compactOperator_topologicalClosure | [] | [
445,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Matrix/Reflection.lean | Matrix.etaExpand_eq | [
{
"state_after": "no goals",
"state_before": "l m✝ n✝ : ℕ\nα : Type u_1\nβ : Type ?u.58966\nm n : ℕ\nA : Matrix (Fin m) (Fin n) α\n⊢ etaExpand A = A",
"tactic": "simp_rw [etaExpand, FinVec.etaExpand_eq, Matrix.of, Equiv.refl_apply]"
}
] | [
236,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Order/LocallyFinite.lean | Iic_toDual | [] | [
902,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.injective | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.3022378\ninst✝¹ : CommRing P\nK : Type ?u.3022384\ninst✝ : IsLocalization M S\nhM : M ≤ nonZeroDivisors R\n⊢ ∀ (a : R), ↑(algebraMap R S) a = 0 → a = 0",
"state_before":... | [
1175,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
11
] |
Mathlib/Data/Set/Basic.lean | Set.sep_empty | [] | [
1454,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1453,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.update_comm | [
{
"state_after": "case h\nα✝ : Sort u\nβ✝ : α✝ → Sort v\nα' : Sort w\ninst✝² : DecidableEq α✝\ninst✝¹ : DecidableEq α'\nf✝ g : (a : α✝) → β✝ a\na✝ : α✝\nb✝ : β✝ a✝\nα : Sort u_1\ninst✝ : DecidableEq α\nβ : α → Sort u_2\na b : α\nh : a ≠ b\nv : β a\nw : β b\nf : (a : α) → β a\nc : α\n⊢ update (update f a v) b w ... | [
675,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_triangle_left | [
{
"state_after": "α : Type ?u.5285\nι : Type u_1\nβ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.5317\ninst✝ : (i : ι) → DecidableEq (γ i)\nx y z : (i : ι) → β i\n⊢ hammingDist x y ≤ hammingDist x z + hammingDist z y",
"state_before": "α : Type ?u.5285\nι : Type ... | [
78,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.inter | [] | [
297,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Subgroup.fg_iff_submonoid_fg | [
{
"state_after": "case mp\nM : Type ?u.69638\nN : Type ?u.69641\ninst✝³ : Monoid M\ninst✝² : AddMonoid N\nG : Type u_1\nH : Type ?u.69653\ninst✝¹ : Group G\ninst✝ : AddGroup H\nP : Subgroup G\n⊢ FG P → Submonoid.FG P.toSubmonoid\n\ncase mpr\nM : Type ?u.69638\nN : Type ?u.69641\ninst✝³ : Monoid M\ninst✝² : AddM... | [
261,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | idealFactorsEquivOfQuotEquiv_symm | [] | [
1118,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.fix_eval | [
{
"state_after": "no goals",
"state_before": "f : Code\n⊢ eval (fix f) =\n PFun.fix fun v =>\n Part.map (fun v => if List.headI v = 0 then Sum.inl (List.tail v) else Sum.inr (List.tail v)) (eval f v)",
"tactic": "simp [eval]"
}
] | [
169,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/List/Basic.lean | List.drop_drop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.216866\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn m : ℕ\n⊢ drop n (drop m []) = drop (n + m) []",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.216866\nα : Type u\nβ : Type v\nγ ... | [
2254,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2247,
1
] |
Mathlib/Data/Prod/PProd.lean | Function.Injective.pprod_map | [] | [
53,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | Subalgebra.separatesPoints_monotone | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝⁹ : TopologicalSpace α\nR : Type u_3\ninst✝⁸ : CommSemiring R\nA : Type u_2\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : Semiring A\ninst✝⁵ : Algebra R A\ninst✝⁴ : TopologicalSemiring A\nA₂ : Type ?u.1479689\ninst✝³ : TopologicalSpace A₂\ninst✝² : Semiring A₂\nin... | [
792,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_smul_left | [
{
"state_after": "case intro\nS : Type ?u.150446\nR : Type u_1\nR₁ : Type ?u.150452\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : CommRing R₁\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nQ : QuadraticForm R M\na : R\nx y : M\nB : BilinForm R M\nh : ∀ (x y : M), ↑Q (x + y) = ↑Q x + ↑Q y + BilinForm.bilin B x y\n⊢ po... | [
273,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.coe_inf | [] | [
413,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ι_map | [
{
"state_after": "J : Type w\nC : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nf g : J → C\ninst✝¹ : HasBiproduct f\ninst✝ : HasBiproduct g\np : (j : J) → f j ⟶ g j\nj : J\n⊢ ι f j ≫ map' p = p j ≫ ι g j",
"state_before": "J : Type w\nC : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C... | [
536,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.QInfty_f_idem | [] | [
120,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_one | [] | [
1706,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1705,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnityEquivNthRoots_symm_apply | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_plift | [] | [
113,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.pi_mem_of_mulSingle_mem | [
{
"state_after": "case intro\nG : Type ?u.35743\ninst✝⁴ : Group G\nA : Type ?u.35749\ninst✝³ : AddGroup A\nη : Type u_1\nf : η → Type u_2\ninst✝² : (i : η) → Group (f i)\ninst✝¹ : Finite η\ninst✝ : DecidableEq η\nH : Subgroup ((i : η) → f i)\nx : (i : η) → f i\nh : ∀ (i : η), Pi.mulSingle i (x i) ∈ H\nval✝ : Fi... | [
226,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_pow_left_iff | [
{
"state_after": "case intro\na b n : ℕ\nhn : 0 < succ n\n⊢ coprime (a ^ succ n) b ↔ coprime a b",
"state_before": "n : ℕ\nhn : 0 < n\na b : ℕ\n⊢ coprime (a ^ n) b ↔ coprime a b",
"tactic": "obtain ⟨n, rfl⟩ := exists_eq_succ_of_ne_zero hn.ne'"
},
{
"state_after": "case intro\na b n : ℕ\nhn : 0 <... | [
197,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | isBoundedBilinearMap_comp | [] | [
454,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_eq_one_iff_of_one_le' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.27020\nβ : Type ?u.27023\nM : Type ?u.27026\nN : Type u_2\nG : Type ?u.27032\nk : Type ?u.27035\nR : Type ?u.27038\ninst✝¹ : CommMonoid M\ninst✝ : OrderedCommMonoid N\nf g : ι → N\ns t : Finset ι\n⊢ (∀ (i : ι), i ∈ s → 1 ≤ f i) → (∏ i i... | [
193,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimit.isoOfNatIso_inv_desc | [] | [
936,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/Order/WithBot.lean | WithBot.ofDual_apply_bot | [] | [
939,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.fst_comp_mk | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.isEmpty | [] | [
1068,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
11
] |
Mathlib/Data/Set/NAry.lean | Set.image_image2_antidistrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nα' : Type u_5\nβ : Type u_4\nβ' : Type ?u.48235\nγ : Type u_2\nγ' : Type ?u.48241\nδ : Type u_1\nδ' : Type ?u.48247\nε : Type ?u.48250\nε' : Type ?u.48253\nζ : Type ?u.48256\nζ' : Type ?u.48259\nν : Type ?u.48262\nf f'✝ : α → β → γ\ng✝ g'✝ : α → β ... | [
415,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
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