file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Finsupp/Order.lean | Finsupp.single_le_iff | [
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}
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173,
55
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172,
1
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Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.mul | [] | [
160,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/Algebra/Order/SMul.lean | smul_lt_smul_iff_of_pos | [] | [
125,
85
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124,
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.rank_pow_quot_aux | [
{
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.degree_eq_card_roots | [
{
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327,
69
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325,
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.refl_apply | [
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442,
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441,
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableWithinAt.smul_const | [] | [
246,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.mul_inverse_cancel_left | [
{
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"tactic": "rw [← mul_assoc, mul_inverse_cancel x h... | [
125,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.Meq.equiv_symm_eq_apply | [
{
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140,
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136,
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Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_lt_sum_fiber_of_sum_fiber_nonpos_of_nsmul_lt_sum | [
{
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146,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.ext_iff | [] | [
116,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.iInf_adj_of_nonempty | [
{
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"tactic": "rw [iInf, ... | [
337,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
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Mathlib/Data/Finset/Lattice.lean | Finset.inf'_lt_iff | [] | [
1108,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset | [
{
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1758,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.comap_apply₀ | [
{
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Mathlib/Algebra/Group/Basic.lean | mul_left_comm | [] | [
98,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Hom/Freiman.lean | map_prod_eq_map_prod_of_le | [
{
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523,
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Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.matPolyEquiv_eval | [
{
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182,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanCompIso_app_right | [] | [
348,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
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Mathlib/Data/Complex/Module.lean | Complex.finrank_real_complex | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.167341\nS : Type ?u.167344\n⊢ finrank ℝ ℂ = 2",
"tactic": "rw [finrank_eq_card_basis basisOneI, Fintype.card_fin]"
}
] | [
187,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_mul_descFactorial | [
{
"state_after": "no goals",
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"tactic": "rw [descFactorial_zero, mul_one, tsub_zero]"
},
{
"state_after": "case h\nk : ℕ\nh : succ k ≤ 0\n⊢ False",
"state_before": "k : ℕ\nh : succ k ≤ 0\n⊢ (0 - succ k)! * descFactoria... | [
425,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
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Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetAux_perm_powersetAux' | [
{
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"state_before": "α : Type u_1\nl : List α\n⊢ powersetAux l ~ powersetAux' l",
"tactic": "rw [powersetAux_eq_map_coe]"
},
{
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71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Lipschitz.lean | lipschitz_on_univ | [
{
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"tactic": "simp [LipschitzOnWith, LipschitzWith]"
}
] | [
99,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Gcd.lean | Nat.lcm_assoc | [] | [
222,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
214,
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Mathlib/Algebra/DualQuaternion.lean | Quaternion.imJ_fst_dualNumberEquiv | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.one_submatrix_mul | [
{
"state_after": "case intro\nl : Type u_4\nm : Type u_1\nn : Type u_3\no : Type u_2\nm' : o → Type ?u.1177977\nn' : o → Type ?u.1177982\nR : Type ?u.1177985\nS : Type ?u.1177988\nα : Type v\nβ : Type w\nγ : Type ?u.1177995\ninst✝³ : Fintype m\ninst✝² : Finite o\ninst✝¹ : NonAssocSemiring α\ninst✝ : DecidableEq... | [
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Mathlib/Topology/Order/Basic.lean | Dense.exists_gt | [] | [
762,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
11
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Mathlib/RingTheory/ChainOfDivisors.lean | pow_image_of_prime_by_factor_orderIso_dvd | [
{
"state_after": "case pos\nM : Type u_1\ninst✝⁴ : CancelCommMonoidWithZero M\nN : Type u_2\ninst✝³ : CancelCommMonoidWithZero N\ninst✝² : UniqueFactorizationMonoid N\ninst✝¹ : UniqueFactorizationMonoid M\ninst✝ : DecidableEq (Associates M)\nm p : Associates M\nn : Associates N\nhn : n ≠ 0\nhp : p ∈ normalizedF... | [
284,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.map_mul | [] | [
242,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
11
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Mathlib/Data/Set/Intervals/Basic.lean | Set.nonempty_Ici | [] | [
286,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.card_sups_le | [] | [
74,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.sInf_toAddSubmonoid | [] | [
449,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
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Mathlib/Init/CcLemmas.lean | and_eq_of_eq_true_right | [] | [
25,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_eval_one | [
{
"state_after": "no goals",
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"tactic": "rw_mod_cast [pochhammer_nat_eq_ascFactorial, Nat.zero_ascFactorial]"
}
] | [
193,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsLowerSet.smul | [] | [
56,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Algebra/Ring/Units.lean | IsUnit.neg_iff | [] | [
104,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/Data/List/Nodup.lean | List.Nodup.mem_erase_iff | [
{
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"tactic": "rw [d.erase_eq_filter, mem_filter, and_comm, decide_eq_true_iff]"
}
] | [
325,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasLimits_of_hasColimits_op | [] | [
275,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_eq | [
{
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77,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_finset_sum_measure | [
{
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560,
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558,
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Mathlib/Order/FixedPoints.lean | OrderHom.le_prevFixed_iff | [] | [
236,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Analysis/Convex/Function.lean | strictConcaveOn_iff_div | [] | [
1079,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1075,
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Mathlib/Data/Finset/Basic.lean | Finset.filter_empty | [] | [
2725,
38
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2724,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.lt_of_succ_lt_succ | [] | [
308,
21
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
307,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_b_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.579663\nF : Type ?u.579666\nK : Type ?u.579669\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b ≠ 0\n⊢ degree (toPoly P) = 2",
"tactic": "rw [of_a_eq_zero ha, degree_quadratic hb]"
}
] | [
323,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_self_nonneg | [] | [
213,
16
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212,
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.option_iff | [
{
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497,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_neg | [] | [
363,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.support_map_subset | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nf : R →+* S\np : R[X]\nx : ℕ\n⊢ x ∈ support (map f p) → x ∈ support p",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ :... | [
1179,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.one_def | [] | [
887,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
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Mathlib/Order/Filter/Basic.lean | Filter.iSup_sets_eq | [] | [
531,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_smul_vsub_vadd_left | [
{
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334,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
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Mathlib/Analysis/Complex/Basic.lean | Complex.dist_of_re_eq | [
{
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}
] | [
107,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
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Mathlib/Analysis/Complex/RealDeriv.lean | ContDiff.real_of_complex | [] | [
97,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Computability/Primrec.lean | Primrec.unpair | [
{
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}
] | [
375,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
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Mathlib/LinearAlgebra/Span.lean | Submodule.comap_map_eq | [
{
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861,
79
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858,
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Mathlib/Algebra/Quaternion.lean | Quaternion.rat_cast_imJ | [] | [
1361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1360,
1
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Mathlib/Data/List/Chain.lean | List.chain_map | [
{
"state_after": "no goals",
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"tactic": "induction l generalizing b <;> simp only [map, Chain.nil, chain_cons, *]"
}... | [
87,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Data/Quot.lean | Quotient.surjective_Quotient_mk'' | [] | [
612,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
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Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.comp | [
{
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}
] | [
345,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.div_add_div_same | [] | [
1691,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1690,
11
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Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow_iff_of_lt_one | [] | [
519,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
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Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.coe_top | [] | [
516,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
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Mathlib/Data/Finmap.lean | Finmap.mem_insert | [] | [
497,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
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Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_le_prod | [
{
"state_after": "case empty\nι : Type u_1\nα : Type ?u.149270\nβ : Type ?u.149273\nM : Type ?u.149276\nN : Type ?u.149279\nG : Type ?u.149282\nk : Type ?u.149285\nR : Type u_2\ninst✝ : OrderedCommSemiring R\nf g : ι → R\ns t : Finset ι\nh0✝ : ∀ (i : ι), i ∈ s → 0 ≤ f i\nh1✝ : ∀ (i : ι), i ∈ s → f i ≤ g i\nh0 :... | [
604,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
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Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_eq_smul_one' | [] | [
363,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
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Mathlib/Topology/Perfect.lean | exists_perfect_nonempty_of_isClosed_of_not_countable | [
{
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"state_be... | [
217,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_mul_X_pow | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nx : R\n⊢ eval x (p * X ^ Nat.zero) = eval x p * x ^ Nat.zero\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nx : R\nk... | [
466,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
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Mathlib/Data/Nat/Bitwise.lean | Nat.land'_assoc | [
{
"state_after": "no goals",
"state_before": "n m k : ℕ\n⊢ land' (land' n m) k = land' n (land' m k)",
"tactic": "bitwise_assoc_tac"
}
] | [
231,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineSubspace.coe_subtypeₐᵢ | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_iUnion₂ | [] | [
389,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.dist_pointReflection_self' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nV : Type u_2\nV₁ : Type ?u.2060153\nV₂ : Type ?u.2060156\nV₃ : Type ?u.2060159\nV₄ : Type ?u.2060162\nP₁ : Type ?u.2060165\nP : Type u_1\nP₂ : Type ?u.2060171\nP₃ : Type ?u.2060174\nP₄ : Type ?u.2060177\ninst✝²¹ : NormedField 𝕜\ninst✝²⁰ : Seminor... | [
810,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
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Mathlib/Data/List/Basic.lean | List.zipLeft_cons_nil | [] | [
4188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4186,
1
] |
Mathlib/Topology/MetricSpace/Baire.lean | dense_iInter_of_open_nat | [] | [
195,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.smul_apply | [] | [
725,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.odd_sub' | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nh : n ≤ m\n⊢ Odd (m - n) ↔ (Odd n ↔ Even m)",
"tactic": "rw [odd_iff_not_even, even_sub h, not_iff, not_iff_comm, odd_iff_not_even]"
}
] | [
205,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | AddMonoidHom.mul_apply | [] | [
312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.AnalyticSet.iUnion | [
{
"state_after": "α : Type u_2\ninst✝¹ : TopologicalSpace α\nι : Type u_1\ninst✝ : Countable ι\ns : ι → Set α\nhs : ∀ (n : ι), AnalyticSet (s n)\nβ : ι → Type\nhβ : (n : ι) → TopologicalSpace (β n)\nh'β : ∀ (n : ι), PolishSpace (β n)\nf : (n : ι) → β n → α\nf_cont : ∀ (n : ι), Continuous (f n)\nf_range : ∀ (n :... | [
209,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/Analysis/NormedSpace/Banach.lean | LinearMap.continuous_of_seq_closed_graph | [
{
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478,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym2_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ Finset.Nonempty (Finset.sym2 s) ↔ Finset.Nonempty s",
"tactic": "rw [Finset.sym2, Nonempty.image_iff, nonempty_product, and_self_iff]"
}
] | [
81,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Analysis/NormedSpace/Extend.lean | LinearMap.norm_extendTo𝕜'_apply_sq | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nF : Type u_1\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : Module ℝ F\ninst✝ : IsScalarTower ℝ 𝕜 F\nfr : F →ₗ[ℝ] ℝ\nx : F\n⊢ ‖↑(extendTo𝕜' fr) x‖ ^ 2 = ↑re (↑(starRingEnd ((fun x => 𝕜) x)) (↑(extend... | [
102,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.dual_comp | [] | [
1384,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1382,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.map_P | [
{
"state_after": "case zero\nC : Type u_4\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\nX✝ : SimplicialObject C\nD : Type u_1\ninst✝² : Category D\ninst✝¹ : Preadditive D\nG : C ⥤ D\ninst✝ : Functor.Additive G\nX : SimplicialObject C\nn : ℕ\n⊢ G.map (HomologicalComplex.Hom.f (P Nat.zero) n) = HomologicalComplex... | [
229,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/List/Basic.lean | List.intercalate_splitOn | [
{
"state_after": "ι : Type ?u.305889\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nxs ys : List α\nls : List (List α)\nf : List α → List α\nx : α\ninst✝ : DecidableEq α\n⊢ join (intersperse [x] (splitOnP (fun x_1 => x_1 == x) xs)) = xs",
"state_before": "ι : Type ?u.305889\n... | [
2995,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2985,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.FilteredColimit.isColimit_eq_iff | [
{
"state_after": "J : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ TypeMax\ninst✝ : IsFilteredOrEmpty J\nt : Cocone F\nht : IsColimit t\ni j : J\nxi : F.obj i\nxj : F.obj j\nt' : Cocone F := colimitCocone F\n⊢ t.ι.app i xi = t.ι.app j xj ↔ ∃ k f g, F.map f xi = F.map g xj",
"state_before": "J : Type v\ninst✝¹ ... | [
487,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_colon_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nF : Type ?u.187576\nG : Type ?u.187579\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nN✝ N₁ N₂ P P₁ P₂ N : Submodule R M\nx : M\nr : R\n⊢ r ∈ colon N (span R {x}) ↔ ∀ (a : R), r • a • x ∈ N",
"tactic": "simp [Submo... | [
398,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.map.valid | [] | [
1597,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
] |
Mathlib/ModelTheory/Order.lean | FirstOrder.Language.Term.realize_le | [
{
"state_after": "no goals",
"state_before": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝³ : IsOrdered L\ninst✝² : Structure L M\ninst✝¹ : LE M\ninst✝ : OrderedStructure L M\nt₁ t₂ : Term L (α ⊕ Fin n)\nv : α → M\nxs : Fin n → M\n⊢ BoundedFormula.Realize (le t₁ t₂) v xs ↔ realize (Sum.elim v xs) t₁ ... | [
218,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_lt_natDegree | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ r p q : R[X]\nhp : p ≠ 0\nhpq : degree p < degree q\nhq : q = 0\n⊢ natDegree p < natDegree q\n\ncase neg\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ r p q : R[X]\nhp : p ≠ 0\nhpq : de... | [
245,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Algebra/Category/MonCat/Basic.lean | CommMonCat.coe_of | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Control/Bifunctor.lean | Bifunctor.snd_fst | [
{
"state_after": "no goals",
"state_before": "F : Type u₀ → Type u₁ → Type u₂\ninst✝¹ : Bifunctor F\ninst✝ : LawfulBifunctor F\nα₀ α₁ : Type u₀\nβ₀ β₁ : Type u₁\nf : α₀ → α₁\nf' : β₀ → β₁\nx : F α₀ β₀\n⊢ snd f' (fst f x) = bimap f f' x",
"tactic": "simp [snd, bimap_bimap]"
}
] | [
105,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.map_sum_finset | [] | [
383,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_neg | [] | [
85,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
82,
19
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.coeff_iterate_derivative_as_prod_range | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np : R[X]\n⊢ ∀ (m : ℕ), coeff ((↑derivative^[Nat.zero]) p) m = (∏ i in range Nat.zero, (m + Nat.zero - i)) • coeff p (m + Nat.zero)\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Ty... | [
425,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/List/Basic.lean | List.length_pmap | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.330264\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nH : ∀ (a : α), a ∈ l → p a\n⊢ length (pmap f l H) = length l",
"tactic": "induction l <;> [rfl; simp only [*, pmap, length]]"... | [
3148,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3147,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.inv_rev | [
{
"state_after": "α : Type u_1\nβ : Type ?u.533106\nE : Type ?u.533109\nF : Type ?u.533112\nG : Type ?u.533115\nE' : Type ?u.533118\nF' : Type ?u.533121\nG' : Type ?u.533124\nE'' : Type ?u.533127\nF'' : Type ?u.533130\nG'' : Type ?u.533133\nR : Type ?u.533136\nR' : Type ?u.533139\n𝕜 : Type u_2\n𝕜' : Type u_3\... | [
1675,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1668,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.eq_false_eq_not_eq_true | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (¬b = true) = (b = false)",
"tactic": "simp"
}
] | [
72,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/NeZero.lean | NeZero.of_pos | [] | [
90,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_def | [] | [
442,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_self | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nU : Set G\nhU : Set.Nonempty (interior U)\n⊢ 0 < ↑(index (↑K₀.toCompacts) U)",
"tactic": "exact_mod_cast index_pos K₀ hU"
}
] | [
330,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
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