Documentation Verification Report

Prod

📁 Source: Mathlib/Data/Finset/Prod.lean

Statistics

MetricCount
Definitionsdiag, instSProd, offDiag, product
4
Theoremsfst, product, snd, card_product, coe_offDiag, coe_product, diag_card, diag_empty, diag_eq_empty, diag_eq_filter, diag_insert, diag_inter, diag_mono, diag_nonempty, diag_singleton, diag_union, diag_union_offDiag, disjUnion_product, disjoint_diag_offDiag, disjoint_product, empty_product, filter_product, filter_product_card, filter_product_left, filter_product_right, image_diag, image_swap_product, inter_product, map_swap_product, mem_diag, mem_offDiag, mem_product, mk_mem_product, nonempty_product, nontrivial_prod_iff, offDiag_card, offDiag_empty, offDiag_filter_lt_eq_filter_le, offDiag_insert, offDiag_inter, offDiag_mono, offDiag_singleton, offDiag_union, prodMap_image_product, prodMap_map_product, product_biUnion, product_disjUnion, product_empty, product_eq_biUnion, product_eq_biUnion_right, product_eq_empty, product_eq_sprod, product_image_fst, product_image_snd, product_inter, product_inter_product, product_sdiff_diag, product_sdiff_offDiag, product_singleton, product_subset_product, product_subset_product_left, product_subset_product_right, product_union, product_val, singleton_product, singleton_product_singleton, subset_product, subset_product_image_fst, subset_product_image_snd, union_product
70
Total74

Finset

Definitions

NameCategoryTheorems
diag 📖CompOp
21 mathmath: diag_union, prod_diag, diag_card, image_diag, Sym2.filter_image_mk_isDiag, sum_diag, diag_union_offDiag, Sym2.card_image_diag, mem_diag, product_sdiff_diag, diag_eq_empty, image_diag_union_image_offDiag, diag_inter, product_sdiff_offDiag, diag_mono, disjoint_diag_offDiag, diag_insert, diag_nonempty, diag_singleton, diag_eq_filter, diag_empty
instSProd 📖CompOp
180 mathmath: WittVector.remainder_vars, sup_add_sup, Set.Finite.toFinset_prod, addEnergy_eq_sum_sq', Nat.smoothNumbersUpTo_subset_image, sup_product_right, product_biUnion, image₂_curry, SupIndep.product, product_union, product_image_fst, subset_product_image_snd, empty_product, inf'_sup_inf', Rel.interedges_biUnion, image_uncurry_product, product_pow, product_singleton, le_addRothNumber_product, disjUnion_product, image_smul_product, filter_product_right, map_consEquiv_filter_piFinset, prodMk_sup'_sup', Sym2.filter_image_mk_isDiag, UniqueMul.exists_iff_exists_existsUnique, map_snocEquiv_filter_piFinset, Rel.card_interedges_finpartition, image_div_product, image_swap_product, product_inter, product_image_snd, union_product, card_product, inf_prodMap, singleton_product_singleton, SimpleGraph.neighborFinset_completeEquipartiteGraph, product_subset_product, wittStructureRat_vars, addEnergy_eq_sum_sq, zero_product_zero, mulEnergy_eq_sum_sq', filter_product_card, product_subset_product_left, TwoUniqueProds.uniqueMul_of_one_lt_card, product_eq_biUnion, diag_union_offDiag, sup_product_left, UniqueMul.iff_existsUnique, uIcc_product_uIcc, offDiag_union, div_def, product_eq_sprod, WittVector.wittZSMul_vars, card_mul_inv_eq_convolution_inv, SimpleGraph.neighborFinset_boxProd, prod_product_right', product_sdiff_diag, univ_product_univ, Real.pow_mul_norm_iteratedFDeriv_fourier_le, inf_product_left, filter_piFinset_eq_map_consEquiv, DirectSum.coe_mul_apply, Filter.tendsto_finset_prod_atTop, Nonempty.product, mk_mem_product, SimpleGraph.interedges_def, TwoUniqueSums.uniqueAdd_of_one_lt_card, image_sub_product, inf_product_right, product_disjUnion, UniqueAdd.exists_iff_exists_existsUnique, WittVector.mul_polyOfInterest_vars, filter_piFinset_eq_map_insertNthEquiv, sup_prodMap, inv_product, sup'_inf_sup', WittVector.wittAdd_vars, uIcc_prod_def, product_eq_empty, image_sdiff_product, neg_product, product_eq_biUnion_right, ArithmeticFunction.sum_Ioc_mul_eq_sum_prod_filter, sum_product', card_sq_le_card_mul_mulEnergy, product_nsmul, UniqueMul.iff_card_le_one, SimpleGraph.unreduced_edges_subset, EMetric.pair_reduction, subset_product_image_fst, prod_product_right, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, image_add_product, product_eq_univ, sum_product_right', expect_product, le_mulRothNumber_product, wittStructureInt_vars, product_val, prodMap_map_product, prodMap_image_product, card_sq_le_card_mul_addEnergy, Ici_prod_def, offDiag_insert, SimpleGraph.triangle_counting', prodMk_inf'_inf', Icc_prod_def, product_mul_product_comm, prod_product, sub_def, WittVector.wittSub_vars, disjoint_product, Finpartition.IsEquipartition.sum_nonUniforms_lt, YoungDiagram.row_eq_prod, image_sup_product, map_insertNthEquiv_filter_piFinset, WittVector.wittPow_vars, smul_def, mulEnergy_eq_sum_sq, Ici_product_Ici, Sym2.filter_image_mk_not_isDiag, Nat.divisorsAntidiagonal_eq_prod_filter_of_le, UniqueAdd.iff_card_le_one, filter_piFinset_eq_map_snocEquiv, nontrivial_prod_iff, WittVector.polyOfInterest_vars, Real.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, DirectSum.mul_eq_sum_support_ghas_mul, image_mul_product, inf_sup_inf, product_sdiff_offDiag, coe_product, map_swap_product, product_empty, image₂_mk_eq_product, nonempty_product, sup_inf_sup, YoungDiagram.col_eq_prod, SimpleGraph.interedges_biUnion, WittVector.wittNSMul_vars, singleton_product, Iic_product_Iic, product_subset_product_right, subset_product, mul_def, Icc_product_Icc, sum_product_right, Nat.card_pair_lcm_eq, one_product_one, addEnergy_eq_card_filter, sum_product, mulEnergy_eq_card_filter, add_def, PairReduction.pairSet_subset, mem_product, Iic_prod_def, product_add_product_comm, inter_product, prod_product', diag_eq_filter, product_self_eq_disjiUnion_perm, filter_product, product_inter_product, WittVector.wittNeg_vars, vadd_def, card_add_neg_eq_addConvolution_neg, filter_product_left, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, image_vadd_product, UniqueAdd.iff_existsUnique, WittVector.wittPolyProd_vars, Multiset.toEnumFinset_filter_eq, Set.toFinset_prod, sym2_eq_image, expect_product', WittVector.wittPolyProdRemainder_vars, Finpartition.parts_inf, WittVector.wittMul_vars, image_inf_product
offDiag 📖CompOp
29 mathmath: SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, Finpartition.IsEquipartition.card_biUnion_offDiag_le', Finpartition.IsEquipartition.card_biUnion_offDiag_le, Set.Finset.coe_einfsep, offDiag_card, offDiag_singleton, coe_offDiag, diag_union_offDiag, offDiag_union, offDiag_mono, product_sdiff_diag, Set.toFinset_offDiag, coe_infsep, Finpartition.coe_energy, SimpleGraph.unreduced_edges_subset, Set.Finite.toFinset_offDiag, Set.toFinset_off_diag, offDiag_insert, image_diag_union_image_offDiag, Sym2.filter_image_mk_not_isDiag, product_sdiff_offDiag, Sym2.card_image_offDiag, offDiag_empty, mem_offDiag, disjoint_diag_offDiag, sum_sym2_filter_not_isDiag, offDiag_filter_lt_eq_filter_le, Sym2.two_mul_card_image_offDiag, offDiag_inter
product 📖CompOp
4 mathmath: product_eq_sprod, SzemerediRegularity.edgeDensity_chunk_uniform, supIndep_product_iff, SzemerediRegularity.edgeDensity_chunk_not_uniform

Theorems

NameKindAssumesProvesValidatesDepends On
card_product 📖mathematicalcard
SProd.sprod
Finset
instSProd
Multiset.card_product
coe_offDiag 📖mathematicalSetLike.coe
Finset
instSetLike
offDiag
Set.offDiag
Set.ext
mem_offDiag
coe_product 📖mathematicalSetLike.coe
Finset
instSetLike
SProd.sprod
instSProd
Set
Set.instSProd
Set.ext
mem_product
diag_card 📖mathematicalcard
diag
card_map
diag_empty 📖mathematicaldiag
Finset
instEmptyCollection
diag_eq_empty 📖mathematicaldiag
Finset
instEmptyCollection
diag_eq_filter 📖mathematicaldiag
filter
SProd.sprod
Finset
instSProd
ext
diag_insert 📖mathematicaldiag
Finset
instInsert
diag_inter 📖mathematicaldiag
Finset
instInter
diag_mono 📖mathematicalMonotone
Finset
PartialOrder.toPreorder
partialOrder
diag
diag_nonempty 📖mathematicalNonempty
diag
diag_singleton 📖mathematicaldiag
Finset
instSingleton
diag_union 📖mathematicaldiag
Finset
instUnion
diag_union_offDiag 📖mathematicalFinset
instUnion
diag
offDiag
SProd.sprod
instSProd
disjUnion_product 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
SProd.sprod
instSProd
disjUnion
disjoint_product
eq_of_veq
disjoint_product
Multiset.add_product
disjoint_diag_offDiag 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
diag
offDiag
disjoint_product 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
SProd.sprod
instSProd
coe_product
empty_product 📖mathematicalSProd.sprod
Finset
instSProd
instEmptyCollection
filter_product 📖mathematicalfilter
SProd.sprod
Finset
instSProd
filter_product_card 📖mathematicalcard
filter
SProd.sprod
Finset
instSProd
card_product
filter_product
card_union_of_disjoint
disjoint_filter_filter'
Disjoint.inf_right
Disjoint.inf_left
disjoint_compl_right
filter_product_left 📖mathematicalfilter
SProd.sprod
Finset
instSProd
filter.congr_simp
filter_true
filter_product
filter_product_right 📖mathematicalfilter
SProd.sprod
Finset
instSProd
filter.congr_simp
filter_true
filter_product
image_diag 📖mathematicalimage
diag
image_swap_product 📖mathematicalimage
SProd.sprod
Finset
instSProd
coe_injective
coe_image
coe_product
Set.image_swap_prod
inter_product 📖mathematicalSProd.sprod
Finset
instSProd
instInter
map_swap_product 📖mathematicalmap
Prod.swap_injective
SProd.sprod
Finset
instSProd
coe_injective
Prod.swap_injective
coe_map
coe_product
Set.image_swap_prod
mem_diag 📖mathematicalFinset
instMembership
diag
mem_offDiag 📖mathematicalFinset
instMembership
offDiag
List.Nodup.mem_offDiag
mem_product 📖mathematicalFinset
instMembership
SProd.sprod
instSProd
Multiset.mem_product
mk_mem_product 📖mathematicalFinset
instMembership
SProd.sprod
instSProd
mem_product
nonempty_product 📖mathematicalNonempty
SProd.sprod
Finset
instSProd
Nonempty.fst
Nonempty.snd
Nonempty.product
nontrivial_prod_iff 📖mathematicalNontrivial
SProd.sprod
Finset
instSProd
Nonempty
card_product
offDiag_card 📖mathematicalcard
offDiag
sq
List.length_offDiag
offDiag_empty 📖mathematicaloffDiag
Finset
instEmptyCollection
offDiag_filter_lt_eq_filter_le 📖mathematicalfilter
Preorder.toLT
PartialOrder.toPreorder
offDiag
Preorder.toLE
ext
Ne.le_iff_lt
offDiag_insert 📖mathematicalFinset
instMembership
offDiag
instInsert
instUnion
SProd.sprod
instSProd
instSingleton
offDiag_inter 📖mathematicaloffDiag
Finset
instInter
coe_injective
coe_offDiag
coe_inter
Set.offDiag_inter
offDiag_mono 📖mathematicalMonotone
Finset
PartialOrder.toPreorder
partialOrder
offDiag
mem_offDiag
offDiag_singleton 📖mathematicaloffDiag
Finset
instSingleton
instEmptyCollection
offDiag_card
card_singleton
mul_one
offDiag_union 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
offDiag
instUnion
SProd.sprod
instSProd
coe_injective
coe_offDiag
coe_union
coe_product
Set.offDiag_union
disjoint_coe
prodMap_image_product 📖mathematicalimage
SProd.sprod
Finset
instSProd
Set.prodMap_image_prod
prodMap_map_product 📖mathematicalmap
Function.Embedding.prodMap
SProd.sprod
Finset
instSProd
coe_map
Set.image_congr
coe_product
Set.prodMap_image_prod
product_biUnion 📖mathematicalbiUnion
SProd.sprod
Finset
instSProd
product_disjUnion 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
SProd.sprod
instSProd
disjUnion
disjoint_product
eq_of_veq
disjoint_product
Multiset.product_add
product_empty 📖mathematicalSProd.sprod
Finset
instSProd
instEmptyCollection
eq_empty_of_forall_notMem
notMem_empty
mem_product
product_eq_biUnion 📖mathematicalSProd.sprod
Finset
instSProd
biUnion
image
product_eq_biUnion_right 📖mathematicalSProd.sprod
Finset
instSProd
biUnion
image
product_eq_empty 📖mathematicalSProd.sprod
Finset
instSProd
instEmptyCollection
Mathlib.Tactic.Contrapose.contrapose_iff₁
nonempty_product
product_eq_sprod 📖mathematicalproduct
SProd.sprod
Finset
instSProd
product_image_fst 📖mathematicalNonemptyimage
SProd.sprod
Finset
instSProd
ext
Nonempty.exists_mem
product_image_snd 📖mathematicalNonemptyimage
SProd.sprod
Finset
instSProd
ext
Nonempty.exists_mem
product_inter 📖mathematicalSProd.sprod
Finset
instSProd
instInter
product_inter_product 📖mathematicalFinset
instInter
SProd.sprod
instSProd
product_sdiff_diag 📖mathematicalFinset
instSDiff
SProd.sprod
instSProd
diag
offDiag
product_sdiff_offDiag 📖mathematicalFinset
instSDiff
SProd.sprod
instSProd
offDiag
diag
product_singleton 📖mathematicalSProd.sprod
Finset
instSProd
instSingleton
map
Prod.mk_left_injective
ext
Prod.mk_left_injective
product_subset_product 📖mathematicalFinset
instHasSubset
SProd.sprod
instSProd
mem_product
product_subset_product_left 📖mathematicalFinset
instHasSubset
SProd.sprod
instSProd
product_subset_product
Subset.refl
product_subset_product_right 📖mathematicalFinset
instHasSubset
SProd.sprod
instSProd
product_subset_product
Subset.refl
product_union 📖mathematicalSProd.sprod
Finset
instSProd
instUnion
product_val 📖mathematicalval
SProd.sprod
Finset
instSProd
Multiset
Multiset.instSProd
singleton_product 📖mathematicalSProd.sprod
Finset
instSProd
instSingleton
map
Prod.mk_right_injective
ext
Prod.mk_right_injective
singleton_product_singleton 📖mathematicalSProd.sprod
Finset
instSProd
instSingleton
Prod.mk_left_injective
product_singleton
map_singleton
subset_product 📖mathematicalFinset
instHasSubset
SProd.sprod
instSProd
image
subset_product_image_fst 📖mathematicalFinset
instHasSubset
image
SProd.sprod
instSProd
subset_product_image_snd 📖mathematicalFinset
instHasSubset
image
SProd.sprod
instSProd
union_product 📖mathematicalSProd.sprod
Finset
instSProd
instUnion

Finset.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
fst 📖Finset.Nonempty
SProd.sprod
Finset
Finset.instSProd
Finset.mem_product
product 📖mathematicalFinset.NonemptySProd.sprod
Finset
Finset.instSProd
Finset.mem_product
snd 📖Finset.Nonempty
SProd.sprod
Finset
Finset.instSProd
Finset.mem_product

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