file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.one_le_norm_mul_norm_symm | [
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Mathlib/Data/List/Nodup.lean | List.Nodup.diff_eq_filter | [
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Mathlib/Order/SuccPred/Basic.lean | Order.pred_covby | [] | [
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Mathlib/Topology/ContinuousOn.lean | Inducing.continuousOn_iff | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.exists_pos_ball | [] | [
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Mathlib/Data/Set/Basic.lean | Disjoint.inter_left | [] | [
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Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.congr_obj | [
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Mathlib/Data/Stream/Init.lean | Stream'.tails_eq | [
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Mathlib/Logic/Equiv/Fin.lean | finSumFinEquiv_apply_right | [] | [
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Mathlib/Order/Interval.lean | Interval.mem_pure | [
{
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Mathlib/Algebra/Homology/Single.lean | ChainComplex.single₀_obj_X_d | [] | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_eq_bot_iff_le_ker | [
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2097,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin'_mul | [] | [
370,
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_top | [
{
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Mathlib/Data/List/Basic.lean | List.getLast_reverse | [
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_eq_zero_iff | [
{
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Mathlib/Algebra/Algebra/Tower.lean | AlgHom.coe_restrictScalars' | [] | [
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Mathlib/Algebra/AddTorsor.lean | Equiv.pointReflection_apply | [] | [
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Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_succ_succ | [] | [
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Mathlib/Algebra/Order/Pointwise.lean | LinearOrderedField.smul_Ioc | [
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Mathlib/Order/Minimal.lean | maximals_inter_subset | [] | [
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Mathlib/Algebra/Free.lean | FreeSemigroup.mul_seq | [] | [
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Monotone.locallyIntegrable | [
{
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_range_eq_lift | [] | [
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Mathlib/Order/Bounded.lean | Set.unbounded_lt_Ioi | [] | [
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Mathlib/Algebra/RingQuot.lean | RingQuot.ringQuotToIdealQuotient_apply | [
{
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_monomial_eq | [] | [
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.map_lie₂ | [
{
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_vsub_lineMap | [] | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_ofReal | [
{
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.finSuccEquiv_support' | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffAt.eventually | [
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_apply_same | [] | [
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Mathlib/GroupTheory/GroupAction/Defs.lean | toAdd_vadd | [] | [
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_diff_singleton | [] | [
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Mathlib/Algebra/Group/Basic.lean | self_ne_mul_right | [] | [
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Mathlib/LinearAlgebra/Pi.lean | LinearEquiv.sumArrowLequivProdArrow_apply_fst | [] | [
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450,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_le | [] | [
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50
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Mathlib/Analysis/Normed/Group/Pointwise.lean | Metric.Bounded.inv | [
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Mathlib/Data/Set/Basic.lean | Set.powerset_singleton | [
{
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... | [
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Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_card_fiber_lt_of_card_lt_mul | [] | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.iSup_lintegral_le | [
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Mathlib/Order/Filter/CountableInter.lean | EventuallyEq.countable_iUnion | [] | [
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Mathlib/Logic/Equiv/Fin.lean | coe_finRotate | [
{
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Mathlib/Algebra/GroupPower/Lemmas.lean | isUnit_pow_iff | [] | [
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Mathlib/LinearAlgebra/Matrix/Charpoly/Minpoly.lean | Matrix.minpoly_toLin' | [] | [
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Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma_one_top | [
{
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Mathlib/Data/ZMod/Parity.lean | ZMod.eq_zero_iff_even | [] | [
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Mathlib/Analysis/Quaternion.lean | Quaternion.inner_def | [] | [
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] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc | [] | [
788,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/List/Rotate.lean | List.mem_rotate | [
{
"state_after": "no goals",
"state_before": "α : Type u\nx✝ : α\nn : ℕ\n⊢ x✝ ∈ rotate [] n ↔ x✝ ∈ []",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\na : α\nl : List α\nx✝ : α\n⊢ x✝ ∈ rotate (a :: l) 0 ↔ x✝ ∈ a :: l",
"tactic": "simp"
},
{
"state_a... | [
128,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.add | [] | [
404,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_map | [] | [
1292,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | not_isCoprime_zero_zero | [] | [
73,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.iInf_orthogonal | [] | [
182,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_min | [] | [
913,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mk_mul_mk | [] | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.leftInverse_invFun | [] | [
459,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.map_t₀ | [] | [
209,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/List/Basic.lean | List.modifyNth_eq_take_drop | [] | [
2283,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2281,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.le_def | [] | [
263,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_toLin | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁹ : CommRing R\nM : Type u_3\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nM' : Type ?u.521225\ninst✝⁶ : AddCommGroup M'\ninst✝⁵ : Module R M'\nι : Type u_1\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ne : Basis ι R M\nA : Type ?u.522245\nins... | [
227,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | Commute.zpow_right | [] | [
482,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_eq_pi_div_two_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal θ = π / 2 ↔ θ = ↑(π / 2)",
"tactic": "rw [← toReal_inj, toReal_pi_div_two]"
}
] | [
619,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.measurableEmbedding | [] | [
1319,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_induction | [
{
"state_after": "case zero\nι : Type ?u.615906\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf s : ℕ → β\nbase : s 0 = 1\nstep : ∀ (n : ℕ), s (n + 1) = s n * f n\n⊢ ∏ k in range Nat.zero, f k = s Nat.zero\n\ncase succ\nι : Type ?u.615906\nβ : Type u\nα : T... | [
1390,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
] |
Mathlib/LinearAlgebra/Ray.lean | RayVector.equiv_neg_iff | [] | [
447,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_diff | [] | [
1796,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1795,
1
] |
Mathlib/Data/MvPolynomial/Counit.lean | MvPolynomial.counitNat_surjective | [] | [
90,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Erased.lean | Erased.join_eq_out | [] | [
122,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.trans_induction_on | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.20321\nγ : Type ?u.20324\nδ : Type ?u.20327\nr : α → α → Prop\na✝ b✝ c d : α\nP : {a b : α} → TransGen r a b → Prop\na b : α\nh : TransGen r a b\nbase : ∀ {a b : α} (h : r a b), P (_ : TransGen r a b)\nih : ∀ {a b c : α} (h₁ : TransGen ... | [
409,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_eq_cancelAux | [
{
"state_after": "no goals",
"state_before": "case zero\nctx : Context\nm₁ m₂ r₁ r₂ : Poly\nh : denote_eq ctx (List.reverse r₁ ++ m₁, List.reverse r₂ ++ m₂)\n⊢ denote_eq ctx (cancelAux zero m₁ m₂ r₁ r₂)",
"tactic": "assumption"
},
{
"state_after": "case succ\nctx : Context\nfuel : Nat\nih :\n ∀... | [
382,
41
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
350,
1
] |
Mathlib/Order/CompleteLattice.lean | eq_singleton_bot_of_sSup_eq_bot_of_nonempty | [
{
"state_after": "α : Type u_1\nβ : Type ?u.56847\nβ₂ : Type ?u.56850\nγ : Type ?u.56853\nι : Sort ?u.56856\nι' : Sort ?u.56859\nκ : ι → Sort ?u.56864\nκ' : ι' → Sort ?u.56869\ninst✝ : CompleteLattice α\ns✝ t : Set α\na b : α\ns : Set α\nh_sup : sSup s = ⊥\nhne : Set.Nonempty s\n⊢ Set.Nonempty s ∧ ∀ (x : α), x ... | [
556,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Computability/Reduce.lean | Equiv.Computable.symm | [] | [
216,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | ContinuousWithinAt.exp | [] | [
149,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.exists_ne_map_eq_of_card_lt_of_maps_to | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ns t✝ : Finset α\nf✝ : α → β\nn : ℕ\nt : Finset β\nhc : card t < card s\nf : α → β\nhf : ∀ (a : α), a ∈ s → f a ∈ t\n⊢ ∃ x, x ∈ s ∧ ∃ y, y ∈ s ∧ x ≠ y ∧ f x = f y",
"tactic": "classical\n by_contra' hz\n refine' hc.not_le (card_l... | [
346,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.ratio_le_op_norm | [] | [
358,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isWf_iff_isPwo | [] | [
531,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_isCycle_iff_of_injective | [
{
"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\np : Walk G u u\nhinj : Injective ↑f\n⊢ IsCycle (Walk.map f p) ↔ IsCycle p",
"tactic": "rw [isCy... | [
1573,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | Differentiable.snd | [] | [
294,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
11
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.seq_pre | [] | [
145,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
142,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_empty | [] | [
1686,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1685,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_pos | [
{
"state_after": "case mp\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\nx : α\nhx : x ≠ 0\n⊢ 0 < factors x → ¬IsUnit x\n\ncase mpr\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\nx... | [
543,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
src/lean/Init/Prelude.lean | Nat.le_of_lt_succ | [] | [
1632,
21
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1631,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_le | [] | [
136,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.choose_spec | [] | [
1115,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_eq_uniformity_interior | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.89348\ninst✝ : UniformSpace α\nd : Set (α × α)\nhd : d ∈ 𝓤 α\ns : Set (α × α)\nhs : s ∈ 𝓤 α\nhs_comp : s ○ (s ○ s) ⊆ d\n⊢ 𝓤 α ≤ (𝓟 ∘ interior) d",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : So... | [
996,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.differentiableAt | [] | [
382,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.apply_inv_self | [] | [
85,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.lieSpan_le | [
{
"state_after": "case mp\nR : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK✝ K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\ns : Set L\nK : LieSubalgebra R L\n⊢ lieSpan R L s ≤ K → s ⊆ ↑K\n\nca... | [
701,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.le_u_l | [] | [
103,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.not_beq_to_not_eq | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ ((!a == b) = true) = ¬a = b",
"tactic": "cases a <;> cases b <;> decide"
}
] | [
134,
62
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
133,
9
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.ext_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7710\nm : MeasurableSpace α\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv w : VectorMeasure α M\n⊢ v = w ↔ ∀ (i : Set α), ↑v i = ↑w i",
"tactic": "rw [← coe_injective.eq_iff, Function.funext_iff]"
}
] | [
127,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMap₂_apply | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.coe_comp | [] | [
402,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.algebraMap_apply' | [] | [
1219,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_reverse_noncomm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.114628\nα : Type ?u.114631\nM : Type ?u.114634\nN : Type ?u.114637\nP : Type ?u.114640\nM₀ : Type ?u.114643\nG : Type u_1\nR : Type ?u.114649\ninst✝ : Group G\n⊢ ∀ (L : List G), prod (reverse L) = (prod (map (fun x => x⁻¹) L))⁻¹",
"tactic": "simp... | [
424,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.op_eq_self_of_principal | [
{
"state_after": "op : Ordinal → Ordinal → Ordinal\na o : Ordinal\nhao : a < o\nH : IsNormal (op a)\nho : Principal op o\nho' : IsLimit o\n⊢ op a o ≤ o",
"state_before": "op : Ordinal → Ordinal → Ordinal\na o : Ordinal\nhao : a < o\nH : IsNormal (op a)\nho : Principal op o\nho' : IsLimit o\n⊢ op a o = o",
... | [
84,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.le_infsep_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.58192\ninst✝ : PseudoMetricSpace α\nx y z : α\ns t : Set α\nd : ℝ\nhs : Set.Nontrivial s\n⊢ d ≤ infsep s ↔ ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → x ≠ y → d ≤ dist x y",
"tactic": "simp_rw [infsep, ← ENNReal.ofReal_le_iff_le_toReal hs... | [
401,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.neg_sub | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b : X ⟶ Y\n⊢ -a - b = -b - a",
"tactic": "conv_lhs => rw [neg_def, ← sub_zero b, sub_sub_sub, sub_zero, ← neg_def]"
}
] | [
379,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
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