file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.one_imI | [] | [
196,
58
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196,
9
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Mathlib/FieldTheory/Laurent.lean | RatFunc.laurent_div | [] | [
91,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Real.isPiSystem_Ioo_rat | [
{
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1689,
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Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.supportsStmt_read | [
{
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1728,
50
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1721,
1
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Mathlib/Analysis/Seminorm.lean | Seminorm.bot_eq_zero | [] | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
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Mathlib/GroupTheory/Coset.lean | rightCoset_mem_rightCoset | [
{
"state_after": "no goals",
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"tactic": "simp [mem_rightCoset_iff, mul_mem_cancel_right (s.inv_mem ha)]"
}
] | [
230,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_top | [] | [
516,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/Analysis/Normed/Field/Basic.lean | norm_inv | [] | [
576,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_le | [
{
"state_after": "α✝ β✝ : Type u\na b : Cardinal\nα β : Type u\n⊢ lift (#α) ≤ lift (#β) ↔ (#α) ≤ (#β)",
"state_before": "α✝ β✝ : Type u\na b : Cardinal\nα β : Type u\n⊢ lift (#α) ≤ lift (#β) ↔ (#α) ≤ (#β)",
"tactic": "rw [← lift_umax]"
},
{
"state_after": "no goals",
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336,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
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Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.embedding_inl | [] | [
78,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
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Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.Walk.ofBoxProdLeft_boxProdRight | [
{
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165,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_sub_le | [] | [
934,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
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Mathlib/Data/List/Rotate.lean | List.singleton_eq_rotate_iff | [
{
"state_after": "no goals",
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"tactic": "rw [eq_comm, rotate_eq_singleton_iff, eq_comm]"
}
] | [
357,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
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Std/Data/Array/Init/Lemmas.lean | Array.SatisfiesM_mapM | [
{
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159,
85
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143,
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Mathlib/Data/Finset/Pointwise.lean | Set.Finite.toFinset_smul | [] | [
2233,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2231,
1
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Mathlib/LinearAlgebra/Finrank.lean | span_lt_of_subset_of_card_lt_finrank | [] | [
358,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
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Mathlib/Topology/UniformSpace/Basic.lean | tendsto_swap_uniformity | [] | [
455,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/Set/Function.lean | Set.RightInvOn.mapsTo | [] | [
1131,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
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Mathlib/Logic/Equiv/Option.lean | Equiv.optionCongr_injective | [] | [
169,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.zero_div | [] | [
265,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
264,
19
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_pow | [] | [
290,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_transpose | [] | [
622,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
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Mathlib/Data/List/Chain.lean | List.Chain.iff_mem | [
{
"state_after": "no goals",
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"tactic": "induction' p with _ a b l r _ IH <;> constructor <;>\n [exact ⟨mem_cons_self _ _, mem_co... | [
54,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.pos_finrank_generalizedEigenspace_of_hasEigenvalue | [
{
"state_after": "no goals",
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444,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.nodup_Icc | [] | [
32,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iInf_mul_right | [] | [
512,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.basicOpen_mul | [
{
"state_after": "no goals",
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"tactic": "simp [zeroLocus_singleton_m... | [
423,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
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Mathlib/RingTheory/Noetherian.lean | IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot | [
{
"state_after": "case intro\nR : Type u_1\nM : Type u_2\nP : Type ?u.247455\nN : Type w\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup P\ninst✝ : Module R P\nI : IsNoetherian R M\nf : M →ₗ[R] M\nn : ℕ\nw :\n ∀ (m : ℕ),\n n... | [
428,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_add_iff_left | [] | [
272,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
11
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_zsmul_add | [
{
"state_after": "no goals",
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"tactic": "rw [add_comm, toIcoMod_add_zsmul]"
}
] | [
430,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.continuousAt | [] | [
878,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
11
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Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ico_mul_zpow | [
{
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... | [
199,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.pow_dvd_iff_le_factorization | [
{
"state_after": "no goals",
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"tactic": "rw [← factorization_le_iff_dvd (pow_pos pp.pos k).ne' hn, pp.factorization_pow, single_le_iff]"
}
] | [
492,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_imp_of_ae_restrict | [
{
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2806,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2803,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOn.cauchy_map | [
{
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"state_befor... | [
553,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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] |
Mathlib/Data/Real/Basic.lean | Real.ratCast_lt | [
{
"state_after": "x✝ y✝ : ℝ\nx y : ℚ\n⊢ const abs ↑x < const abs ↑y ↔ x < y",
"state_before": "x✝ y✝ : ℝ\nx y : ℚ\n⊢ ↑x < ↑y ↔ x < y",
"tactic": "erw [mk_lt]"
},
{
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401,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.ext | [] | [
422,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_surjective | [] | [
473,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Algebra/Tropical/BigOperators.lean | Finset.untrop_sum' | [
{
"state_after": "case h.e'_3\nR : Type u_1\nS : Type u_2\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\ns : Finset S\nf : S → Tropical R\n⊢ inf s (untrop ∘ f) = Multiset.inf (Multiset.map untrop (Multiset.map f s.val))",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\... | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
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] |
Mathlib/LinearAlgebra/Basis.lean | Basis.range_ofVectorSpace | [] | [
1493,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1492,
1
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Mathlib/Algebra/BigOperators/Basic.lean | toAdd_multiset_sum | [
{
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2354,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.preimage_div_preimage_subset | [
{
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1322,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.copy_eq | [] | [
126,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.comp_linearIsometryEquiv | [] | [
1333,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
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] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_isMaxOn | [] | [
258,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
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] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_induction_nonempty | [
{
"state_after": "no goals",
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1373,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_inter' | [
{
"state_after": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nhs : Set.Finite s\n⊢ ↑↑(condCount s) (u ∩ t) = ↑↑(condCount (s ∩ u)) t * ↑↑(condCount s) u",
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.lift_symm_apply | [] | [
245,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Mathlib/Data/Finset/Basic.lean | Finset.inter_subset_inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.188858\nγ : Type ?u.188861\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na✝ b : α\nx y s t : Finset α\nh : x ⊆ y\nh' : s ⊆ t\na : α\na_in : a ∈ x ∩ s\n⊢ a ∈ y ∩ t",
"state_before": "α : Type u_1\nβ : Type ?u.188858\nγ : Type ?u.188861\ninst✝ : Decidabl... | [
1699,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1696,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.add_le_add_left | [
{
"state_after": "d : ℕ\na b : ℤ√↑d\nab : a ≤ b\nc : ℤ√↑d\n⊢ Nonneg (b - a)",
"state_before": "d : ℕ\na b : ℤ√↑d\nab : a ≤ b\nc : ℤ√↑d\n⊢ Nonneg (c + b - (c + a))",
"tactic": "rw [add_sub_add_left_eq_sub]"
},
{
"state_after": "no goals",
"state_before": "d : ℕ\na b : ℤ√↑d\nab : a ≤ b\nc : ℤ√... | [
786,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
11
] |
Mathlib/Tactic/Linarith/Preprocessing.lean | Linarith.without_one_mul | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : MulOneClass M\na b : M\nh : 1 * a = b\n⊢ a = b",
"tactic": "rwa [one_mul] at h"
}
] | [
282,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na : α\nha : a ≠ 0\nb c : α\n⊢ (fun x => a * x) ⁻¹' [[b, c]] = [[b / a, c / a]]",
"tactic": "simp only [← preimage_mul_const_uIcc ha, mul_comm]"
}
] | [
700,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.Commute.zpow_zpow_self | [] | [
241,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_div | [] | [
298,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | Nat.binCast_eq | [
{
"state_after": "R : Type u_1\ninst✝ : AddMonoidWithOne R\nn : ℕ\n⊢ ∀ (n : ℕ), (∀ (m : ℕ), m < n → Nat.binCast m = ↑m) → Nat.binCast n = ↑n",
"state_before": "R : Type u_1\ninst✝ : AddMonoidWithOne R\nn : ℕ\n⊢ Nat.binCast n = ↑n",
"tactic": "apply Nat.strongInductionOn n"
},
{
"state_after": "R... | [
168,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_injective | [] | [
125,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_le | [] | [
151,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.norm_eq_hammingNorm | [] | [
466,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.cancel_factors_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Field α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : ad ≠ 0\nhbd : bd ≠ 0\nhgcd : gcd ≠ 0\n⊢ (a ≠ b) = (1 / gcd * (bd * a') ≠ 1 / gcd * (ad * b'))",
"tactic": "classical\nrw [eq_iff_iff, not_iff_not, cancel_factor... | [
100,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv | [] | [
754,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.mul_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\nb : α\nhb : b ≠ 0\n⊢ (if ⊤ = 0 ∨ ↑b = 0 then 0 else ⊤) = ⊤",
"tactic": "simp [hb]"
},
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\nb : α\nhb : b ≠ 0\na :... | [
107,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_add | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.265062\nG : Type ?u.265065\n𝕜 : Type ?u.265068\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
467,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Topology/Category/TopCat/Basic.lean | TopCat.openEmbedding_iff_isIso_comp' | [
{
"state_after": "X Y Z : TopCat\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso f\n⊢ OpenEmbedding ((forget TopCat).map (f ≫ g)) ↔ OpenEmbedding ((forget TopCat).map g)",
"state_before": "X Y Z : TopCat\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso f\n⊢ OpenEmbedding ((forget TopCat).map f ≫ (forget TopCat).map g) ↔ OpenEmbed... | [
190,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_bit0 | [] | [
144,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.head_dropn | [
{
"state_after": "case zero\nα : Type u\nβ : Type v\nγ : Type w\ns✝ s : Seq α\n⊢ head (drop s Nat.zero) = get? s Nat.zero\n\ncase succ\nα : Type u\nβ : Type v\nγ : Type w\ns✝ : Seq α\nn : ℕ\nIH : ∀ (s : Seq α), head (drop s n) = get? s n\ns : Seq α\n⊢ head (drop s (Nat.succ n)) = get? s (Nat.succ n)",
"stat... | [
853,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_dist_lt | [] | [
774,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.inv_subset_inv | [] | [
270,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_insert | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.14340\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\ninst✝ : DecidableEq β\nb : β\nh : b ∈ s\n⊢ gcd (insert b s) f = GCDMonoid.gcd (f b) (gcd s f)\n\ncase neg\nα : Type u_2\nβ : Type u_1\nγ ... | [
174,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.finrank_eq_card | [] | [
355,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/List/ProdSigma.lean | List.nil_sigma | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Std/Data/Option/Lemmas.lean | Option.join_ne_none' | [] | [
114,
15
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
113,
1
] |
Mathlib/Data/Set/Prod.lean | Set.image_swap_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.30722\nδ : Type ?u.30725\ns✝ s₁ s₂ : Set α\nt✝ t₁ t₂ : Set β\na : α\nb : β\ns : Set α\nt : Set β\n⊢ Prod.swap '' s ×ˢ t = t ×ˢ s",
"tactic": "rw [image_swap_eq_preimage_swap, preimage_swap_prod]"
}
] | [
274,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.mk_eq_mk | [] | [
206,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Equiv.Perm.prod_comp' | [
{
"state_after": "case h.e'_2.a.h.e'_2\nι : Type ?u.298556\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nσ : Equiv.Perm α\ns : Finset α\nf : α → α → β\nhs : {a | ↑σ a ≠ a} ⊆ ↑s\nx✝ : α\na✝ : x✝ ∈ s\n⊢ x✝ = ↑σ.symm (↑σ x✝)",
"state_before": "ι : Type ?u.... | [
448,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformEmbedding_inr | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\ns : Set (β × β)\nhs : s ∈ 𝓤 β\nx : β × β\nh : x ∈ Prod.map Sum.inr Sum.inr ⁻¹' (range (Prod.map Sum.inl Sum.inl) ∪ Prod.map Sum.inr Sum.inr '' s)\n⊢ x ... | [
190,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.differentiableAt_sin | [] | [
595,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Std/Data/String/Lemmas.lean | String.splitAux_of_valid | [
{
"state_after": "p : Char → Bool\nl m r : List Char\nacc : List String\n⊢ (if h : atEnd { data := l ++ m ++ r } { byteIdx := utf8Len l + utf8Len m } = true then\n let r := extract { data := l ++ m ++ r } { byteIdx := utf8Len l } { byteIdx := utf8Len l + utf8Len m } :: acc;\n List.reverse r\n else\... | [
463,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
452,
1
] |
Mathlib/Algebra/Lie/Quotient.lean | LieSubmodule.Quotient.lieModuleHom_ext | [] | [
216,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | comap_uniformity_mulOpposite | [] | [
1535,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1533,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.eval_indicator_apply_eq_one | [
{
"state_after": "K : Type u_1\nσ : Type u_2\ninst✝² : Fintype K\ninst✝¹ : Fintype σ\ninst✝ : CommRing K\na : σ → K\n✝ : Nontrivial ((fun x => K) (indicator a))\n⊢ ↑(eval a) (indicator a) = 1",
"state_before": "K : Type u_1\nσ : Type u_2\ninst✝² : Fintype K\ninst✝¹ : Fintype σ\ninst✝ : CommRing K\na : σ → K... | [
81,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Disjoint.lean | disjoint_ofDual_iff | [] | [
423,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.isWeightedHomogeneous_zero | [] | [
228,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.submodule_injective | [
{
"state_after": "case h\nK : Type u_2\nV : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nu✝ v : ℙ K V\nh✝ : Projectivization.submodule u✝ = Projectivization.submodule v\nu : V\nhu : u ≠ 0\nh : Projectivization.submodule (mk K u hu) = Projectivization.submodule v\n⊢ mk K u hu =... | [
156,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Finset/Image.lean | Equiv.finsetCongr_refl | [
{
"state_after": "case H.a\nα : Type u_1\nβ : Type ?u.154829\nγ : Type ?u.154832\nx✝ : Finset α\na✝ : α\n⊢ a✝ ∈ ↑(Equiv.finsetCongr (Equiv.refl α)) x✝ ↔ a✝ ∈ ↑(Equiv.refl (Finset α)) x✝",
"state_before": "α : Type u_1\nβ : Type ?u.154829\nγ : Type ?u.154832\n⊢ Equiv.finsetCongr (Equiv.refl α) = Equiv.refl (... | [
791,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsClosed.not_mem_iff_infDist_pos | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.66060\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : IsClosed s\nhs : Set.Nonempty s\n⊢ ¬x ∈ s ↔ 0 < infDist x s",
"tactic": "simp [h.mem_iff_infDist_zero hs, infDist_non... | [
605,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.X_mul_modMonomial | [] | [
186,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.le_symm_apply | [] | [
990,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi | [
{
"state_after": "case refine'_1\nV : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : Collinear ℝ {p₁, p₂, p₃}\n⊢ p₁ = p₂ ∨ p₃ = p₂ ∨ ∠ p₁ p₂ p₃ = 0 ∨ ∠ p₁ p₂ p₃ = π\n\ncase refine'_2\nV : Type u_1\nP :... | [
441,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/Order/Basic.lean | comap_coe_Ioo_nhdsWithin_Iio | [] | [
2491,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2489,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_of_left_inverse | [] | [
215,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\nr : R\nk : ℕ\n⊢ content (↑(monomial k) r) = ↑normalize r",
"tactic": "rw [← C_mul_X_pow_eq_monomial, content_C_mul, content_X_pow, mul_one]"
}
] | [
159,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.comp_inv_eq_id | [] | [
255,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_measure_zero | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.951858\nF : Type u_2\nG : Type ?u.951864\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : MeasurableSpace α\nf : α → F\nh0 : p = 0\n⊢ snorm f p 0... | [
252,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Std/Logic.lean | imp_and | [] | [
311,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
310,
1
] |
Mathlib/Combinatorics/Hindman.lean | Hindman.exists_idempotent_ultrafilter_le_FP | [
{
"state_after": "M : Type u_1\ninst✝ : Semigroup M\na : Stream' M\nS : Set (Ultrafilter M) := ⋂ (n : ℕ), {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop n a)}\n⊢ ∃ U, U * U = U ∧ ∀ᶠ (m : M) in ↑U, m ∈ FP a",
"state_before": "M : Type u_1\ninst✝ : Semigroup M\na : Stream' M\n⊢ ∃ U, U * U = U ∧ ∀ᶠ (m : M) in ↑U,... | [
170,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_add | [
{
"state_after": "x y : ℝ\n⊢ ↑(cosh (x + y)) = ↑(cosh x * cosh y + sinh x * sinh y)",
"state_before": "x y : ℝ\n⊢ cosh (x + y) = cosh x * cosh y + sinh x * sinh y",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cosh (x + y)) = ↑(cosh x * cosh y +... | [
1379,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
8
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.det_conj | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.408621\nm : Type u\nn : Type u'\nα : Type v\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq n\ninst✝² : CommRing α\nA B : Matrix n n α\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nM : Matrix m m α\nh : IsUnit M\nN : Matrix m m α\n⊢ det (M ⬝ N ⬝ M⁻¹) = det N... | [
705,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/LinearAlgebra/Contraction.lean | dualTensorHomEquivOfBasis_toLinearMap | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.ext | [] | [
186,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.set_average_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.198493\nm0 : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nμ : Measure α\ns✝ : Set E... | [
121,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
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