file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/DirectSum/Finsupp.lean | finsuppLEquivDirectSum_single | [] | [
46,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.aposteriori_dist_iterate_fixedPoint_le | [
{
"state_after": "α : Type u_1\ninst✝² : MetricSpace α\nK : ℝ≥0\nf : α → α\nhf : ContractingWith K f\ninst✝¹ : Nonempty α\ninst✝ : CompleteSpace α\nx : α\nn : ℕ\n⊢ dist ((f^[n]) x) (fixedPoint f hf) ≤ dist ((f^[n]) x) ((f ∘ f^[n]) x) / (1 - ↑K)",
"state_before": "α : Type u_1\ninst✝² : MetricSpace α\nK : ℝ≥... | [
331,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_mul_self | [] | [
107,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Dynamics/FixedPoints/Topology.lean | isClosed_fixedPoints | [] | [
45,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | Nat.sq_add_sq_zmodEq | [
{
"state_after": "case intro.intro\nK : Type ?u.853209\nR : Type ?u.853212\np : ℕ\ninst✝ : Fact (Prime p)\nx : ℤ\na b : ZMod p\nhx : a ^ 2 + b ^ 2 = ↑x\n⊢ ∃ a b, a ≤ p / 2 ∧ b ≤ p / 2 ∧ ↑a ^ 2 + ↑b ^ 2 ≡ x [ZMOD ↑p]",
"state_before": "K : Type ?u.853209\nR : Type ?u.853212\np : ℕ\ninst✝ : Fact (Prime p)\nx ... | [
340,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinearForm.toMatrixAux_eq | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1169905\nM : Type ?u.1169908\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : Module R M\nR₁ : Type ?u.1169944\nM₁ : Type ?u.1169947\ninst✝¹⁴ : Ring R₁\ninst✝¹³ : AddCommGroup M₁\ninst✝¹² : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_2\ninst✝... | [
322,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.167346\nγ : Type ?u.167349\nι : Type ?u.167352\nM : Type u_2\nM' : Type ?u.167358\nN : Type ?u.167361\nP : Type ?u.167364\nG : Type ?u.167367\nH : Type ?u.167370\nR : Type ?u.167373\nS : Type ?u.167376\ninst✝ : Zero M\na : α\n⊢ erase a ... | [
676,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.strongInduction_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.74113\ns✝ t : Finset α\nf : α → β\nn : ℕ\np : Finset α → Sort u_2\nH : (s : Finset α) → ((t : Finset α) → t ⊂ s → p t) → p s\ns : Finset α\n⊢ strongInduction H s = H s fun t x => strongInduction H t",
"tactic": "rw [strongInduction]... | [
646,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_smul | [
{
"state_after": "case coeff.h\nR : Type u\nR' : Type ?u.298758\ninst✝³ : Semiring R\ninst✝² : Ring R'\nf g : PowerSeries R\nf' g' : PowerSeries R'\nS : Type u_1\ninst✝¹ : Semiring S\ninst✝ : Module R S\nr : R\nx : PowerSeries S\nx✝ : ℤ\n⊢ HahnSeries.coeff (↑(ofPowerSeries ℤ S) (r • x)) x✝ = HahnSeries.coeff (r... | [
245,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/LinearAlgebra/TensorProductBasis.lean | Basis.tensorProduct_repr_tmul_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_3\nN : Type u_5\nι : Type u_1\nκ : Type u_4\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nb : Basis ι R M\nc : Basis κ R N\nm : M\nn : N\ni : ι\nj : κ\n⊢ ↑(↑(tensorProduc... | [
55,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Star/Basic.lean | commute_star_star | [] | [
160,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\n⊢ order 1 = 0",
"tactic": "simpa using order_monomial_of_ne_zero 0 (1 : R) one_ne_zero"
}
] | [
2486,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2485,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_lt | [] | [
621,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_max' | [] | [
1355,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.const.mk_get | [
{
"state_after": "case mk\nn m : ℕ\nP : MvPFunctor n\nA : Type u\nα β : TypeVec n\nfst✝ : (const n A).A\nsnd✝ : B (const n A) fst✝ ⟹ α\n⊢ mk n (get { fst := fst✝, snd := snd✝ }) = { fst := fst✝, snd := snd✝ }",
"state_before": "n m : ℕ\nP : MvPFunctor n\nA : Type u\nα β : TypeVec n\nx : Obj (const n A) α\n⊢... | [
117,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.mem_map | [
{
"state_after": "case a\nR : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³... | [
827,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_filter_le_smul_filter | [] | [
1227,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_inf | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.trans_app | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_one_left' | [] | [
470,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | deriv_inv | [
{
"state_after": "case inl\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\ns t : Set 𝕜\nL : Filter 𝕜\n⊢ deriv (fun x => x⁻¹) 0 = ... | [
99,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_nonpos_iff | [] | [
189,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.le_exp_log | [
{
"state_after": "case pos\nx✝ y x : ℝ\nh_zero : x = 0\n⊢ x ≤ exp (log x)\n\ncase neg\nx✝ y x : ℝ\nh_zero : ¬x = 0\n⊢ x ≤ exp (log x)",
"state_before": "x✝ y x : ℝ\n⊢ x ≤ exp (log x)",
"tactic": "by_cases h_zero : x = 0"
},
{
"state_after": "case pos\nx✝ y x : ℝ\nh_zero : x = 0\n⊢ 0 ≤ 1",
"s... | [
77,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_natCast | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.127287\nα : Type u_1\nβ : Type ?u.127293\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ : α\nn : ℕ\na : ℤ\n⊢ a ≤ ⌊↑n⌋ ↔ a ≤ ↑n",
"tactic": "rw [le_floor, ← cast_ofNat, cast_le]"
}
] | [
702,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : CommSemiring R\np q : R[X]\nx : R\ninst✝ : CommSemiring S\nf : R →+* S\n⊢ eval x (comp p q) = eval (eval x q) p",
"tactic": "induction p using Polynomial.induction_on' with\n| h_add r... | [
1082,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Order/RelClasses.lean | wellFoundedGT_dual_iff | [] | [
370,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.ext_iff | [] | [
725,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.addHom_ext' | [] | [
1146,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Algebra/Group/Conj.lean | isConj_comm | [] | [
46,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.shiftl_add | [
{
"state_after": "m n✝ k i n : ℕ\n⊢ ↑(Nat.shiftl m i) = ↑(Nat.shiftr (Nat.shiftl m (n + i)) n)",
"state_before": "m n✝ k i n : ℕ\n⊢ (fun n k i => shiftl (↑m) i = ↑(Nat.shiftr (Nat.shiftl m n) k)) (n + i) n ↑i",
"tactic": "dsimp"
},
{
"state_after": "case a\nm n✝ k i n : ℕ\n⊢ n ≤ n + i",
"sta... | [
426,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Analysis/PSeries.lean | Real.summable_nat_rpow | [
{
"state_after": "case intro\np : ℝ\n⊢ (Summable fun n => ↑n ^ (-p)) ↔ -p < -1",
"state_before": "p : ℝ\n⊢ (Summable fun n => ↑n ^ p) ↔ p < -1",
"tactic": "rcases neg_surjective p with ⟨p, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\np : ℝ\n⊢ (Summable fun n => ↑n ^ (-p... | [
198,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mk_injective | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns✝ : Finset ι\nx✝ : (i : ↑↑s✝) → β ↑i\ni : ι\ns : Finset ι\nx y : (i : ↑↑s) → β ↑i\nH : mk s x = mk s y\n⊢ x = y",
"state_before": "ι : Type u\nγ : Type w\nβ : ι →... | [
601,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.snd' | [] | [
807,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_gcd_helper_1 | [] | [
47,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.le_of_lip' | [
{
"state_after": "case refine'_1\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.135450\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' :... | [
340,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.hasFDerivWithinAt_iff | [] | [
859,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Topology/StoneCech.lean | denseEmbedding_pure | [] | [
153,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_transpose | [
{
"state_after": "case h\nl : Type ?u.916196\nm : Type u_1\nn : Type u_2\no : Type ?u.916205\nm' : o → Type ?u.916210\nn' : o → Type ?u.916215\nR : Type ?u.916218\nS : Type ?u.916221\nα : Type v\nβ : Type w\nγ : Type ?u.916228\ninst✝¹ : NonUnitalCommSemiring α\ninst✝ : Fintype m\nA : Matrix m n α\nx : m → α\nx✝... | [
1932,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1930,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_sin | [] | [
1026,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.cos_eq_zero_iff | [
{
"state_after": "θ : ℂ\nh : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1\n⊢ cos θ = 0 ↔ ∃ k, θ = (2 * ↑k + 1) * ↑π / 2",
"state_before": "θ : ℂ\n⊢ cos θ = 0 ↔ ∃ k, θ = (2 * ↑k + 1) * ↑π / 2",
"tactic": "have h : (exp (θ * I) + exp (-θ * I)) / 2 = 0 ↔ exp (2 * θ * I) = -1 := by\n rw [@di... | [
42,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_monomial | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\nn : σ →₀ ℕ\na : R\nm : σ →₀ ℕ\n⊢ (if n = m then a else 0) = if m = n then a else 0",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\nn : σ →₀ ℕ\na : R\nm : σ →₀ ℕ\n⊢ ↑(M... | [
1084,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/Deprecated/Subfield.lean | Range.isSubfield | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nS : Set F\nK : Type u_1\ninst✝ : Field K\nf : F →+* K\n⊢ IsSubfield (↑f '' Set.univ)",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nS : Set F\nK : Type u_1\ninst✝ : Field K\nf : F →+* K\n⊢ IsSubfield (Set.range ↑f)",
"tactic": "rw [← Set.image_univ]"... | [
79,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.dualBasis_apply_self | [
{
"state_after": "case h.e'_3.h₁.a\nR : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : DecidableEq ι\nb : Basis ι R M\ninst✝ : _root_.Finite ι\ni j : ι\n⊢ j = i ↔ i = j",
"state_before": "R : Type u\nM : Type v\nK : Type ... | [
425,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_congr | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.27036\nι : Sort ?u.27039\nι' : Sort ?u.27042\nf✝ : α → β\ns✝ t : Set α\nf g : α → β\ns : Set α\nh : ∀ (a : α), a ∈ s → f a = g a\nx : β\n⊢ x ∈ f '' s ↔ x ∈ g '' s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.27036\nι : Sort ?u.2... | [
264,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.smul_zero_nonneg | [] | [
1354,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1351,
1
] |
Mathlib/Data/Set/Sups.lean | Set.image_subset_infs_left | [] | [
253,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.of_append_left | [] | [
211,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.image_div_divisors_eq_divisors | [
{
"state_after": "case pos\nn✝ n : ℕ\nhn : n = 0\n⊢ image (fun x => n / x) (divisors n) = divisors n\n\ncase neg\nn✝ n : ℕ\nhn : ¬n = 0\n⊢ image (fun x => n / x) (divisors n) = divisors n",
"state_before": "n✝ n : ℕ\n⊢ image (fun x => n / x) (divisors n) = divisors n",
"tactic": "by_cases hn : n = 0"
... | [
508,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Init/Logic.lean | or_self_iff | [] | [
187,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.sub_comp | [] | [
1281,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.exists_primitive_lcm_of_isPrimitive | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nhp : IsPrimitive p\nhq : IsPrimitive q\nh : ∃ n r, natDegree r = n ∧ IsPrimitive r ∧ p ∣ r ∧ q ∣ r\n⊢ ∃ r, IsPrimitive r ∧ ∀ (s : R[X]), p ∣ s ∧ q ∣ s ↔ r ∣ s",
"state_before": "R : Type u_1\... | [
476,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | isLittleO_rpow_exp_atTop | [
{
"state_after": "no goals",
"state_before": "s : ℝ\n⊢ (fun x => x ^ s) =o[atTop] exp",
"tactic": "simpa only [one_mul] using isLittleO_rpow_exp_pos_mul_atTop s one_pos"
}
] | [
269,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_clm_comp | [] | [
380,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.preimage_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\na b : β\n⊢ ↑e ⁻¹' Icc a b = Icc (↑(symm e) a) (↑(symm e) b)",
"tactic": "simp [← Ici_inter_Iic]"
}
] | [
51,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.linear_bijective_iff | [] | [
490,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean | CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_rightAdd | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasBinaryBiproducts C\nX Y : C\nh₂ : ∀ (f : X ⟶ Y), biprod.desc 0 f = biprod.snd ≫ f\nh₁ : ∀ (f : X ⟶ Y), biprod.desc f 0 = biprod.fst ≫ f\n⊢ EckmannHilton.IsUnital (fun x x_1 => rightAdd X Y ... | [
86,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.symm_apply_apply | [] | [
345,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.continuousAt | [] | [
227,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
11
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_pow | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.to_rightInvOn | [] | [
156,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.coe_unone | [] | [
144,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.ProjectivePlane.two_lt_pointCount | [
{
"state_after": "no goals",
"state_before": "P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P L\ninst✝¹ : Finite P\ninst✝ : Finite L\nl : L\n⊢ 2 < pointCount P l",
"tactic": "simpa only [pointCount_eq P l, Nat.succ_lt_succ_iff] using one_lt_order P L"
}
] | [
487,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.Nonempty.of_sUnion | [] | [
1123,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.extLit | [] | [
605,
71
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
601,
1
] |
Mathlib/Topology/Inseparable.lean | Continuous.specialization_monotone | [] | [
246,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/RingTheory/RootsOfUnity/Complex.lean | IsPrimitiveRoot.arg_ext | [] | [
118,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_sub | [
{
"state_after": "case h\nR : Type u_1\ninst✝¹⁶ : Ring R\nR₂ : Type u_2\ninst✝¹⁵ : Ring R₂\nR₃ : Type u_3\ninst✝¹⁴ : Ring R₃\nM : Type u_6\ninst✝¹³ : TopologicalSpace M\ninst✝¹² : AddCommGroup M\nM₂ : Type u_4\ninst✝¹¹ : TopologicalSpace M₂\ninst✝¹⁰ : AddCommGroup M₂\nM₃ : Type u_5\ninst✝⁹ : TopologicalSpace M₃... | [
1415,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1412,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_conj | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.37340\nα : Type u_1\nβ : Type ?u.37346\nf g : Perm α\np : α → Prop\nx y z : α\ni : ℤ\n⊢ ↑((g * f * g⁻¹) ^ i) x = y ↔ ↑(f ^ i) (↑g⁻¹ x) = ↑g⁻¹ y",
"tactic": "simp [conj_zpow, eq_inv_iff_eq]"
}
] | [
121,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.rfl | [] | [
176,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
11
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_eq_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocMod hp a b = toIocMod hp 0 (b - a) + a",
"tactic": "rw [toIocMod_sub_eq_sub, zero_add, sub_add_cancel]"
}
] | [
781,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | hasStrictDerivAt_zpow | [
{
"state_after": "case inl\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx✝ : 𝕜\ns : Set 𝕜\nm✝ m : ℤ\nx : 𝕜\nh : x ≠ 0 ∨ 0 ≤ m\nthis : ∀ (m : ℤ), 0 < m → HasStrictDerivAt (fun x => x ^ m) (↑m * x ^ (m - 1)) x\nhm : m < 0\n⊢ HasStrictDe... | [
64,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | finsuppLequivDfinsupp_symm_apply | [] | [
272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | lt_inv | [] | [
296,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | tendsto_const_mul_zpow_atTop_zero | [] | [
173,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_id | [
{
"state_after": "a b : ℝ\nn : ℕ\nthis : (∫ (x : ℝ) in a..b, x ^ 1) = (b ^ (1 + 1) - a ^ (1 + 1)) / (↑1 + 1)\n⊢ (∫ (x : ℝ) in a..b, x) = (b ^ 2 - a ^ 2) / 2",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, x) = (b ^ 2 - a ^ 2) / 2",
"tactic": "have := @integral_pow a b 1"
},
{
"state_aft... | [
414,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_preimage_im | [] | [
93,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.image_smul_comm | [] | [
759,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_insert_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.48083\ninst✝ : PartialOrder α\na b c : α\nh : a ≤ b\n⊢ insert b (Ico a b) = Icc a b",
"tactic": "rw [insert_eq, union_comm, Ico_union_right h]"
}
] | [
877,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_eq_zero_iff_isEmpty | [] | [
232,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Topology/Maps.lean | OpenEmbedding.open_iff_image_open | [
{
"state_after": "case h.e'_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.236323\nδ : Type ?u.236326\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\nhf : OpenEmbedding f\ns : Set α\nh : IsOpen (f '' s)\n⊢ f ⁻¹' (f '' s) = s",
"state_before": "α : Type u_1\nβ : ... | [
565,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_le_inv' | [] | [
1504,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1503,
21
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_iSup | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nκ : ι → Sort ?u.18544\na a₁ a₂ : α\nb b₁ b₂ : β\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nl : α → β\nu : β → α\ngc : GaloisConnection l u\nf : ι → α\n⊢ IsLUB (l '' range f) (l (sSup (range f)))",
"state_before": "α : Type u\nβ :... | [
292,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.diamond | [] | [
223,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/WithBot.lean | WithBot.none_le | [] | [
212,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.multiset_sum_mem | [] | [
347,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
11
] |
Std/Logic.lean | not_exists | [] | [
419,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
419,
9
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.dvd_span_singleton | [] | [
703,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.abs_top | [] | [
1056,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
9
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.iff_preimage_eq' | [] | [
536,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | PiTensorProduct.gradedMonoid_eq_of_reindex_cast | [
{
"state_after": "R : Type u_4\nM : Type u_3\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nιι : Type u_1\nι : ιι → Type u_2\nai : ιι\na b : ⨂[R] (x : ι ai), M\nh : ↑(reindex R M (Equiv.cast (_ : ι { fst := ai, snd := a }.fst = ι { fst := ai, snd := b }.fst))) a = b\n⊢ { fst := ai, snd ... | [
60,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | IsEquivalent.summable_iff_nat | [] | [
717,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Data/W/Constructions.lean | WType.rightInverse_list | [
{
"state_after": "no goals",
"state_before": "γ : Type u\nhd : γ\ntl : List γ\n⊢ toList γ (ofList γ (hd :: tl)) = hd :: tl",
"tactic": "simp only [toList, rightInverse_list tl]"
}
] | [
178,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_one | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nh1 : ¬1 ≈ 0\n⊢ norm 1 = 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ norm 1 = 1",
"tactic": "have h1 : ¬(1 : PadicSeq p) ≈ 0 := one_not_equiv_zero _"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nh... | [
325,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ioc_subset | [] | [
80,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.le_inv_iff_mul_le | [
{
"state_after": "no goals",
"state_before": "r p : ℝ≥0\nh : p ≠ 0\n⊢ r ≤ p⁻¹ ↔ r * p ≤ 1",
"tactic": "rw [← mul_le_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h, mul_comm]"
}
] | [
791,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Data/Nat/Parity.lean | Odd.mod_even_iff | [] | [
347,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.mapBicone_whisker | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | norm_expSeries_summable' | [] | [
417,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_lt_inter_lt | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : NoMaxOrder α\na : α\n⊢ Bounded (fun x x_1 => x < x_1) (s ∩ {b | a < b}) ↔ Bounded (fun x x_1 => x < x_1) s",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : NoMaxOrder... | [
389,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map_pure | [] | [
1034,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.