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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_lt_rpow_of_exponent_lt | [
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Mathlib/Logic/Equiv/Basic.lean | Equiv.sumAssoc_symm_apply_inr_inl | [] | [
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Mathlib/RingTheory/PrincipalIdealDomain.lean | Submodule.IsPrincipal.generator_map_dvd_of_mem | [
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Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_vec_bit0_eq_alt0 | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_smul' | [] | [
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Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.deleteMin_fst | [
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.map_Iic | [
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Mathlib/GroupTheory/Index.lean | Subgroup.relindex_sup_left | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_inj | [
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_vecCons_add | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.eq_of_epi_equalizer | [] | [
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Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.id_apply | [] | [
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Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_shiftFunctorCompIsoId_inv_app | [
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{
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Mathlib/Order/Bounded.lean | Set.bounded_gt_Ioi | [] | [
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Mathlib/Analysis/Convex/Topology.lean | closure_openSegment | [
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Mathlib/Data/BinaryHeap.lean | BinaryHeap.size_insert | [
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Mathlib/Algebra/CovariantAndContravariant.lean | covariant_le_of_covariant_lt | [
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.mk'_eq_bot | [
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... | [
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Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.indep_biSup_compl | [] | [
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Mathlib/Order/CompleteLattice.lean | OrderIso.map_sInf | [] | [
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Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearEquiv.homothety_inverse | [
{
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.order_ineq | [] | [
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Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.transferNatTransSelf_counit | [
{
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_add_index | [
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Std/Data/Option/Lemmas.lean | Option.map_congr | [
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.liftOn₂_mk' | [
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.generateFrom_le | [] | [
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Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.comonadToFunctor_mapIso_comonad_iso_mk | [
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Mathlib/Data/Set/Sigma.lean | Set.mk_preimage_sigma_eq_empty | [] | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_add | [] | [
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Mathlib/Order/Heyting/Hom.lean | HeytingHom.comp_id | [] | [
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Mathlib/Algebra/Group/Basic.lean | div_div | [
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Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_monomial | [
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Mathlib/Data/Set/Basic.lean | Set.mem_dite_univ_right | [
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.ImageMap.map_uniq | [
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Equalizers.lean | CategoryTheory.Limits.map_π_preserves_coequalizer_inv_desc | [
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.mul_edist_le | [
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Mathlib/LinearAlgebra/Span.lean | Submodule.mem_span_singleton_trans | [
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.prod_multiset_X_sub_C_dvd | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | centroid_mem_affineSpan_of_card_ne_zero | [] | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_updateColumn_equiv | [
{
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2897,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2894,
1
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Mathlib/Topology/Algebra/UniformGroup.lean | Filter.HasBasis.uniformity_of_nhds_one_inv_mul_swapped | [
{
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370,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_subset_ge_of_subset_image | [
{
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},
{
"sta... | [
2220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2215,
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Mathlib/Order/Monotone/Basic.lean | AntitoneOn.dual | [] | [
235,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
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Mathlib/Algebra/GeomSum.lean | sub_dvd_pow_sub_pow | [] | [
197,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_erase_lt_of_mem | [] | [
1115,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
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Mathlib/Order/Hom/Basic.lean | OrderHom.fst_comp_prod | [] | [
465,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.coe_fn_mk | [] | [
108,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
9
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Mathlib/CategoryTheory/Abelian/Opposite.lean | CategoryTheory.cokernel.π_op | [
{
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] | [
105,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Data/Nat/Fib.lean | Nat.fib_le_fib_succ | [
{
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}
] | [
97,
91
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_pos_add_filter_neg | [
{
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422,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.chain'_dartAdj_darts | [
{
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}
] | [
667,
47
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Mathlib/Order/OrderIsoNat.lean | WellFounded.monotone_chain_condition' | [
{
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227,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.surjective_units_map_of_local_ringHom | [
{
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344,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.nnnorm_map | [] | [
976,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | eq_one_of_one_le_mul_right | [] | [
1174,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_subset_Ici_self | [
{
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}
] | [
397,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.prod_eq_zero | [
{
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"tactic": "lift f to ι → Type u using fun _ => trivial"
},
{
"state_aft... | [
1065,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.zero_div | [
{
"state_after": "no goals",
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"tactic": "simpa [mem_div] using hs"
}
] | [
1285,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.rightInverse_trop | [] | [
113,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.range_coe | [] | [
158,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.card_subset_divisors_le_length_of_chain | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : CancelCommMonoidWithZero M\nq : Associates M\nn : ℕ\nc : Fin (n + 1) → Associates M\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nm : Finset (Associates M)\nhm : ∀ (r : Associates M), r ∈ m → r ≤ q\n⊢ Finset.card m ≤ n + 1",
"tactic... | [
148,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Data/Set/Function.lean | Function.monotoneOn_of_rightInvOn_of_mapsTo | [
{
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1703,
20
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1694,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.Ici_iSup | [
{
"state_after": "no goals",
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"tactic": "simp only [mem_Ici_iff, mem_iSup_iff, iSup_le_iff]"
... | [
1149,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
1
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Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsFractionRing.isFractionRing_of_isDomain_of_isLocalization | [
{
"state_after": "R : Type u_1\ninst✝¹² : CommRing R\nM : Submonoid R\nS✝ : Type ?u.712246\ninst✝¹¹ : CommRing S✝\ninst✝¹⁰ : Algebra R S✝\nP : Type ?u.712502\ninst✝⁹ : CommRing P\ninst✝⁸ : IsDomain R\nS : Type u_2\nT : Type u_3\ninst✝⁷ : CommRing S\ninst✝⁶ : CommRing T\ninst✝⁵ : Algebra R S\ninst✝⁴ : Algebra R ... | [
307,
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296,
1
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Mathlib/Computability/Reduce.lean | ManyOneDegree.le_antisymm | [
{
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"state_before": "α : Type u\ninst✝⁵ ... | [
450,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
9
] |
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.ConcreteCategory.mono_iff_injective_of_preservesPullback | [] | [
170,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.gc_lcs_ucs | [] | [
418,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Algebra/Group/Units.lean | inv_eq_one_divp' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b c : α\nu : αˣ\n⊢ ↑(1 / u) = 1 /ₚ u",
"tactic": "rw [one_div, one_divp]"
}
] | [
518,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_sphere | [] | [
2330,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2329,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_map_eq_self_of_injective | [] | [
3071,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3069,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coeFn_injective | [] | [
448,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_lt | [
{
"state_after": "m n : ℕ\nhn : 0 < n\nh : n < m\n⊢ n ! < m !",
"state_before": "m n : ℕ\nhn : 0 < n\n⊢ n ! < m ! ↔ n < m",
"tactic": "refine' ⟨fun h => not_le.mp fun hmn => not_le_of_lt h (factorial_le hmn), fun h => _⟩"
},
{
"state_after": "m n : ℕ\nhn : 0 < n\nh : n < m\nthis : ∀ {n : ℕ}, 0 <... | [
117,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_rpow | [] | [
71,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Data/Finset/Basic.lean | Finset.mem_mk | [] | [
192,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.not_isUnit | [
{
"state_after": "A : Type u_2\nB : Type u_1\nB' : Type ?u.29630\ninst✝⁵ : CommRing A\ninst✝⁴ : Ring B\ninst✝³ : Ring B'\ninst✝² : Algebra A B\ninst✝¹ : Algebra A B'\nx : B\ninst✝ : Nontrivial B\nthis : Nontrivial A\n⊢ ¬IsUnit (minpoly A x)",
"state_before": "A : Type u_2\nB : Type u_1\nB' : Type ?u.29630\n... | [
115,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.projIcc | [] | [
470,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mul_lt_aleph0 | [
{
"state_after": "α β : Type u\na b : Cardinal\nm n : ℕ\nha : ↑m < ℵ₀\nhb : ↑n < ℵ₀\n⊢ ↑(m * n) < ℵ₀",
"state_before": "α β : Type u\na b : Cardinal\nm n : ℕ\nha : ↑m < ℵ₀\nhb : ↑n < ℵ₀\n⊢ ↑m * ↑n < ℵ₀",
"tactic": "rw [← Nat.cast_mul]"
},
{
"state_after": "no goals",
"state_before": "α β : T... | [
1556,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1554,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_atTop_eq | [] | [
355,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Cotrident.π_eq_app_one | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Order/UpperLower/Basic.lean | lowerClosure_singleton | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.158776\nγ : Type ?u... | [
1409,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.mk''_prod_swap_eq | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.4166\nγ : Type ?u.4169\nfst✝ snd✝ : α\n⊢ Quotient.mk (Rel.setoid α) (Prod.swap (fst✝, snd✝)) = Quotient.mk (Rel.setoid α) (fst✝, snd✝)",
"state_before": "α : Type u_1\nβ : Type ?u.4166\nγ : Type ?u.4169\np : α × α\n⊢ Quotient.mk (Rel.setoid α) (Prod.swap ... | [
151,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/CompleteLattice.lean | eq_singleton_top_of_sInf_eq_top_of_nonempty | [] | [
560,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.Fin.circulant_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1682\nm : Type ?u.1685\nn : Type ?u.1688\nR : Type ?u.1691\n⊢ Injective fun v => circulant v",
"tactic": "simp [Injective]"
}
] | [
70,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nnrealPart_coeFn_eq | [] | [
1596,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.comap_eq | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nr✝ : Setoid α\nf✝ f : α → β\nr : Setoid β\nx y : α\n⊢ Setoid.r x y ↔ f x ≈ f y",
"state_before": "α : Type u_2\nβ : Type u_1\nr✝ : Setoid α\nf✝ f : α → β\nr : Setoid β\nx y : α\n⊢ Setoid.r x y ↔ Quotient.mk r (f x) = Quotient.mk r (f y)",
"tactic": "rw [Quot... | [
404,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.decide_False | [] | [
33,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Int/Cast/Prod.lean | Prod.snd_intCast | [] | [
36,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
src/lean/Init/SimpLemmas.lean | iff_true | [] | [
93,
121
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
93,
9
] |
Mathlib/Topology/NhdsSet.lean | IsOpen.mem_nhdsSet | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11087\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\nhU : IsOpen s\n⊢ s ∈ 𝓝ˢ t ↔ t ⊆ s",
"tactic": "rw [← subset_interior_iff_mem_nhdsSet, hU.interior_eq]"
}
] | [
79,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_inr_inter_range_inl | [] | [
914,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_cast_of_lt | [
{
"state_after": "n✝ m n : ℕ\ninst✝ : NeZero n\na : ℕ\nh : a < n\n⊢ ↑(ofNat'' a) = a",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\na : ℕ\nh : a < n\n⊢ ↑↑a = a",
"tactic": "rw [← ofNat_eq_val]"
},
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\na : ℕ\nh : a < n\... | [
802,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.mul | [
{
"state_after": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : IsMultiplicative f\nhg : IsMultiplicative g\nf1 : ↑f 1 = 1\n⊢ ↑(f * g) 1 = 1",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : IsMultiplicative f\nhg : IsMultiplicative g\n⊢ ↑(f *... | [
691,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_nonempty_iff | [
{
"state_after": "α : Type u_2\nα' : Type ?u.21579\nβ : Type u_3\nβ' : Type ?u.21585\nγ : Type u_1\nγ' : Type ?u.21591\nδ : Type ?u.21594\nδ' : Type ?u.21597\nε : Type ?u.21600\nε' : Type ?u.21603\nζ : Type ?u.21606\nζ' : Type ?u.21609\nν : Type ?u.21612\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵... | [
123,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/LinearAlgebra/FreeModule/Rank.lean | rank_matrix | [
{
"state_after": "case intro\nR : Type u\nM : Type v\nN : Type w\ninst✝⁹ : Ring R\ninst✝⁸ : StrongRankCondition R\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : Module.Free R M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module R N\ninst✝² : Module.Free R N\nm : Type v\nn : Type w\ninst✝¹ : Finite m\ninst✝ : Fi... | [
82,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_two_mul_add_one | [
{
"state_after": "n : ℕ\n⊢ fib n * fib n + fib (n + 1) * fib (n + 1) = fib (n + 1) ^ 2 + fib n ^ 2",
"state_before": "n : ℕ\n⊢ fib (2 * n + 1) = fib (n + 1) ^ 2 + fib n ^ 2",
"tactic": "rw [two_mul, fib_add]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ fib n * fib n + fib (n + ... | [
170,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Std/Data/List/Lemmas.lean | List.mem_append_eq | [] | [
144,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
143,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_lt_nat_iff | [
{
"state_after": "no goals",
"state_before": "α β : Type u\na : Cardinal\nn : ℕ\n⊢ lift a < ↑n ↔ a < ↑n",
"tactic": "rw [← lift_natCast.{v,u}, lift_lt]"
}
] | [
1308,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1307,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_smul_right | [] | [
493,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na✝ a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf : R →+* S₁\ng : σ → S₁\na : R\n⊢ eval₂ f g (↑C a) = ↑f a",
"tactic": "rw... | [
967,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
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