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/Order/Monotone/Basic.lean | StrictAnti.antitone | [] | [
470,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
11
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.smulRight_apply | [] | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.nnnorm_map | [] | [
239,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.lcm_coe | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Order/Atoms.lean | GaloisInsertion.isCoatom_of_image | [] | [
747,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_I | [
{
"state_after": "no goals",
"state_before": "⊢ log I = ↑π / 2 * I",
"tactic": "simp [log]"
}
] | [
103,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Option/Basic.lean | Option.orElse_eq_none | [
{
"state_after": "case none\nα : Type u_1\nβ : Type ?u.19607\nγ : Type ?u.19610\nδ : Type ?u.19613\no' : Option α\n⊢ (HOrElse.hOrElse none fun x => o') = none ↔ none = none ∧ o' = none\n\ncase some\nα : Type u_1\nβ : Type ?u.19607\nγ : Type ?u.19610\nδ : Type ?u.19613\no' : Option α\nval✝ : α\n⊢ (HOrElse.hOrEls... | [
384,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.isOpenMap_iff | [
{
"state_after": "α : Type u\nt : TopologicalSpace α\nβ : Type u_1\ninst✝ : TopologicalSpace β\nB : Set (Set α)\nhB : IsTopologicalBasis B\nf : α → β\nhf : ∀ (s : Set α), s ∈ B → IsOpen (f '' s)\no : Set α\nho : IsOpen o\n⊢ IsOpen (f '' o)",
"state_before": "α : Type u\nt : TopologicalSpace α\nβ : Type u_1\... | [
230,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.rename_eval₂ | [
{
"state_after": "case h_X\nσ : Type u_1\nτ : Type u_3\nα : Type ?u.539883\nR : Type u_2\nS : Type ?u.539889\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : R →+* S\nk : σ → τ\ng✝ : τ → S\np : MvPolynomial σ R\ng : τ → MvPolynomial σ R\np✝ : MvPolynomial σ R\nn✝ : σ\na✝ : ↑(rename k) (eval₂ C (g ∘ k) p✝) ... | [
206,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_diagonal | [
{
"state_after": "case inl\nl : Type ?u.178877\nm : Type u_2\nn : Type ?u.178883\no : Type u_1\np : Type ?u.178889\nq : Type ?u.178892\nm' : o → Type ?u.178897\nn' : o → Type ?u.178902\np' : o → Type ?u.178907\nR : Type ?u.178910\nS : Type ?u.178913\nα : Type u_3\nβ : Type ?u.178919\ninst✝³ : Zero α\ninst✝² : Z... | [
545,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | norm_eq_iInf_iff_real_inner_le_zero | [
{
"state_after": "𝕜 : Type ?u.190458\nE : Type ?u.190461\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace ℝ F\nK : Set F\nh : Convex ℝ K\nu v : F\nhv : v ∈ K\nthis : Nonempty ↑K := Nonempty.intro { val :=... | [
286,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/PFun.lean | PFun.fn_apply | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_mk_eq_map_mk_of_rel | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.478700\nγ : Type ?u.478703\nr : α → α → Prop\ns t : Multiset α\nhst : Rel r s t\na✝ b✝ : α\nas✝ bs✝ : Multiset α\nhab : r a✝ b✝\n_hst : Rel r as✝ bs✝\nih : map (Quot.mk r) as✝ = map (Quot.mk r) bs✝\n⊢ map (Quot.mk r) (a✝ ::ₘ as✝) = map ... | [
2866,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2864,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_sumCongr | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝³ : DecidableEq α\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nσa : Perm α\nσb : Perm β\n⊢ ↑sign (sumCongr σa 1) = ↑sign σa ∧ ↑sign (sumCongr 1 σb) = ↑sign σb",
"state_before": "α : Type u\nβ : Type v\ninst✝³ : DecidableEq α\ninst✝² : Fintype... | [
782,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Topology/Basic.lean | isOpen_fold | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.lt_sq_of_sqrt_lt | [
{
"state_after": "x y : ℝ\nh : sqrt x < y\nhy : 0 < y\n⊢ x < y ^ 2",
"state_before": "x y : ℝ\nh : sqrt x < y\n⊢ x < y ^ 2",
"tactic": "have hy := x.sqrt_nonneg.trans_lt h"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : sqrt x < y\nhy : 0 < y\n⊢ x < y ^ 2",
"tactic": "rwa ... | [
450,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.sum_card_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.105253\nα : Type u_1\nβ : Type ?u.105259\nM : Type ?u.105262\nN : Type ?u.105265\nG : Type ?u.105268\nk : Type ?u.105271\nR : Type ?u.105274\ninst✝¹ : DecidableEq α\ns : Finset α\nB : Finset (Finset α)\nn : ℕ\ninst✝ : Fintype α\nh : ∀ (a : α), card (... | [
334,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.lift_range_le | [
{
"state_after": "case intro\nι : Type u_3\nM : ι → Type ?u.337350\ninst✝³ : (i : ι) → Monoid (M i)\nN✝ : Type ?u.337361\ninst✝² : Monoid N✝\nG : ι → Type u_2\ninst✝¹ : (i : ι) → Group (G i)\nN : Type u_1\ninst✝ : Group N\nf : (i : ι) → G i →* N\ns : Subgroup N\nh : ∀ (i : ι), MonoidHom.range (f i) ≤ s\nx : Fre... | [
251,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.sub | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\n⊢ padicNorm p (q + -r) ≤ max (padicNorm p q) (padicNorm p (-r))",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\n⊢ padicNorm p (q - r) ≤ max (padicNorm p q) (padicNorm p r)",
"tactic": "rw [sub_eq_add_neg, ← padicNorm.neg r]"
},
{... | [
227,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
11
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_terminates_of_get?_terminates | [] | [
907,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_comm | [] | [
204,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | EqualCharZero.of_algebraRat | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Algebra ℚ R\nI : Ideal R\nhI : I ≠ ⊤\n⊢ CharZero (R ⧸ I)",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Algebra ℚ R\n⊢ ∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I)",
"tactic": "intro I hI"
},
{
"state_after": "case cast_inj... | [
173,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_sup | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.56171\nP : Type ?u.56174\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv : α → M\nxs : Fin l → M\n⊢ Realize (∼φ ⟹ ψ... | [
330,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotToQuotSupₐ_toRingHom | [] | [
703,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_pointReflection_of_ne | [
{
"state_after": "R : Type u_2\nV : Type u_3\nV' : Type ?u.622495\nP : Type u_1\nP' : Type ?u.622501\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y : P\nh : x ≠ y\n⊢ x ≠ ↑(pointReflection R x) y",
"state_before": "R : Type u_2\nV : Type u_3\nV' : Typ... | [
920,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_Ioi | [] | [
185,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.vcomp_eq_comp | [] | [
65,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.one_lt_val_iff | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nF : Type ?u.2467266\nR : Type ?u.2467269\ninst✝³ : DivisionRing K\nΓ₀ : Type u_2\nΓ'₀ : Type ?u.2467278\nΓ''₀ : Type ?u.2467281\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv✝ : Valuati... | [
352,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_pos_left | [] | [
611,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_coe_sort | [] | [
909,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.div_le_div_right | [] | [
525,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
11
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.map_pow_of_pos | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Ring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : IsAlgClosed 𝕜\na : A\nn : ℕ\nhn : 0 < n\n⊢ σ (a ^ n) = (fun x => x ^ n) '' σ a",
"tactic": "simpa only [aeval_X_pow, eval_pow, eval_X]\n using map_polynomial_aeval_... | [
145,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_preserving_transvectionStruct | [
{
"state_after": "ι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nt : TransvectionStruct ι ℝ\np : ι → Prop := fun i => i ≠ t.i\n⊢ MeasurePreserving ↑(↑toLin' (TransvectionStruct.toMatrix t))",
"state_before": "ι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nt : TransvectionStruct ι ℝ\n⊢ Me... | [
421,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_pow' | [] | [
172,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.minpoly_eq_minpoly | [] | [
270,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.monotone_close | [] | [
142,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_robust' | [
{
"state_after": "case zero\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\n_i : Fact (finrank ℝ E = Nat.zero)\no : Orientation ℝ E (Fin Nat.zero)\nb : OrthonormalBasis (Fin Nat.zero) ℝ E\nv : Fin Nat.zero → E\n⊢ abs (↑(volumeForm o) v) = abs (↑(Basis.det (OrthonormalBasis.toBasis b... | [
262,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.coe_toEmbedding | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClosed_irreducibleComponent | [] | [
1815,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1814,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDeriv_smul_le | [] | [
2497,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2492,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.Iic_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.297838\nγ : Type ?u.297841\nι : Sort ?u.297844\nι' : Sort ?u.297847\nι₂ : Sort ?u.297850\nκ : ι → Sort ?u.297855\nκ₁ : ι → Sort ?u.297860\nκ₂ : ι → Sort ?u.297865\nκ' : ι' → Sort ?u.297870\ninst✝ : CompleteLattice α\ns : Set α\n⊢ Iic (s... | [
2145,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2145,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.edist_eq_card | [] | [
149,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/GroupTheory/GroupAction/BigOperators.lean | List.smul_prod | [] | [
42,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Iio_iff_exists_Ioo_subset | [] | [
1705,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_succ_lt_self | [
{
"state_after": "a i : Nat\nh : i < a\n⊢ pred (a - i) < a - i",
"state_before": "a i : Nat\nh : i < a\n⊢ a - (i + 1) < a - i",
"tactic": "rw [Nat.add_succ, Nat.sub_succ]"
},
{
"state_after": "case a\na i : Nat\nh : i < a\n⊢ a - i ≠ 0",
"state_before": "a i : Nat\nh : i < a\n⊢ pred (a - i) <... | [
562,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
557,
1
] |
Mathlib/Logic/Denumerable.lean | Nat.Subtype.right_inverse_aux | [
{
"state_after": "α : Type ?u.72857\nβ : Type ?u.72860\ns : Set ℕ\ninst✝¹ : Infinite ↑s\ninst✝ : DecidablePred fun x => x ∈ s\n⊢ ∀ (x : ℕ), ¬x ∈ filter (fun x => x ∈ s) (range ↑(ofNat s 0))",
"state_before": "α : Type ?u.72857\nβ : Type ?u.72860\ns : Set ℕ\ninst✝¹ : Infinite ↑s\ninst✝ : DecidablePred fun x ... | [
352,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
9
] |
Mathlib/Order/BooleanAlgebra.lean | Disjoint.sdiff_eq_of_sup_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.12230\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nhi : Disjoint x z\nhs : x ⊔ z = y\nh : y ⊓ x = x\n⊢ y ⊓ x ⊔ z = y",
"tactic": "rw [h, hs]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.1... | [
233,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_comm | [] | [
1227,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.decreasingInduction_succ_left | [
{
"state_after": "case msm\nm✝ n✝ k : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → P (n + 1) → P n\nm n : ℕ\nsmn : m + 1 ≤ n\nmn : m ≤ n\nhP : P n\n⊢ m ≤ m + 1",
"state_before": "m✝ n✝ k : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → P (n + 1) → P n\nm n : ℕ\nsmn : m + 1 ≤ n\nmn : m ≤ n\nhP : P n\n⊢ decreasingInduction h mn hP... | [
536,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | ChartedSpaceCore.open_source' | [
{
"state_after": "case a\nH : Type u\nH' : Type ?u.56289\nM : Type u_1\nM' : Type ?u.56295\nM'' : Type ?u.56298\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne : LocalEquiv M H\nhe : e ∈ c.atlas\n⊢ e.source ∈ ⋃ (e : LocalEquiv M H) (_ : e ∈ c.atlas) (s : Set H) (_ : IsOpen s), {↑e ⁻¹' s ∩ e.source}",
... | [
793,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.pure_one | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfLocalizations_id | [
{
"state_after": "case h\nM : Type u_1\ninst✝³ : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝² : CommMonoid N\nP : Type ?u.2927330\ninst✝¹ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nT : Submonoid P\nQ : Type ?u.2935815\ninst✝ : CommMonoid Q\nx✝ : M\n⊢... | [
1467,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1466,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_gcd_right | [] | [
107,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.union | [
{
"state_after": "Ω : Type u_1\nι : Type ?u.972730\ninst✝ : MeasurableSpace Ω\ns₁ s₂ s' : Set (Set Ω)\nμ : MeasureTheory.Measure Ω\nh₁ : IndepSets s₁ s'\nh₂ : IndepSets s₂ s'\nt1 t2 : Set Ω\nht1 : t1 ∈ s₁ ∪ s₂\nht2 : t2 ∈ s'\n⊢ ↑↑μ (t1 ∩ t2) = ↑↑μ t1 * ↑↑μ t2",
"state_before": "Ω : Type u_1\nι : Type ?u.972... | [
207,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.abs_eq_one_iff | [
{
"state_after": "case refine'_1\nz : ℂ\nhz : ↑abs z = 1\n⊢ exp (↑(arg z) * I) = z\n\ncase refine'_2\nz : ℂ\n⊢ (∃ θ, exp (↑θ * I) = z) → ↑abs z = 1",
"state_before": "z : ℂ\n⊢ ↑abs z = 1 ↔ ∃ θ, exp (↑θ * I) = z",
"tactic": "refine' ⟨fun hz => ⟨arg z, _⟩, _⟩"
},
{
"state_after": "no goals",
"... | [
82,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.exponent | [
{
"state_after": "n : ℕ\n⊢ Monoid.exponent (QuaternionGroup n) = lcm (2 * n) (2 * 2)",
"state_before": "n : ℕ\n⊢ Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2",
"tactic": "rw [← normalize_eq 2, ← lcm_mul_left, normalize_eq]"
},
{
"state_after": "n : ℕ\n⊢ Monoid.exponent (QuaternionGroup n) =... | [
285,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Order/Concept.lean | extentClosure_intentClosure_extentClosure | [] | [
156,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_rel₂ | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.237419\nP : Type ?u.237422\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nφ ψ : Formula L α\nv : α → M\nR : Relations L 2\nt₁ t₂ : Term L α\n⊢ (RelMap R fun i => Term.realize v (Matri... | [
660,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.trans_apply | [] | [
417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInf_neBot_iff_of_directed | [] | [
944,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.dist_apply_le_dist | [] | [
243,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_multiset_sum | [] | [
1152,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Std/Data/List/Lemmas.lean | List.map_subset | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nl₁ l₂ : List α\nf : α → β\nH : l₁ ⊆ l₂\nx : β\n⊢ (∃ a, a ∈ l₁ ∧ f a = x) → ∃ a, a ∈ l₂ ∧ f a = x",
"state_before": "α : Type u_1\nβ : Type u_2\nl₁ l₂ : List α\nf : α → β\nH : l₁ ⊆ l₂\nx : β\n⊢ x ∈ map f l₁ → x ∈ map f l₂",
"tactic": "simp only [mem_map]"
}... | [
272,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
271,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Nat.cast_finsupp_sum | [] | [
397,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Order/RelIso/Set.lean | RelHomClass.map_inf | [] | [
36,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.eventually_hasSum | [] | [
492,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/Fintype/Basic.lean | Function.Injective.invFun_restrict | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.62111\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\nf : α → β\nhf : Injective f\ninst✝ : Nonempty α\nb : β\nh : b ∈ Set.range f\n⊢ Set.restrict (Set.range f) (invFun f) { val := b, property := h } = invOfMemRange hf { val := b, property := h }"... | [
508,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.mk_eq_zero | [] | [
297,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_succ_iff | [] | [
208,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.prod_atTop_atTop_eq | [
{
"state_after": "case inl\nι : Type ?u.270965\nι' : Type ?u.270968\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.270977\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nh✝ : IsEmpty α\n⊢ atTop ×ˢ atTop = atTop\n\ncase inr\nι : Type ?u.270965\nι' : Type ?u.270968\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.270977\ninst✝¹ : Pr... | [
1403,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
1
] |
Mathlib/Topology/Basic.lean | dense_iff_inter_open | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\nh : Dense s\n⊢ ∀ (U : Set α), IsOpen U → Set.Nonempty U → Set.Nonempty (U ∩ s)\n\ncase mpr\nα : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ ... | [
646,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.Functor.coe_mapAddHom | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_iSup | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.159728\nA : Type u_4\ninst✝⁵ : Semiring A\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\nκ : Sort u_1\ns : κ → HomogeneousIdeal 𝒜\n⊢... | [
396,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_mul_single | [
{
"state_after": "case h\nF : Type ?u.225850\nι : Type u_1\nα : Type ?u.225856\nβ : Type ?u.225859\nγ : Type ?u.225862\nf : α → β → β\nop : α → α → α\ninst✝⁴ : Monoid β\ninst✝³ : Monoid γ\nM : ι → Type u_2\ninst✝² : (i : ι) → Monoid (M i)\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nx : (i : ι) → M i\ni : ι\n⊢ n... | [
437,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_nnreal_eq_coe_real | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_le_self | [] | [
104,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.surjOn_logb | [] | [
116,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_le_toReal | [
{
"state_after": "case intro\ny : EReal\nhy : y ≠ ⊤\nx : ℝ\nh : ↑x ≤ y\nhx : ↑x ≠ ⊥\n⊢ toReal ↑x ≤ toReal y",
"state_before": "x y : EReal\nh : x ≤ y\nhx : x ≠ ⊥\nhy : y ≠ ⊤\n⊢ toReal x ≤ toReal y",
"tactic": "lift x to ℝ using ⟨ne_top_of_le_ne_top hy h, hx⟩"
},
{
"state_after": "case intro.intr... | [
410,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_iff_left | [] | [
242,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.mem_source | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.4968\nB : Type u_2\nF : Type u_3\nE : B → Type ?u.4979\nZ : Type u_1\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne : Pretrivialization F proj\nx : Z\n⊢ x ∈ e.source ↔ proj x ∈ e.baseSet",
"tactic": "rw [e.source_eq, me... | [
121,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_cancel_common_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns s' : { x // x ∈ S }\nm : M\n⊢ 1 • s • s' • m = 1 • (s * s') • m",
"tactic": "simp [mul_smul]"
}
] | [
412,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_lt_of_translationNumber_lt_int | [] | [
861,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_two | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Semiring α\nx : α\n⊢ ∑ i in range 2, x ^ i = x + 1",
"tactic": "simp [geom_sum_succ']"
}
] | [
67,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/WithBot.lean | WithBot.monotone_iff | [] | [
343,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.Subtype.volume_def | [] | [
1449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1448,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_self | [] | [
216,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.ker_fg_of_mvPolynomial | [
{
"state_after": "case intro.intro.intro.intro\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] A\nhf : Surjective ↑f\nm : ℕ\nf' : MvPolynomial (Fin m) R →ₐ[R] A\nhf' : Surjec... | [
382,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_mul_apply_aux | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.511413\ninst✝¹ : Semiring k\ninst✝ : Mul G\nf : MonoidAlgebra k G\nr : k\nx y z : G\nH : ∀ (a : G), x * a = y ↔ a = z\n⊢ ↑(single x r * f) y = r * ↑f z",
"tactic": "classical exact\n have : (f.sum fun a b => ite (x * ... | [
584,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableAt.norm_sq | [] | [
234,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | map_nonneg | [
{
"state_after": "F : Type u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.30583\nδ : Type ?u.30586\ninst✝² : OrderedAddCommMonoid α\ninst✝¹ : OrderedAddCommMonoid β\ninst✝ : OrderAddMonoidHomClass F α β\nf : F\na : α\nha : 0 ≤ a\n⊢ ↑f 0 ≤ ↑f a",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\nγ : T... | [
224,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.cycle_g_cons | [] | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
11
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfLocalizations_right_inv_apply | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝³ : CommMonoid M\nS : Submonoid M\nN : Type u_3\ninst✝² : CommMonoid N\nP : Type u_2\ninst✝¹ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nT : Submonoid P\nQ : Type ?u.2863324\ninst✝ : CommMo... | [
1447,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_inf | [] | [
823,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
11
] |
Mathlib/Topology/Order/Basic.lean | pi_Ico_mem_nhds' | [] | [
1518,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.prod_map_prod_atTop | [
{
"state_after": "ι : Type ?u.284969\nι' : Type ?u.284972\nα : Type u_2\nβ : Type u_3\nγ : Type u_1\ninst✝ : SemilatticeSup γ\nF : Filter α\nG : Filter β\nf : α → γ\ng : β → γ\nhf : Tendsto f F atTop\nhg : Tendsto g G atTop\n⊢ Tendsto (Prod.map f g) (F ×ˢ G) (atTop ×ˢ atTop)",
"state_before": "ι : Type ?u.2... | [
1451,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Order/Cover.lean | Set.OrdConnected.apply_wcovby_apply_iff | [] | [
129,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | Subalgebra.mem_star_iff | [] | [
358,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_triangle4_left | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.10546\nι : Type ?u.10549\ninst✝ : PseudoMetricSpace α\nx₁ y₁ x₂ y₂ : α\n⊢ dist x₂ y₂ ≤ dist x₂ x₁ + dist x₁ y₁ + dist y₁ y₂",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.10546\nι : Type ?u.10549\ninst✝ : PseudoMetricSpace α\nx₁ y₁ x₂ y₂ : α\n⊢ d... | [
220,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.isometry_optimalGHInjl | [] | [
475,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.inv_le_inv | [] | [
150,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.