file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Topology/Sober.lean | ClosedEmbedding.quasiSober | [
{
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192,
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184,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_add | [] | [
345,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/Order/Closure.lean | LowerAdjoint.monotone | [] | [
344,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.add_tsub_cancel_right | [
{
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"tactic": "rw [add_comm]"
}
] | [
303,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
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Mathlib/Algebra/Order/Ring/Defs.lean | lt_neg_self_iff | [
{
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"state_before": "α : Type u\nβ : Type ?u.188778\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ a < -a ↔ - -a < -a",
"tactic": "rw [neg_neg]"
}
] | [
1123,
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1119,
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Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Ioc_iff_right | [] | [
131,
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130,
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src/lean/Init/Data/List/Basic.lean | List.length_map | [
{
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},
{
"state_after": "no goals",
"state_before": "case nil... | [
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Std/Data/Int/Lemmas.lean | Int.natAbs_eq_natAbs_iff | [
{
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{
"state_after": "no goals",
"state_... | [
188,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Logic/Pairwise.lean | Pairwise.set_pairwise | [] | [
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98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_singleton | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/LinearAlgebra/AffineSpace/Slope.lean | slope_fun_def | [] | [
38,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_top | [] | [
133,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_eval_const' | [] | [
190,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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Mathlib/Algebra/Parity.lean | isSquare_zero | [] | [
156,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.surjective_of_iterate_surjective | [
{
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.cons_left_iff | [
{
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163,
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Mathlib/Data/Multiset/Powerset.lean | Multiset.powerset_coe | [] | [
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85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.set_lintegral_lt_top | [] | [
385,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
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Mathlib/LinearAlgebra/Determinant.lean | LinearEquiv.det_coe_symm | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1737265\ninst✝⁸ : CommRing R\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nM' : Type ?u.1737856\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M'\nι : Type ?u.1738398\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\ne : Basis ι R M\n𝕜 : Typ... | [
445,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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Mathlib/Data/Finmap.lean | Finmap.insert_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb b' : β a\ns✝ : Finmap β\ns : AList β\n⊢ insert a b' (insert a b ⟦s⟧) = insert a b' ⟦s⟧",
"tactic": "simp only [insert_toFinmap, AList.insert_insert]"
}
] | [
514,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
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Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.mem_ordConnectedComponent | [] | [
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10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
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Mathlib/Analysis/NormedSpace/WeakDual.lean | NormedSpace.Dual.toWeakDual_continuous | [] | [
135,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Analysis/Normed/Group/Pointwise.lean | closedBall_mul_singleton | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ closedBall x δ * {y} = closedBall (x * y) δ",
"tactic": "simp [mul_comm _ {y}, mul_comm y]"
}
] | [
170,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement_iff_existsUnique | [] | [
81,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.monotone | [] | [
1002,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.preimage | [] | [
320,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
11
] |
Mathlib/Logic/IsEmpty.lean | isEmpty_sigma | [
{
"state_after": "no goals",
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"tactic": "simp only [← not_nonempty_iff, nonempty_sigma, not_exists]"
}
] | [
156,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_left_cancel' | [] | [
167,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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] |
Mathlib/MeasureTheory/Measure/Complex.lean | MeasureTheory.SignedMeasure.im_toComplexMeasure | [] | [
86,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.coe_one | [] | [
484,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
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Mathlib/RingTheory/Algebraic.lean | isAlgebraic_nat | [
{
"state_after": "R : Type u\nS : Type ?u.96110\nA : Type v\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Ring A\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R S\ninst✝² : Algebra S A\ninst✝¹ : IsScalarTower R S A\ninst✝ : Nontrivial R\nn : ℕ\n⊢ IsAlgebraic R (↑?m.98260 ↑n)\n\nR : Type u\nS : Type ?u.96110\nA ... | [
121,
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Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.eventually | [] | [
2839,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.map_C | [] | [
1208,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictFDerivAt.sin | [] | [
991,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
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Mathlib/Algebra/Associated.lean | Prime.dvd_prime_iff_associated | [] | [
620,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousOn.prod_map_equivL | [] | [
1093,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ixx | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Sort u_2\nι' : Sort u_3\ninst✝ : LinearOrder α\nIxx : α → α → Set α\np : α → α → Prop\nHne : ∀ {a b : α}, Set.Nonempty (Ixx a b) → p a b\nHi : ∀ {a₁ b₁ a₂ b₂ : α}, Ixx a₁ b₁ ∩ Ixx a₂ b₂ = Ixx (max a₁ a₂) (min b₁ b₂)\nf : ι → α\ng : ι' → α\n⊢ Is... | [
170,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Data/List/Sublists.lean | List.length_sublists | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\n⊢ length (sublists l) = 2 ^ length l",
"tactic": "simp only [sublists_eq_sublists', length_map, length_sublists', length_reverse]"
}
] | [
211,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coe_fst | [] | [
354,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_disjiUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.483883\ns s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\nb : β\nh : Set.PairwiseDisjoint (↑s) t\n⊢ b ∈ disjiUnion s t h ↔ ∃ a, a ∈ s ∧ b ∈ t a",
"tactic": "simp only [mem_def, disjiUnion_val, mem_bind, exists_prop]"
}
] | [
3454,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3453,
1
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Mathlib/Data/Finsupp/Pwo.lean | Finsupp.isPwo | [] | [
39,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.jacobson_bot_polynomial_of_jacobson_bot | [
{
"state_after": "R : Type u\nS : Type v\ninst✝ : CommRing R\nh : jacobson ⊥ = ⊥\n⊢ sInf (map C '' {J | IsMaximal J}) ≤ ⊥",
"state_before": "R : Type u\nS : Type v\ninst✝ : CommRing R\nh : jacobson ⊥ = ⊥\n⊢ jacobson ⊥ = ⊥",
"tactic": "refine' eq_bot_iff.2 (le_trans jacobson_bot_polynomial_le_sInf_map_ma... | [
355,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.list_prod_mem | [] | [
157,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
11
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_zero_of_row_eq | [] | [
380,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.symm_apply_mem_iff | [] | [
486,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
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Mathlib/Order/CompleteLattice.lean | iInf_congr_Prop | [] | [
724,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.leadingCoeff_multiset_prod | [
{
"state_after": "R : Type u\nι : Type w\ns : Finset ι\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf : ι → R[X]\nt : Multiset R[X]\n⊢ prod (Multiset.map (↑leadingCoeffHom) t) = prod (Multiset.map (fun f => leadingCoeff f) t)",
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352,
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.ω_pow_eq_neg_one | [
{
"state_after": "case intro\np' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\nk : ℤ\nw : ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1\n⊢ ω ^ 2 ^ (p' + 1) = -1",
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"tactic": "cases' ω_pow_formula p' h with... | [
446,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
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Mathlib/Order/WellFoundedSet.lean | Pi.isPwo | [
{
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812,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
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Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.det_toSquareBlock_id | [] | [
163,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseRange.induction_on₂ | [] | [
345,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.restrictScalars_injective | [] | [
458,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.smul | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.775481\nδ : Type ?u.775484\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁵ : MeasurableSpace δ\ninst✝⁴ : NormedAddCommGroup β\ninst✝³ : NormedAddCommGroup γ\n𝕜 : Type u_1\ninst✝² : NormedAddCommGroup 𝕜\ninst✝¹ : SMulZeroClass 𝕜 β\ninst✝ : BoundedSMul ... | [
405,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
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Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm | [
{
"state_after": "case h\nR : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁹ : NontriviallyNormedField R\ninst✝⁸ : (x : B) → AddCommMonoid (E x)\ninst✝⁷ : (x : B) → Module R (E x)\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace R F\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace (To... | [
533,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_const | [] | [
837,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | zpow_add' | [
{
"state_after": "case pos\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nm n : ℤ\nh : a ≠ 0 ∨ m + n ≠ 0 ∨ m = 0 ∧ n = 0\nhm : m = 0\n⊢ a ^ (m + n) = a ^ m * a ^ n\n\ncase neg\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nm n : ℤ\nh : a ≠ 0 ∨ m + n ≠ 0 ∨ m = 0 ∧ n = 0\nhm : ¬m = 0\n⊢ a ^ (m + n) = a ^ m ... | [
110,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_iSup | [] | [
2173,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_union | [] | [
1051,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Fintype.total_apply_single | [
{
"state_after": "α : Type u_2\nM : Type u_1\nR : Type u_3\ninst✝⁶ : Fintype α\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nS : Type u_4\ninst✝² : Semiring S\ninst✝¹ : Module S M\ninst✝ : SMulCommClass R S M\nv : α → M\ni : α\nr : R\n⊢ (∑ x : α, if x = i then r • v x else 0) = r • v i",
... | [
1066,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/Algebra/Group/Basic.lean | bit1_add | [] | [
138,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.coe_quotientInfToSupQuotient | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | rel_iSup_tsum | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nγ : Type u_3\nδ : Type ?u.374689\ninst✝⁴ : AddCommMonoid α\ninst✝³ : TopologicalSpace α\ninst✝² : T2Space α\nf g : β → α\na a₁ a₂ : α\ninst✝¹ : Countable γ\ninst✝ : CompleteLattice β\nm : β → α\nm0 : m ⊥ = 0\nR : α → α → Prop\nm_iSup : ∀ (s : ℕ → β), R (... | [
748,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_refl_real | [] | [
361,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/List/MinMax.lean | List.min_le_of_le | [] | [
447,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_union | [] | [
1041,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_add_const_Ioi | [] | [
87,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_prod | [] | [
1107,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.inr_apply | [] | [
512,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.one_apply | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.find_dom | [] | [
786,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.sub | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.51081\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSp... | [
156,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_rec_on | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nC : WSeq α → Prop\na : α\ns : WSeq α\nM : a ∈ s\nh1 : ∀ (b : α) (s' : WSeq α), a = b ∨ C s' → C (cons b s')\nh2 : ∀ (s : WSeq α), C s → C (think s)\n⊢ ∀ (b : Option α) (s' : Seq (Option α)), some a = b ∨ C s' → C (Seq.cons b s')",
"state_before": "α : Ty... | [
921,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.subset_zeroLocus_vanishingIdeal | [] | [
177,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivWithinAt.ccosh | [] | [
452,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | LinearIsometryEquiv.inner_map_map | [] | [
1284,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_erase_top | [] | [
442,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.Lp_add_le_tsum_of_nonneg | [
{
"state_after": "case intro\nι : Type u\ns : Finset ι\ng : ι → ℝ\np q : ℝ\nhp : 1 ≤ p\nhg : ∀ (i : ι), 0 ≤ g i\nhg_sum : Summable fun i => g i ^ p\nf : ι → ℝ≥0\nhf_sum : Summable fun i => (fun i => ↑(f i)) i ^ p\n⊢ (Summable fun i => ((fun i => ↑(f i)) i + g i) ^ p) ∧\n (∑' (i : ι), ((fun i => ↑(f i)) i + g... | [
681,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.isLUB_sSup | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.88320\nγ : Type ?u.88323\nι : Sort ?u.88326\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Set (WithTop α)\nhs : s = ∅\n⊢ IsLUB s (sSup s)\n\ncase inr\nα : Type u_1\nβ : Type ?u.88320\nγ : Type ?u.88323\nι : Sort ?u.88326\ninst✝ : ConditionallyCompleteL... | [
1159,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_lt_coe | [] | [
266,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Submonoid.powers_fg | [] | [
195,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : ℕ\na : α\ns : Multiset α\nl : List α\n⊢ powersetLen (n + 1) (a ::ₘ Quotient.mk (isSetoid α) l) =\n powersetLen (n + 1) (Quotient.mk (isSetoid α) l) + map (cons a) (powersetLen n (Quotient.mk (isSetoid α) l))",
"tactic": "simp [powersetLe... | [
257,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_int_add | [
{
"state_after": "q : ℚ\nx y : ℝ\nm : ℤ\nh : Irrational (↑↑m + x)\n⊢ Irrational x",
"state_before": "q : ℚ\nx y : ℝ\nm : ℤ\nh : Irrational (↑m + x)\n⊢ Irrational x",
"tactic": "rw [← cast_coe_int] at h"
},
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nm : ℤ\nh : Irrational (↑... | [
230,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_sub | [] | [
1267,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.div_nat | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\nm : ℕ\nhm : m ≠ 0\n⊢ ↑m ≠ 0",
"tactic": "rwa [Int.coe_nat_ne_zero]"
}
] | [
458,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivAt.real_of_complex | [
{
"state_after": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nh : HasDerivAt e e' ↑z\nA : HasFDerivAt ofReal' ofRealClm z\n⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nh : HasDerivAt e e' ↑z\n⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z",
"tactic": "have A : HasFDerivAt ((↑) : ℝ → ℂ... | [
84,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comap_id_apply | [
{
"state_after": "case h\nσ : Type u_1\nτ : Type ?u.59131\nυ : Type ?u.59134\nR : Type u_2\ninst✝ : CommSemiring R\nx : σ → R\ni : σ\n⊢ comap (AlgHom.id R (MvPolynomial σ R)) x i = x i",
"state_before": "σ : Type u_1\nτ : Type ?u.59131\nυ : Type ?u.59134\nR : Type u_2\ninst✝ : CommSemiring R\nx : σ → R\n⊢ c... | [
53,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.IsUnit.Submonoid.coe_inv | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Std/Data/List/Lemmas.lean | List.exists_cons_of_ne_nil | [] | [
32,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
31,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_fmod_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : b = 0\n⊢ fmod (a * b) b = 0",
"tactic": "simp [h, Int.mul_zero]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : ¬b = 0\n⊢ fmod (a * b) b = 0",
"tactic": "rw [Int.fmod_def, Int.mul_fdiv_cancel _ h, Int.mul_comm,... | [
459,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
457,
9
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | nnnorm_star | [] | [
61,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.biUnion_empty | [] | [
3536,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3535,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_zero | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_div | [] | [
321,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Topology/Bases.lean | Set.PairwiseDisjoint.countable_of_nonempty_interior | [] | [
373,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\ne : ℕ\nhe : e ≠ 0\nhle : map f p ≤ P ^ e\nhnle : ¬map f p ≤ P ^ (e + 1)\n⊢ ramificationIdx f p P ≠ 0",
"tactic": "rwa [ramificationIdx_spec hle hnle]"
}... | [
124,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_eq_prod_iff_of_nonempty | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.88331\nδ : Type ?u.88334\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nh : Set.Nonempty (s ×ˢ t)\n⊢ s ×ˢ t = s₁ ×ˢ t₁ → s = s₁ ∧ t = t₁\n\ncase mpr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.88331\nδ : Type ?u.88334\ns s₁ s₂ : Set α\nt t₁ t₂ : ... | [
406,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Analysis/Convex/Segment.lean | Convex.combo_le_max | [] | [
478,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.balance2_eq | [
{
"state_after": "α : Type u_1\nc : RBColor\nn : Nat\nl : RBNode α\nv : α\nr : RBNode α\nhr : Balanced r c n\n⊢ (match l, v, r with\n | a, x, node red (node red b y c) z d => node red (node black a x b) y (node black c z d)\n | a, x, node red b y (node red c z d) => node red (node black a x b) y (node bla... | [
185,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
183,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.contDiffAt_rpow_const_of_le | [] | [
389,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.desc_self | [] | [
600,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
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