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/Logic/Function/Basic.lean | eq_mpr_bijective | [
{
"state_after": "case refl\nα : Sort u_1\n⊢ Bijective (Eq.mpr (_ : α = α))",
"state_before": "α β : Sort u_1\nh : α = β\n⊢ Bijective (Eq.mpr h)",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": "case refl\nα : Sort u_1\n⊢ Bijective (Eq.mpr (_ : α = α))",
"tactic": "r... | [
1009,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | constantCoeff_wittStructureRat | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type ?u.1929960\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nh : ↑constantCoeff Φ = 0\nn : ℕ\n⊢ ↑constantCoeff (wittStructureRat p Φ n) = 0",
"tactic": "simp only [wittStructureRat, eval₂Hom_zero'_apply, h,... | [
370,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.pow_prime_pow_mul_eq_one_iff | [
{
"state_after": "case zero\nR : Type u_1\ninst✝³ : CommRing R\ninst✝² : IsReduced R\np m : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP R p\nx : R\n⊢ x ^ (p ^ Nat.zero * m) = 1 ↔ x ^ m = 1\n\ncase succ\nR : Type u_1\ninst✝³ : CommRing R\ninst✝² : IsReduced R\np m : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Char... | [
504,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.left_inv_eq_left_inv | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.259825\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B C : Matrix n n α\nh : B ⬝ A = 1\ng : C ⬝ A = 1\n⊢ B = C",
"tactic": "rw [← inv_eq_left_inv h, ← inv_eq_left_inv g]"
}
] | [
463,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_top | [] | [
363,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.preimage_symm_proj_baseSet | [
{
"state_after": "ι : Type ?u.9079\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.9090\nZ : Type u_3\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne : Pretrivialization F proj\nx✝ : Z\nx : B × F\nhx : x ∈ e.target\n⊢ x ∈ ↑(LocalEquiv.symm e.toLocalEquiv) ⁻¹' (proj ⁻¹' e.baseSet)",
"s... | [
188,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
src/lean/Init/SimpLemmas.lean | decide_eq_true_eq | [] | [
139,
129
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
139,
9
] |
Mathlib/Algebra/Homology/Homotopy.lean | prevD_eq | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf✝ g : C ⟶ D\nh k : D ⟶ E\ni : ι\nf : (i j : ι) → X C i ⟶ X D j\nj : ι\nw : ComplexShape.Rel c (ComplexShape.prev c j) j\n⊢ ↑(prevD j) f = f j (ComplexShape.prev c j) ≫ d D... | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_three | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Ring R\n⊢ cyclotomic 3 R = X ^ 2 + X + 1",
"tactic": "simp [cyclotomic_prime, sum_range_succ']"
}
] | [
419,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.continuous_proj | [] | [
785,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Topology/Order.lean | isClosed_induced_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.19398\nt : TopologicalSpace β\ns : Set α\nf : α → β\nthis : TopologicalSpace α := TopologicalSpace.induced f t\n⊢ IsClosed s ↔ ∃ t_1, IsClosed t_1 ∧ f ⁻¹' t_1 = s",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.19398\nt : TopologicalSpace ... | [
377,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.coe_toFinsupp | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.coprime_div_left | [
{
"state_after": "no goals",
"state_before": "m n a : Nat\ncmn : coprime m n\ndvd : a ∣ m\n⊢ coprime (m / a) n",
"tactic": "match eq_zero_or_pos a with\n| .inl h0 =>\n rw [h0] at dvd\n rw [Nat.eq_zero_of_zero_dvd dvd] at cmn ⊢\n simp; assumption\n| .inr hpos =>\n let ⟨k, hk⟩ := dvd\n rw [hk, Nat.mu... | [
328,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
318,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_radius_of_summable_norm | [] | [
276,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_none | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.map | [] | [
88,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Init/Algebra/Order.lean | not_le | [] | [
378,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subsingleton.antitone' | [] | [
495,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.finset_inf_factors | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nI : Type u_1\nA B : C\ns : Finset I\nP : I → Subobject B\nf : A ⟶ B\n⊢ Factors (Finset.inf s P) f ↔ ∀ (i : I), i ∈ s → Factors (P i) f",
"tactic": "classic... | [
442,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.SimpleFunc.exists_upperSemicontinuous_le_lintegral_le | [
{
"state_after": "case h_ind\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : WeaklyRegular μ\nf : α →ₛ ℝ≥0\nint_f✝ : (∫⁻ (x : α), ↑(↑f x) ∂μ) ≠ ⊤\nε✝ : ℝ≥0∞\nε0✝ : ε✝ ≠ 0\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nint_f : (∫⁻ (x : α), ↑(↑(pie... | [
388,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_eq_pow_mod | [
{
"state_after": "α : Type ?u.27674\nM✝ : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝² : Monoid M✝\ninst✝¹ : AddMonoid A\nM : Type u_1\ninst✝ : Monoid M\nx : M\nm n : ℕ\nh : x ^ n = 1\nt : x ^ m = x ^ (n * (m / n) + m % n)\n⊢ x ^ m = x ^ (m % n)",
"sta... | [
183,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.symplectic_det | [
{
"state_after": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\nhA : A ∈ symplecticGroup l R\n⊢ ∃ b, det A * b = 1",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Ma... | [
154,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Order/Atoms.lean | IsCompl.isCoatom_iff_isAtom | [] | [
853,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_eq_of_two_nsmul_eq | [
{
"state_after": "θ ψ : Angle\nh : θ = ψ ∨ θ = ψ + ↑π\n⊢ tan θ = tan ψ",
"state_before": "θ ψ : Angle\nh : 2 • θ = 2 • ψ\n⊢ tan θ = tan ψ",
"tactic": "rw [two_nsmul_eq_iff] at h"
},
{
"state_after": "case inl\nθ : Angle\n⊢ tan θ = tan θ\n\ncase inr\nψ : Angle\n⊢ tan (ψ + ↑π) = tan ψ",
"state... | [
822,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Combinatorics/Partition.lean | Nat.Partition.count_ofSums_zero | [] | [
131,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.coe_copy | [] | [
425,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.mem_map | [] | [
713,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Data/Set/Semiring.lean | SetSemiring.mul_def | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/Spectral/Hom.lean | SpectralMap.id_comp | [] | [
213,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Equiv.embeddingCongr_apply_trans | [
{
"state_after": "case h\nα₁ : Sort u_1\nβ₁ : Sort u_2\nγ₁ : Sort u_3\nα₂ : Sort u_4\nβ₂ : Sort u_5\nγ₂ : Sort u_6\nea : α₁ ≃ α₂\neb : β₁ ≃ β₂\nec : γ₁ ≃ γ₂\nf : α₁ ↪ β₁\ng : β₁ ↪ γ₁\nx✝ : α₂\n⊢ ↑(↑(embeddingCongr ea ec) (Embedding.trans f g)) x✝ =\n ↑(Embedding.trans (↑(embeddingCongr ea eb) f) (↑(embedding... | [
452,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | Nat.cast_eq_ofNat | [] | [
62,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.symm_apply_apply | [] | [
791,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.mem_orthogonal' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.19423\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nK : Submodule 𝕜 E\nv : E\n⊢ v ∈ Kᗮ ↔ ∀ (u : E), u ∈ K → inner v u ... | [
63,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.trans_apply | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.13479101\n𝕜✝ : Type ?u.13479104\nE : Type ?u.13479107\nF : Type ?u.13479110\nA : Type ?u.13479113\ninst✝³ : NormedAddCommGroup E\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\na b : ℝ\nf✝ g : ℝ → E\nμ : MeasureTheory.Measure ℝ\n𝕜 : Type u_1\n... | [
631,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.pairwise_zero | [] | [
3003,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3002,
1
] |
Mathlib/Topology/List.lean | Vector.tendsto_insertNth | [
{
"state_after": "α : Type u_1\nβ : Type ?u.65317\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nn : ℕ\ni : Fin (n + 1)\na : α\nl : List α\nhl : List.length l = n\n⊢ Tendsto (fun x => ↑(insertNth x.fst i x.snd)) (𝓝 a ×ˢ 𝓝 { val := l, property := hl })\n (𝓝\n ↑{ val := List.insertNth (↑i) a... | [
204,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | div_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.23833\nM₀ : Type ?u.23836\nG₀ : Type u_1\nM₀' : Type ?u.23842\nG₀' : Type ?u.23845\nF : Type ?u.23848\nF' : Type ?u.23851\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\n⊢ a / 0 = 0",
"tactic": "rw [div_eq_mul_inv, inv_zero, mul_zero]"
}
] | [
339,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_succ_iterate' | [] | [
274,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.mod_mul_left_mod | [] | [
407,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.toMatrix_vecMul_coords | [
{
"state_after": "case h\nι : Type u₁\nk : Type u₂\nV : Type u₃\nP : Type u₄\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : AffineSpace V P\ninst✝³ : Ring k\ninst✝² : Module k V\nb : AffineBasis ι k P\nι' : Type ?u.37207\ninst✝¹ : Fintype ι'\ninst✝ : Fintype ι\nb₂ : AffineBasis ι k P\nx : P\nj : ι\n⊢ vecMul (↑(coords b₂) x... | [
118,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.top_prod_top | [] | [
1753,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1752,
1
] |
Mathlib/Data/List/Basic.lean | List.reduceOption_nil | [] | [
3430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3429,
1
] |
Mathlib/RingTheory/WittVector/MulP.lean | WittVector.mulN_isPoly | [
{
"state_after": "case h\np : ℕ\nR✝ : Type ?u.50758\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R✝\nn : ℕ\nR : Type u_1\n_Rcr : CommRing R\nx : 𝕎 R\nk : ℕ\n⊢ coeff (x * ↑n) k = ↑(aeval x.coeff) (wittMulN p n k)",
"state_before": "p : ℕ\nR✝ : Type ?u.50758\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R✝\nn : ℕ... | [
72,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.wcovby_succ | [] | [
246,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Fintype/Prod.lean | Set.toFinset_prod | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.32\ns✝ t✝ s : Set α\nt : Set β\ninst✝² : Fintype ↑s\ninst✝¹ : Fintype ↑t\ninst✝ : Fintype ↑(s ×ˢ t)\na✝ : α × β\n⊢ a✝ ∈ toFinset (s ×ˢ t) ↔ a✝ ∈ toFinset s ×ˢ toFinset t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.32\ns✝ t✝ s :... | [
37,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.types_comp_apply | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/EuclideanDomain.lean | right_div_gcd_ne_zero | [
{
"state_after": "case intro\nR : Type u_1\ninst✝¹ : EuclideanDomain R\ninst✝ : GCDMonoid R\np q : R\nhq : q ≠ 0\nr : R\nhr : q = GCDMonoid.gcd p q * r\n⊢ q / GCDMonoid.gcd p q ≠ 0",
"state_before": "R : Type u_1\ninst✝¹ : EuclideanDomain R\ninst✝ : GCDMonoid R\np q : R\nhq : q ≠ 0\n⊢ q / GCDMonoid.gcd p q ... | [
60,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.continuousAt_extend | [] | [
833,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.sum_repr | [] | [
933,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_finsupp_of_fintype | [
{
"state_after": "no goals",
"state_before": "α✝ β✝ α β : Type u\ninst✝¹ : Fintype α\ninst✝ : Zero β\n⊢ (#α →₀ β) = (#β) ^ Fintype.card α",
"tactic": "simp"
}
] | [
1333,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sinh_sub_cosh | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sinh x - cosh x = -exp (-x)",
"tactic": "rw [← neg_sub, cosh_sub_sinh]"
}
] | [
751,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Data/List/Indexes.lean | List.foldrIdx_eq_foldrIdxSpec | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nf : ℕ → α → β → β\nb : β\nstart : ℕ\n⊢ foldrIdx f b [] start = foldrIdxSpec f b [] start\n\ncase cons\nα : Type u\nβ : Type v\nf : ℕ → α → β → β\nb : β\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : ∀ (start : ℕ), foldrIdx f b tail✝ start = foldrIdxSpec f b tail✝ star... | [
231,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_prod_of_nonneg | [
{
"state_after": "α : Type u_1\ns : Finset α\nf : α → ℝ\nhf : ∀ (a : α), a ∈ s → 0 ≤ f a\n⊢ ∏ i in s, f i = ∏ a in s, ↑(Real.toNNReal (f a))",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℝ\nhf : ∀ (a : α), a ∈ s → 0 ≤ f a\n⊢ Real.toNNReal (∏ a in s, f a) = ∏ a in s, Real.toNNReal (f a)",
"tacti... | [
349,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_map | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' : V\np : Walk G u v\n⊢ reverse (Walk.map f p) = Walk.map f (reverse p)",
"tactic": "induction p <;> simp [map_append,... | [
1507,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
] |
Std/Data/String/Lemmas.lean | String.set_of_valid | [] | [
247,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
245,
1
] |
Mathlib/MeasureTheory/Integral/Layercake.lean | MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable | [
{
"state_after": "α : Type u_1\ninst✝¹ : MeasurableSpace α\nf : α → ℝ\ng : ℝ → ℝ\ns : Set α\nμ : Measure α\ninst✝ : SigmaFinite μ\nf_nn : 0 ≤ f\nf_mble : Measurable f\ng_intble : ∀ (t : ℝ), t > 0 → IntervalIntegrable g volume 0 t\ng_mble : Measurable g\ng_nn : ∀ (t : ℝ), t > 0 → 0 ≤ g t\ng_intble' : ∀ (t : ℝ), ... | [
162,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.filter_eq_iff | [] | [
130,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mul_mem | [] | [
318,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
11
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_zero | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | dvd_sub_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10227\ninst✝ : NonUnitalRing α\na b c : α\nh : a ∣ c\n⊢ a ∣ b - c ↔ a ∣ b",
"tactic": "simpa only [← sub_eq_add_neg] using dvd_add_left ((dvd_neg (α := α)).2 h)"
}
] | [
108,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.156251\nf g : α → β\nc c₁ c₂ x : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh : Antiperiodic f c\n⊢ Antiperiodic f (-c)",
"tactic": "simpa only [sub_eq_add_neg, Antiperiodic] using h.sub_eq"
}
] | [
416,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_surjective | [] | [
1729,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1728,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.countable_biInf_eq_iInf_seq | [] | [
1031,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.stalkSpecializes_stalk_to_fiber | [
{
"state_after": "R✝ : Type u\ninst✝¹ : CommRing R✝\nR : Type u_1\ninst✝ : CommRing R\nx y : PrimeSpectrum R\nh : x ⤳ y\n⊢ stalkSpecializes (Sheaf.presheaf (structureSheaf R)) h ≫ (stalkIso R x).hom =\n (stalkIso R y).hom ≫\n let_fun this := PrimeSpectrum.localizationMapOfSpecializes h;\n this",
... | [
1053,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.induction_succ | [
{
"state_after": "case mk\nn m : ℕ\nC : Fin (n + 1) → Sort u_1\nh0 : C 0\nhs : (i : Fin n) → C (↑castSucc i) → C (succ i)\nval✝ : ℕ\nisLt✝ : val✝ < n\n⊢ (fun i => induction h0 hs i) (succ { val := val✝, isLt := isLt✝ }) =\n hs { val := val✝, isLt := isLt✝ } (induction h0 hs (↑castSucc { val := val✝, isLt := ... | [
1712,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_le_zero_iff''' | [
{
"state_after": "𝓕 : Type ?u.499976\n𝕜 : Type ?u.499979\nα : Type ?u.499982\nι : Type ?u.499985\nκ : Type ?u.499988\nE : Type u_1\nF : Type ?u.499994\nG : Type ?u.499997\ninst✝³ : SeminormedGroup E\ninst✝² : SeminormedGroup F\ninst✝¹ : SeminormedGroup G\ns : Set E\na✝ a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\ninst✝ : ... | [
1275,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_union | [
{
"state_after": "α : Type u_1\nP : Set α → Prop\nm : (s : Set α) → P s → ℝ≥0∞\nP0 : P ∅\nm0 : m ∅ P0 = 0\nPU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ (i : ℕ), f i)\nmU :\n ∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), P (f i)),\n Pairwise (Disjoint on f) → m (⋃ (i : ℕ), f i) (_ : P (⋃ (i : ℕ), f i)) = ∑' (i :... | [
1434,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.smul_const | [] | [
255,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.Decomposition.decompose'_eq | [] | [
103,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/GroupTheory/CommutingProbability.lean | card_comm_eq_card_conjClasses_mul_card | [
{
"state_after": "M : Type ?u.6837\ninst✝³ : Mul M\ninst✝² : Finite M\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : Finite G\nthis : Fintype G\n⊢ Nat.card { p // p.fst * p.snd = p.snd * p.fst } = Nat.card (ConjClasses G) * Nat.card G",
"state_before": "M : Type ?u.6837\ninst✝³ : Mul M\ninst✝² : Finite M\nG : Typ... | [
87,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.linear_eq_sumCoords | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Category/ModuleCat/EpiMono.lean | ModuleCat.range_eq_top_of_epi | [] | [
38,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | List.nnnorm_prod_le' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.112914\nγ : Type ?u.112917\nι : Type ?u.112920\ninst✝ : SeminormedRing α\nl : List α\nhl : l ≠ []\n⊢ prod (map norm l) = (fun a => ↑a) (prod (map nnnorm l))",
"tactic": "simp [NNReal.coe_list_prod, List.map_map]"
}
] | [
324,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Logic/Relation.lean | flip_eq_iff | [] | [
93,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.continuousAt_add_bot_coe | [
{
"state_after": "α : Type ?u.23308\ninst✝ : TopologicalSpace α\na : ℝ\n⊢ ∀ (x : ℝ), ∀ᶠ (a : EReal × EReal) in 𝓝 (⊥, ↑a), a.fst + a.snd < ↑x",
"state_before": "α : Type ?u.23308\ninst✝ : TopologicalSpace α\na : ℝ\n⊢ ContinuousAt (fun p => p.fst + p.snd) (⊥, ↑a)",
"tactic": "simp only [ContinuousAt, ten... | [
210,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_sum_fiber_le_of_maps_to_of_sum_le_nsmul | [] | [
180,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictAnti.mul_antitone' | [] | [
1539,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1537,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.trans_conjAut | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nα : X ≅ Y\nZ : C\nβ : Y ≅ Z\nf : Aut X\n⊢ ↑(conjAut (α ≪≫ β)) f = ↑(conjAut β) (↑(conjAut α) f)",
"tactic": "simp only [conjAut_apply, Iso.trans_symm, Iso.trans_assoc]"
}
] | [
144,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_insert | [] | [
1456,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovary_toDual_right | [] | [
254,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.mem_upShadow_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\n⊢ s ∈ (∂⁺ ) 𝒜 ↔ ∃ t, t ∈ 𝒜 ∧ ∃ a x, insert a t = s",
"tactic": "simp_rw [upShadow, mem_sup, mem_image, exists_prop, mem_compl]"
}
] | [
209,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_mul_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\np q : R[X]\n⊢ degree (p * X) = degree p + 1",
"tactic": "simp [monic_X.degree_mul]"
}
] | [
1280,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.one_lt_rpow | [
{
"state_after": "x✝ y z✝ x z : ℝ\nhx : 1 < x\nhz : 0 < z\n⊢ 1 ^ z < x ^ z",
"state_before": "x✝ y z✝ x z : ℝ\nhx : 1 < x\nhz : 0 < z\n⊢ 1 < x ^ z",
"tactic": "rw [← one_rpow z]"
},
{
"state_after": "no goals",
"state_before": "x✝ y z✝ x z : ℝ\nhx : 1 < x\nhz : 0 < z\n⊢ 1 ^ z < x ^ z",
"... | [
536,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_normalizer_iff | [] | [
2154,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2153,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.disjoint_list_sum_left | [
{
"state_after": "case nil\nι : Type ?u.892330\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na✝ : α\nf g : α → β\na : Multiset α\n⊢ Disjoint (List.sum []) a ↔ ∀ (b : Multiset α), b ∈ [] → Disjoint b a\n\ncase cons\nι : Type ?u.892330\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na✝ : α\nf ... | [
2059,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2054,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_toIocMod | [
{
"state_after": "θ ψ : ℝ\n⊢ ∃ k, toIocMod two_pi_pos ψ θ - θ = 2 * π * ↑k",
"state_before": "θ ψ : ℝ\n⊢ ↑(toIocMod two_pi_pos ψ θ) = ↑θ",
"tactic": "rw [angle_eq_iff_two_pi_dvd_sub]"
},
{
"state_after": "θ ψ : ℝ\n⊢ toIocMod two_pi_pos ψ θ - θ = 2 * π * ↑(-toIocDiv two_pi_pos ψ θ)",
"state_b... | [
518,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.one_div_pow | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nn : ℕ\n⊢ (1 / A) ^ n = 1 / A ^ n",
"tactic": "simp only [one_div, inv_pow']"
}
] | [
331,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/RingTheory/Derivation/ToSquareZero.lean | liftOfDerivationToSquareZero_mk_apply | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra R A\ninst✝² : Algebra R B\nI : Ideal B\nhI : I ^ 2 = ⊥\ninst✝¹ : Algebra A B\ninst✝ : IsScalarTower R A B\nd : Derivation R A { x // x ∈ I }\nx : A\n⊢ ↑(Ideal.Quotient.mk... | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.pathEquivList_symm_nil | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.map_neg | [] | [
322,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.map_swap_antidiagonal | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (map { toFun := Prod.swap, inj' := (_ : Function.Injective Prod.swap) } (antidiagonal n)).val = (antidiagonal n).val",
"tactic": "simp [antidiagonal, Multiset.Nat.map_swap_antidiagonal]"
}
] | [
90,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/CharZero/Defs.lean | Nat.cast_injective | [] | [
68,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.smul_mem_orbit_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\ng h : α\na : β\n⊢ g • a ∈ orbit α (h • a)",
"tactic": "simp only [orbit_smul, mem_orbit]"
}
] | [
266,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_zero | [] | [
397,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.singleton_lt_iff_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nr s : α\n⊢ toColex {r} < toColex {s} ↔ r < s",
"tactic": "simp [lt_singleton_iff_mem_lt]"
}
] | [
301,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.injOn_sin | [] | [
611,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.not_lt_iff | [
{
"state_after": "no goals",
"state_before": "z w : ℂ\n⊢ ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im",
"tactic": "rw [lt_def, not_and_or, not_lt]"
}
] | [
1180,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.stronglyMeasurable_uncurry_of_continuous_of_stronglyMeasurable | [
{
"state_after": "α✝ : Type ?u.560896\nβ✝ : Type ?u.560899\nγ : Type ?u.560902\nι✝ : Type ?u.560905\ninst✝⁸ : Countable ι✝\nα : Type u_1\nβ : Type u_2\nι : Type u_3\ninst✝⁷ : TopologicalSpace ι\ninst✝⁶ : MetrizableSpace ι\ninst✝⁵ : MeasurableSpace ι\ninst✝⁴ : SecondCountableTopology ι\ninst✝³ : OpensMeasurableS... | [
2048,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2011,
1
] |
Mathlib/Order/Monotone/Basic.lean | Antitone.ne_of_lt_of_lt_nat | [
{
"state_after": "ι : Type ?u.45443\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.45452\nπ : ι → Type ?u.45457\nr : α → α → Prop\ninst✝ : Preorder α\nf : ℕ → α\nhf : Antitone f\nn a : ℕ\nh1 : f (n + 1) < f a\nh2 : f a < f n\n⊢ False",
"state_before": "ι : Type ?u.45443\nα : Type u\nβ : Type v\nγ : Type w... | [
1112,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1109,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.