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 | Nat.exists_strictMono' | [
{
"state_after": "ι : Type ?u.41282\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.41291\nπ : ι → Type ?u.41296\nr : α → α → Prop\ninst✝¹ : Preorder α\ninst✝ : NoMaxOrder α\na : α\ng : α → α\nhg : ∀ (x : α), x < g x\n⊢ ∃ f, StrictMono f ∧ f 0 = a",
"state_before": "ι : Type ?u.41282\nα : Type u\nβ : Type ... | [
1012,
87
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1010,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Iic | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\nthis : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)\n⊢ (fun x => a - x) '' Iic b = Ici (a - b)",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun ... | [
329,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
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Mathlib/Order/Filter/IndicatorFunction.lean | indicator_eventuallyEq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.51\nM : Type u_2\nE : Type ?u.57\ninst✝ : Zero M\ns t : Set α\nf g : α → M\na : α\nl : Filter α\nhf : f =ᶠ[l ⊓ 𝓟 s] g\nhs : s =ᶠ[l] t\nx : α\nhst : x ∈ s ↔ x ∈ t\nhfg : x ∈ s → f x = g x\nhxs : x ∈ s\n⊢ indicator s f x = indicator t g ... | [
37,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
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Mathlib/LinearAlgebra/Dual.lean | Subspace.dualAnnihilator_inj | [
{
"state_after": "case mp\nK : Type u\nV : Type v\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nW W' : Subspace K V\n⊢ dualAnnihilator W = dualAnnihilator W' → W = W'\n\ncase mpr\nK : Type u\nV : Type v\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nW W' : Subspace K V\n⊢ W = ... | [
1006,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
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Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.congr_F | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nS₁ S₂ : Split C\nΦ₁ Φ₂ : S₁ ⟶ S₂\nh : Φ₁ = Φ₂\n⊢ Φ₁.f = Φ₂.f",
"tactic": "rw [h]"
}
] | [
428,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/Data/Finset/Sups.lean | Finset.biUnion_image_inf_right | [] | [
365,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | AlgEquiv.map_det | [] | [
347,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_unop_pow | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM✝ N P Q : Submodule R A\nm n✝ : A\nn : ℕ\nM : Submodule R Aᵐᵒᵖ\n⊢ map (↑(LinearEquiv.symm (opLinearEquiv R))) (M ^ n) = map (↑(LinearEquiv.symm ... | [
549,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/Topology/Algebra/Group/Basic.lean | subset_interior_mul_left | [] | [
1305,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Right.mul_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : MulZeroClass α\ninst✝¹ : Preorder α\ninst✝ : MulPosMono α\nha : 0 ≤ a\nhb : 0 ≤ b\n⊢ 0 ≤ a * b",
"tactic": "simpa only [zero_mul] using mul_le_mul_of_nonneg_right ha hb"
}
] | [
388,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
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Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.coe_decompose_mul_add_of_right_mem | [
{
"state_after": "case intro\nι : Type u_1\nR : Type ?u.161779\nA : Type u_2\nσ : Type u_3\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Semiring A\ninst✝³ : SetLike σ A\ninst✝² : AddSubmonoidClass σ A\n𝒜 : ι → σ\ni j : ι\ninst✝¹ : AddRightCancelMonoid ι\ninst✝ : GradedRing 𝒜\na : A\nb : { x // x ∈ 𝒜 j }\n⊢ ↑(↑(↑(decomp... | [
151,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/GroupTheory/Submonoid/Centralizer.lean | AddSubmonoid.centralizer_toAddSubsemigroup | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/Computability/Partrec.lean | Partrec.bind_decode₂_iff | [
{
"state_after": "no goals",
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604,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.isDiag_conjTranspose_iff | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.16315\nR : Type ?u.16318\nn : Type u_2\nm : Type ?u.16324\nins... | [
138,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_eq_lintegral_rpow_nnnorm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.376592\nF : Type u_2\nG : Type ?u.376598\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nf :... | [
97,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_tail? | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\nh : NoSibling s\n⊢ Option.map (fun x => x.snd) (deleteMin le s) = some s' → size s = size s' + 1",
"state_before": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\nh : NoSibling s\n⊢ tail? le s = some s' → size s = size s' + 1",
"tactic":... | [
147,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
143,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_eq_of_forall_le_of_forall_lt_exists_gt | [] | [
1106,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
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Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_inj | [] | [
532,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.disjoint_mul_inv_of_mem_cycleFactorsFinset | [
{
"state_after": "ι : Type ?u.2773969\nα : Type u_1\nβ : Type ?u.2773975\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ f g : Perm α\nh : IsCycle f ∧ ∀ (a : α), a ∈ support f → ↑f a = ↑g a\n⊢ Disjoint (g * f⁻¹) f",
"state_before": "ι : Type ?u.2773969\nα : Type u_1\nβ : Type ?u.2773975\ninst✝¹ : DecidableEq... | [
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1502,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.subtypePerm_apply | [] | [
370,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_attach | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.378826\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : α → β\nthis : DecidableEq α\n⊢ ∏ x in image Subtype.val (attach s), f x = ∏ x in s, f x",
"tactic": "rw [attach_image_val]"
}
] | [
859,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.abs_exp_sub_one_le | [
{
"state_after": "x : ℝ\nhx this : abs' x ≤ 1\n⊢ abs' (exp x - 1) ≤ 2 * abs' x",
"state_before": "x : ℝ\nhx : abs' x ≤ 1\n⊢ abs' (exp x - 1) ≤ 2 * abs' x",
"tactic": "have : abs' x ≤ 1 := by exact_mod_cast hx"
},
{
"state_after": "x : ℝ\nhx this✝ : abs' x ≤ 1\nthis : ↑Complex.abs (Complex.exp ↑x... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1724,
1
] |
Mathlib/Algebra/Order/Nonneg/Field.lean | Nonneg.coe_zpow | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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] |
Mathlib/Order/SymmDiff.lean | symmDiff_le_sup | [] | [
159,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Part.lean | Part.bind_toOption | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.25409\nf : α → Part β\no : Part α\ninst✝² : Decidable o.Dom\ninst✝¹ : (a : α) → Decidable (f a).Dom\ninst✝ : Decidable (Part.bind o f).Dom\nh : o.Dom\n⊢ toOption (Part.bind o f) = Option.elim (toOption o) Option.none fun a => toOption (f a)\n\n... | [
539,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Interval.lean | Fin.card_Icc | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ card (Icc a b) = ↑b + 1 - ↑a",
"tactic": "rw [← Nat.card_Icc, ← map_valEmbedding_Icc, card_map]"
}
] | [
80,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsSymm.domRestrict | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.164233\nR₂ : Type ?u.164236\nR₃ : Type ?u.164239\nM : Type u_2\nM₁ : Type ?u.164245\nM₂ : Type ?u.164248\nMₗ₁ : Type ?u.164251\nMₗ₁' : Type ?u.164254\nMₗ₂ : Type ?u.164257\nMₗ₂' : Type ?u.164260\nK : Type ?u.164263\nK₁ : Type ?u.164266\nK₂ : Type ?u.164269\nV : Type ... | [
242,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
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] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_to_real | [] | [
849,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IsROrC.interval_integral_ofReal | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.13951224\n𝕜✝ : Type ?u.13951227\nE : Type ?u.13951230\nF : Type ?u.13951233\nA : Type ?u.13951236\ninst✝³ : NormedAddCommGroup E\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\na b : ℝ\nμ : MeasureTheory.Measur... | [
655,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
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] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_singleton | [
{
"state_after": "case h\nx x✝ : ZFSet\n⊢ x✝ ∈ toSet {x} ↔ x✝ ∈ {x}",
"state_before": "x : ZFSet\n⊢ toSet {x} = {x}",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h\nx x✝ : ZFSet\n⊢ x✝ ∈ toSet {x} ↔ x✝ ∈ {x}",
"tactic": "simp"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.continuous_arsinh | [] | [
202,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInf_sets_eq_finite' | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.101802\nι : Sort x\nf✝ g : Filter α\ns t : Set α\nf : ι → Filter α\n⊢ (⨅ (x : PLift ι), f (↑Equiv.plift x)).sets = (⨅ (i : PLift ι), f i.down).sets",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.101802\nι : Sort x\nf✝ g : ... | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
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] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Function.Injective.hasSum_iff | [
{
"state_after": "no goals",
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... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_zero | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_2\n𝕜₂ : Type ?u.30056\n𝕝 : Type ?u.30059\n𝕝₂ : Type ?u.30062\nE : Type u_1\nF : Type ?u.30068\nG : Type ?u.30071\nι : Type u_3\nι'✝ : Type ?u.30077\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\nU : Set ... | [
121,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.36164\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.36176\nι : Sort ?u.36179\nκ : ι → Sort ?u.36184\ninst✝³ : SupSet α\ninst✝² : SupSet β\ninst✝¹ : SupSet γ\ninst✝ : SupSet δ\ng : sSupHom β γ\nf₁ f₂ : sSupHom α β\nhg : Injective ↑g\nh : comp... | [
350,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | lift_rank_map_le | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.44308\nR : Type u\ninst✝⁶ : Ring R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type v'\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nM₁ : Type v\nin... | [
177,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Opposite.lean | Opposite.op_injective | [] | [
59,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
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Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.unop_comp | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_zero_iff_subsingleton_of_finite | [
{
"state_after": "α : Type u_1\nβ : Type ?u.81138\ninst✝¹ : MetricSpace α\ns : Set α\ninst✝ : Finite ↑s\n⊢ einfsep s = 0 → Set.Subsingleton s",
"state_before": "α : Type u_1\nβ : Type ?u.81138\ninst✝¹ : MetricSpace α\ns : Set α\ninst✝ : Finite ↑s\n⊢ infsep s = 0 ↔ Set.Subsingleton s",
"tactic": "rw [inf... | [
545,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
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Mathlib/MeasureTheory/PiSystem.lean | generatePiSystem_mono | [
{
"state_after": "case base\nα : Type u_1\nS T : Set (Set α)\nhST : S ⊆ T\nt s : Set α\nh_s : s ∈ S\n⊢ s ∈ generatePiSystem T\n\ncase inter\nα : Type u_1\nS T : Set (Set α)\nhST : S ⊆ T\nt s u : Set α\nh_s✝ : generatePiSystem S s\nh_t✝ : generatePiSystem S u\nh_nonempty : Set.Nonempty (s ∩ u)\nh_s : s ∈ generat... | [
254,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/Basic.lean | Set.MapsTo.closure | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.172565\nδ : Type ?u.172568\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ns : Set α\nt : Set β\nf : α → β\nh : MapsTo f s t\nhc : Continuous f\n⊢ ∀ ⦃x : α⦄, ClusterPt x (𝓟 s) → ClusterPt (f x) (𝓟 t)",
"state_... | [
1751,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1748,
11
] |
Mathlib/Order/SymmDiff.lean | top_symmDiff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.54496\nα : Type u_1\nβ : Type ?u.54502\nπ : ι → Type ?u.54507\ninst✝ : CoheytingAlgebra α\na : α\n⊢ ⊤ ∆ a = ￢a",
"tactic": "simp [symmDiff]"
}
] | [
345,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.rangeS_le | [] | [
138,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.completeSpace_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.999131\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\ne : α ≃ᵢ β\n⊢ CompleteSpace α ↔ CompleteSpace β",
"tactic": "simp only [completeSpace_iff_isComplete_univ, ← e... | [
566,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.invRev_length | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\n⊢ List.length (invRev L₁) = List.length L₁",
"tactic": "simp [invRev]"
}
] | [
561,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
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Mathlib/Logic/Function/Basic.lean | Function.extend_def | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf✝ f : α → β\ng : α → γ\ne' : β → γ\nb : β\ninst✝ : Decidable (∃ a, f a = b)\n⊢ (if h : ∃ a, f a = b then g (Classical.choose h) else e' b) =\n if h : ∃ a, f a = b then g (Classical.choose h) else e' b",
"state_before": "α : Sort u_1\nβ : Sort u... | [
712,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
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Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_neg | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np : P\nv : V\n⊢ secondInter s p (-v) = secondInter s p v",
"tactic": "rw [← neg_one_smul ℝ v, s.seco... | [
118,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.sSup | [
{
"state_after": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.129342\nA : Type u_1\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\nℐ : Set (Ideal A)\nh : ∀ (I : Ideal A), I ∈ ℐ → IsHomogeneous 𝒜 I\n⊢ IsHomo... | [
307,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/Data/Finset/Basic.lean | Finset.nonempty_iff_eq_singleton_default | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.32795\nγ : Type ?u.32798\ns✝ : Finset α\na b : α\ninst✝ : Unique α\ns : Finset α\n⊢ Finset.Nonempty s ↔ s = {default}",
"tactic": "simp [eq_singleton_iff_nonempty_unique_mem]"
}
] | [
760,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_add_of_nonneg | [
{
"state_after": "case intro\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nn : ℤ\nhn : 0 ≤ n\nk : ℕ\nhm : 0 ≤ ↑k\n⊢ A ^ (↑k + n) = A ^ ↑k * A ^ n",
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190,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_subset_iff | [] | [
434,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_bot | [] | [
833,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
11
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.eval_toList | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nctx : Context α\ne : Expr\n⊢ evalList α ctx (Expr.toList e) = eval α ctx e",
"tactic": "induction e with\n| var x => rfl\n| op l r ih₁ ih₂ =>\n simp [evalList, Expr.toList, eval, ←ih₁, ←ih₂]\n apply evalList_append <;> apply toList_nonEmpty"
... | [
310,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
305,
1
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Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCopairing_eq | [] | [
1282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_ideal_smul_span_iff_exists_sum | [
{
"state_after": "case mp\nR : Type u\nM : Type v\nF : Type ?u.142173\nG : Type ?u.142176\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nI J : Ideal R\nN P : Submodule R M\nS : Set R\nT : Set M\nM' : Type w\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R M'\nι : Type u_1\nf : ι → M\nx : M... | [
325,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.one_leftMoves | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.mod_two_add_succ_mod_two | [] | [
103,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.hasSum | [] | [
359,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
11
] |
Mathlib/Order/Filter/Lift.lean | Filter.map_lift'_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort ?u.32727\nf f₁ f₂ : Filter α\nh h₁ h₂ : Set α → Set β\nm : β → γ\nhh : Monotone h\n⊢ Filter.lift f (map m ∘ 𝓟 ∘ h) = Filter.lift' f (image m ∘ h)",
"tactic": "simp only [comp, Filter.lift', map_principal]"
... | [
298,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.embedding_coe_ennreal | [
{
"state_after": "α : Type ?u.6443\ninst✝ : TopologicalSpace α\n⊢ OrdConnected (Ici 0)",
"state_before": "α : Type ?u.6443\ninst✝ : TopologicalSpace α\n⊢ OrdConnected (range ENNReal.toEReal)",
"tactic": "rw [range_coe_ennreal]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.644... | [
110,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_map | [] | [
983,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Data/Set/Basic.lean | Set.empty_ne_univ | [] | [
675,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_smul' | [
{
"state_after": "no goals",
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1558,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
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Mathlib/Data/Sum/Basic.lean | Sum.isLeft_iff | [
{
"state_after": "no goals",
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"tactic": "cases x <;> simp"
}
] | [
147,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.swap_mem_divisorsAntidiagonal_aux | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nx : ℕ × ℕ\n⊢ x.snd * x.fst = n ∧ ¬n = 0 ↔ x ∈ divisorsAntidiagonal n",
"tactic": "rw [mem_divisorsAntidiagonal, mul_comm]"
}
] | [
228,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Disjoint.exists_uniform_thickening_of_basis | [
{
"state_after": "case intro.intro\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort u_1\ninst✝ : UniformSpace α\np : ι → Prop\ns : ι → Set (α × α)\nhU : HasBasis (𝓤 α) p s\nA B : Set α\nhA : IsCompact A\nhB : IsClosed B\nh : Disjoint A B\nV : Set (α × α)\nhV : V ∈ 𝓤 α\nhVAB : Disjoint (⋃ (x : α) ... | [
856,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | MulOpposite.op_zpow | [] | [
1267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.size_balance' | [
{
"state_after": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : Sized l\nhr : Sized r\n⊢ size\n (if size l + size r ≤ 1 then node' l x r\n else\n if size r > delta * size l then rotateL l x r\n else if size l > delta * size r then rotateR l x r else node' l x r) =\n size l +... | [
448,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.iInf_Ici | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.143244\nγ : Type ?u.143247\nι : Sort ?u.143250\nκ : ι → Sort ?u.143255\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns✝ t : Set α\nx : α\ns : Set α\nx✝ : α\n⊢ x✝ ∈ ↑(⨅ (a : α) (_ : a ∈ s), Ici a) ↔ x✝ ∈ ↑(upperClosure s)",
"state_before": "α : Type u_1\nβ : ... | [
1344,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk' | [] | [
189,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventuallyLE_congr | [] | [
1638,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.hasSum_eval | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
677,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | zero_pow | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.23\nS : Type ?u.26\nM : Type u_1\ninst✝ : MonoidWithZero M\nn : ℕ\nx✝ : 0 < n + 1\n⊢ 0 ^ (n + 1) = 0",
"tactic": "rw [pow_succ, zero_mul]"
}
] | [
36,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Topology/SubsetProperties.lean | Subtype.preirreducibleSpace | [
{
"state_after": "case intro.intro.intro.intro.intro.mk.intro.intro.mk.intro\nα : Type u\nβ : Type v\nι : Type ?u.189901\nπ : ι → Type ?u.189906\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t s : Set α\nh : IsPreirreducible s\nu : Set α\nhu : IsOpen u\nv : Set α\nhv : IsOpen v\nx : α\nhxs : x ∈ ... | [
1885,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1880,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | UnitAddCircle.norm_eq | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ‖↑x‖ = abs (x - ↑(round x))",
"tactic": "simp [AddCircle.norm_eq]"
}
] | [
283,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coordChange_same_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.55034\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.55045\nZ : Type u_3\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace F\nproj : Z → B\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F proj\nx✝ : Z\n... | [
683,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.congr_arg | [] | [
180,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
11
] |
Mathlib/Order/Lattice.lean | sup_eq_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ a ⊔ b ≤ b ∧ b ≤ a ⊔ b ↔ a ≤ b",
"tactic": "simp [le_rfl]"
}
] | [
185,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_indicator | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45104\nE : Type u_2\nF : Type ?u.45110\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nht : MeasurableSet t\n⊢ (∫... | [
188,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.colorable_iff_exists_bdd_nat_coloring | [
{
"state_after": "case mp\nV : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nn : ℕ\n⊢ Colorable G n → ∃ C, ∀ (v : V), ↑C v < n\n\ncase mpr\nV : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nn : ℕ\n⊢ (∃ C, ∀ (v : V), ↑C v < n) → Colorable G n",
"state_before": "V : Type u\nG : SimpleGra... | [
241,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.funLeft_id | [] | [
2611,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2610,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | iUnion_Ici_eq_Ici_iInf | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝¹ : LinearOrder α\ns : Set α\na : α\nf✝ : ι → α\nR : Type u_1\ninst✝ : CompleteLinearOrder R\nf : ι → R\nhas_least_elem : (⨅ (i : ι), f i) ∈ range f\n⊢ (⋃ (i : ι), Ici (f i)) = Ici (⨅ (i : ι), f i)",
"tactic": "simp o... | [
244,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.transferTransversal_apply'' | [
{
"state_after": "G : Type u\ninst✝ : Group G\nH : Subgroup G\ng : G\nq : orbitRel.Quotient { x // x ∈ zpowers g } (G ⧸ H)\nk : ZMod (minimalPeriod ((fun x x_1 => x • x_1) g) (Quotient.out' q))\n⊢ (g ^\n if k = 0 then ↑(minimalPeriod ((fun x x_1 => x • x_1) g) (Quotient.out' { fst := q, snd := k - 1 }.fs... | [
652,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.centralizer_closure | [] | [
236,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv_symm_some | [] | [
216,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.fun_inv_map | [] | [
231,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffWithinAt_const | [] | [
106,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_inv_cancel_left | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na✝ b✝ c a b : G\n⊢ a * (a⁻¹ * b) = b",
"tactic": "rw [← mul_assoc, mul_right_inv, one_mul]"
}
] | [
1113,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.vertices_subset_space | [] | [
165,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_le_of_le_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.237503\nβ : Type ?u.237506\nγ : Type ?u.237509\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\nh : a ≤ b * c\nb0 : b = 0\n⊢ a / b ≤ c",
"tactic": "simp only [b0, div_zero, Ordinal.zero_le]"
}
] | [
925,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Order/BoundedOrder.lean | bot_inf_eq | [] | [
513,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | eq_zero_of_mul_eq_self_right | [] | [
222,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.norm_eq | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nR : Type ?u.116219\nV : Type u_2\nW : Type u_1\nW₂ : Type ?u.116228\nP : Type ?u.116231\nQ : Type ?u.116234\nQ₂ : Type ?u.116237\ninst✝¹⁶ : NormedAddCommGroup V\ninst✝¹⁵ : MetricSpace P\ninst✝¹⁴ : NormedAddTorsor V P\ninst✝¹³ : NormedAddCommGroup ... | [
189,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.id_mem_iff_eq_top | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y✝ Z : C\nf✝ : Y✝ ⟶ X\nS R : Sieve X\nh : S.arrows (𝟙 X)\nY : C\nf : Y ⟶ X\nx✝ : ⊤.arrows f\n⊢ S.arrows f",
"tactic": "simpa using downward_closed _ h f"
}
] | [
432,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Part.lean | Part.inter_def | [] | [
705,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_log_le_self | [
{
"state_after": "case inl\nx : Ordinal\nhx : x ≠ 0\n⊢ 0 ^ log 0 x ≤ x\n\ncase inr\nb x : Ordinal\nhx : x ≠ 0\nb0 : b ≠ 0\n⊢ b ^ log b x ≤ x",
"state_before": "b x : Ordinal\nhx : x ≠ 0\n⊢ b ^ log b x ≤ x",
"tactic": "rcases eq_or_ne b 0 with (rfl | b0)"
},
{
"state_after": "case inr.inl\nb x : ... | [
327,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Order/Heyting/Basic.lean | compl_sup_le_himp | [] | [
803,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_le_add | [] | [
405,
70
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
404,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_imp | [] | [
637,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_add_toNNReal | [] | [
662,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
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