Documentation Verification Report

SDiff

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

Statistics

MetricCount
DefinitionsinstGeneralizedBooleanAlgebra, instSDiff
2
Theoremssdiff_singleton_nonempty, coe_sdiff, cons_sdiff_cons, empty_sdiff, insert_sdiff_cancel, insert_sdiff_insert, insert_sdiff_insert', insert_sdiff_of_mem, insert_sdiff_of_notMem, insert_sdiff_self_of_mem, inter_sdiff_assoc, inter_sdiff_left_comm, inter_sdiff_self, mem_sdiff, notMem_sdiff_of_mem_right, notMem_sdiff_of_notMem_left, sdiff_empty, sdiff_eq_empty_iff_subset, sdiff_eq_sdiff_iff_inter_eq_inter, sdiff_eq_self_iff_disjoint, sdiff_eq_self_of_disjoint, sdiff_idem, sdiff_insert_of_notMem, sdiff_inter_distrib_right, sdiff_inter_right_comm, sdiff_inter_self, sdiff_inter_self_left, sdiff_inter_self_right, sdiff_nonempty, sdiff_sdiff_eq_sdiff_union, sdiff_sdiff_eq_self, sdiff_sdiff_left', sdiff_sdiff_self_left, sdiff_self, sdiff_ssubset, sdiff_subset, sdiff_subset_sdiff, sdiff_subset_sdiff_iff_subset, sdiff_union_distrib, sdiff_union_inter, sdiff_union_of_subset, sdiff_union_sdiff_cancel, sdiff_union_self_eq_union, sdiff_val, subset_sdiff, union_eq_sdiff_union_sdiff_union_inter, union_sdiff_cancel_left, union_sdiff_cancel_right, union_sdiff_distrib, union_sdiff_left, union_sdiff_of_subset, union_sdiff_right, union_sdiff_self, union_sdiff_self_eq_union, union_sdiff_symm
55
Total57

Finset

Definitions

NameCategoryTheorems
instGeneralizedBooleanAlgebra 📖CompOp
5 mathmath: Set.Sized.uvCompression, fold_sup_bot_singleton, UV.card_compress, UV.toColex_compress_lt_toColex, disjiUnion_Iic_disjointed
instSDiff 📖CompOp
221 mathmath: weightedVSub_sdiff, filter_notMem_eq_sdiff, card_sdiff_lt_card_sdiff_iff, Nat.prod_primeFactors_sdiff_of_squarefree, smul_finset_sdiff, inter_sdiff_assoc, Nat.roughNumbersUpTo_card_le, dens_sdiff_comm, Finpartition.equitabilise_aux, compl_eq_univ_sdiff, affineCombination_sdiff_sub, Icc_eq_image_powerset, sdiff_singleton_eq_erase, dens_inter_add_dens_sdiff, sdiff_nonempty, SimpleGraph.edgeFinset_sdiff, Finpartition.card_parts_equitabilise_subset_le, sdiff_insert_insert_of_mem_of_notMem, mem_shadow_iterate_iff_exists_sdiff, symmDiff_eq_union_iff, union_sdiff_self_eq_union, sdiff_nonempty_of_card_lt_card, prod_add, Colex.toColex_lt_toColex_iff_max'_mem, Equiv.Perm.cycleFactorsFinset_mul_inv_mem_eq_sdiff, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, Set.toFinset_symmDiff, dens_sdiff_add_dens_inter, OrthogonalFamily.norm_sq_diff_sum, Colex.le_iff_max'_mem, notMem_sdiff_of_notMem_left, Colex.toColex_sdiff_le_toColex_sdiff', sdiff_val, sum_sdiff_eq_sum_sdiff_iff, MvPolynomial.support_sdiff_support_subset_support_add, insert_sdiff_self_of_mem, sdiff_sdiff_eq_sdiff_union, prod_sub, sdiff_eq_filter, Ico_diff_Ico_left, Set.toFinset_diff, prod_sdiff_eq_div, inter_sdiff_self, pairwise_coprime_iff_coprime_prod, Equiv.Perm.support_swap_mul_eq, filter_and_not, card_sdiff, erase_eq, SimpleGraph.edgeFinset_deleteIncidenceSet_eq_sdiff, Nat.roughNumbersUpTo_eq_biUnion, card_sdiff_of_subset, Colex.toColex_le_toColex_iff_max'_mem, smul_finset_symmDiff, SimpleGraph.neighborFinset_compl, coe_sdiff, sum_sdiff_eq_sub, insert_sdiff_insert, sum_piecewise, Icc_diff_Ioc_self, SimpleGraph.edgeFinset_replaceVertex_of_adj, prod_eq_prod_diff_singleton_mul, sdiff_eq_self_iff_disjoint, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, weightedVSubOfPoint_sdiff, insert_sdiff_of_mem, Colex.toColex_sdiff_lt_toColex_sdiff, vadd_finset_symmDiff, Colex.toColex_sdiff_le_toColex_sdiff, sum_inter_add_sum_diff, sdiff_union_sdiff_cancel, Nat.primeFactors_div_gcd, SimpleGraph.edgeFinset_replaceVertex_of_not_adj, sum_eq_sum_diff_singleton_add, union_sdiff_cancel_left, sdiff_inter_self, DFinsupp.subset_support_tsub, card_sdiff_add_card_inter, symmDiff_nonempty, insert_sdiff_of_notMem, product_sdiff_diag, prod_eq_prod_range_sdiff, Ioc_diff_Ioo_self, sdiff_insert, card_le_card_sdiff_add_card, notMem_sdiff_of_mem_right, map_sdiff, sdiff_erase, smul_finset_symmDiff₀, erase_sdiff_distrib, Set.Finite.toFinset_symmDiff, union_sdiff_right, dens_sdiff_add_dens, sdiff_inter_distrib_right, prod_sdiff_le_prod_sdiff, mem_upShadow_iterate_iff_exists_card, PairReduction.finset_logSizeBallSeq_add_one, sdiff_union_self_eq_union, toLeft_sdiff, Colex.lt_iff_exists_filter_lt, sdiff_eq_self_of_disjoint, Ico_eq_image_ssubsets, Set.Finite.toFinset_diff, symmDiff_subset_sdiff, sum_sdiff_sub_sum_sdiff, union_sdiff_self, symmDiff_subset_union, sdiff_union_of_subset, inter_sdiff_left_comm, dens_le_dens_sdiff_add_dens, sdiff_sdiff_eq_self, covBy_iff_card_sdiff_eq_one, sdiff_union_erase_cancel, disjoint_sdiff, prod_sdiff, union_sdiff_distrib, sdiff_eq_sdiff_iff_inter_eq_inter, mem_sdiff, Nat.roughNumbersUpTo_card_le', card_inter_add_card_sdiff, Equiv.Perm.support_swap_mul_ge_support_diff, prod_sdiff_div_prod_sdiff, le_dens_sdiff, sum_sdiff_le_sum_sdiff, erase_sdiff_erase, Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd, card_sub_card_eq, subset_sdiff, card_sdiff_eq_card_sdiff_iff, SimpleGraph.sdiff_compl_neighborFinset_inter_eq, sdiff_eq_empty_iff_subset, coe_symmDiff, empty_sdiff, Finsupp.subset_support_tsub, image_sdiff_of_injOn, sdiff_inter_self_right, sdiff_subset_sdiff_iff_subset, sum_update_of_mem, Icc_diff_Ico_self, Icc_diff_both, Colex.lt_iff_max'_mem, Icc_diff_Ioo_self, insert_sdiff_cancel, mem_shadow_iff_exists_sdiff, sum_eq_add_sum_diff_singleton, box_succ_eq_sdiff, sdiff_sdiff_self_left, symmDiff_subset_sdiff', mem_upShadow_iff_exists_sdiff, union_sdiff_symm, le_card_sdiff, Ico_diff_Ico_right, union_sdiff_cancel_right, sdiff_subset_sdiff, prod_sdiff_lt_prod_sdiff, product_sdiff_offDiag, prod_inter_mul_prod_diff, range_sdiff_zero, card_sdiff_comm, filter_not, dens_sdiff_add_dens_eq_dens, prod_eq_mul_prod_diff_singleton, card_le_diff_of_interleaved, sdiff_idem, sdiff_erase_self, symmDiff_eq_empty, jacobiSum_eq_sum_sdiff, cast_card_sdiff, disjoint_sdiff_inter, Colex.toColex_sdiff_lt_toColex_sdiff', Ico_diff_Ioo_self, SimpleGraph.disjoint_sdiff_neighborFinset_image, union_sdiff_of_subset, Nontrivial.sdiff_singleton_nonempty, sdiff_ssubset, mem_symmDiff, card_sdiff_add_card_eq_card, cons_sdiff_cons, toRight_sdiff, sdiff_empty, SimpleGraph.compl_neighborFinset_sdiff_inter_eq, sdiff_self, HallMarriageTheorem.hall_cond_of_compl, dens_sdiff, exists_sum_eq_one_iff_pairwise_coprime, sdiff_inter_right_comm, card_sdiff_le_card_sdiff_iff, pairwise_isRelPrime_iff_isRelPrime_prod, smul_finset_sdiff₀, sdiff_inter_self_left, weightedVSub_sdiff_sub, sum_eq_sum_range_sdiff, prod_sdiff_eq_prod_sdiff_iff, union_sdiff_left, union_eq_sdiff_union_sdiff_union_inter, MvPolynomial.support_symmDiff_support_subset_support_add, sdiff_disjoint, not_linearIndepOn_finset_iffₒₛ, sum_sdiff_lt_sum_sdiff, vadd_finset_sdiff, prod_piecewise, SimpleGraph.edgeFinset_deleteEdges, sdiff_subset, sdiff_insert_of_notMem, erase_sdiff_comm, symmDiff_eq_union, one_half_le_sum_primes_ge_one_div, card_univ_diff, mem_upShadow_iterate_iff_exists_sdiff, insert_sdiff_insert', Iic_diff_Ioc, sdiff_union_inter, prod_update_of_mem, sdiff_union_distrib, sdiff_eq_inter_compl, Iic_diff_Ioc_self_of_le, image_symmDiff, card_sdiff_add_card, weightedVSubOfPoint_sdiff_sub, sum_sdiff, sdiff_sdiff_left', image_sdiff

Theorems

NameKindAssumesProvesValidatesDepends On
coe_sdiff 📖mathematicalSetLike.coe
Finset
instSetLike
instSDiff
Set
Set.instSDiff
Set.ext
mem_sdiff
cons_sdiff_cons 📖mathematicalFinset
instMembership
instSDiff
cons
instSingleton
empty_sdiff 📖mathematicalFinset
instSDiff
instEmptyCollection
bot_sdiff
insert_sdiff_cancel 📖mathematicalFinset
instMembership
instSDiff
instInsert
instSingleton
insert_sdiff_insert 📖mathematicalFinset
instSDiff
instInsert
insert_sdiff_of_mem
mem_insert_self
insert_sdiff_insert' 📖mathematicalFinset
instMembership
instSDiff
instInsert
instSingleton
ext
insert_sdiff_of_mem 📖mathematicalFinset
instMembership
instSDiff
instInsert
insert_sdiff_of_notMem 📖mathematicalFinset
instMembership
instSDiff
instInsert
insert_sdiff_self_of_mem 📖mathematicalFinset
instMembership
instInsert
instSDiff
instSingleton
inter_sdiff_assoc 📖mathematicalFinset
instSDiff
instInter
inf_sdiff_assoc
inter_sdiff_left_comm 📖mathematicalFinset
instInter
instSDiff
inf_sdiff_left_comm
inter_sdiff_self 📖mathematicalFinset
instInter
instSDiff
instEmptyCollection
mem_sdiff 📖mathematicalFinset
instMembership
instSDiff
Multiset.mem_sub_of_nodup
nodup
notMem_sdiff_of_mem_right 📖mathematicalFinset
instMembership
instSDiff
notMem_sdiff_of_notMem_left 📖mathematicalFinset
instMembership
instSDiff
sdiff_empty 📖mathematicalFinset
instSDiff
instEmptyCollection
sdiff_bot
sdiff_eq_empty_iff_subset 📖mathematicalFinset
instSDiff
instEmptyCollection
instHasSubset
sdiff_eq_bot_iff
sdiff_eq_sdiff_iff_inter_eq_inter 📖mathematicalFinset
instSDiff
instInter
sdiff_eq_sdiff_iff_inf_eq_inf
sdiff_eq_self_iff_disjoint 📖mathematicalFinset
instSDiff
Disjoint
partialOrder
instOrderBot
sdiff_eq_left
sdiff_eq_self_of_disjoint 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
instSDiffsdiff_eq_self_iff_disjoint
sdiff_idem 📖mathematicalFinset
instSDiff
sdiff_idem
sdiff_insert_of_notMem 📖mathematicalFinset
instMembership
instSDiff
instInsert
sdiff_inter_distrib_right 📖mathematicalFinset
instSDiff
instInter
instUnion
sdiff_inf
sdiff_inter_right_comm 📖mathematicalFinset
instInter
instSDiff
sdiff_inf_right_comm
sdiff_inter_self 📖mathematicalFinset
instInter
instSDiff
instEmptyCollection
inf_sdiff_self_left
sdiff_inter_self_left 📖mathematicalFinset
instSDiff
instInter
sdiff_inf_self_left
sdiff_inter_self_right 📖mathematicalFinset
instSDiff
instInter
sdiff_inf_self_right
sdiff_nonempty 📖mathematicalNonempty
Finset
instSDiff
instHasSubset
nonempty_iff_ne_empty
Iff.not
sdiff_eq_empty_iff_subset
sdiff_sdiff_eq_sdiff_union 📖mathematicalFinset
instHasSubset
instSDiff
instUnion
sdiff_sdiff_eq_sdiff_sup
sdiff_sdiff_eq_self 📖mathematicalFinset
instHasSubset
instSDiffsdiff_sdiff_eq_self
sdiff_sdiff_left' 📖mathematicalFinset
instSDiff
instInter
sdiff_sdiff_left'
sdiff_sdiff_self_left 📖mathematicalFinset
instSDiff
instInter
sdiff_sdiff_right_self
sdiff_self 📖mathematicalFinset
instSDiff
instEmptyCollection
sdiff_self
sdiff_ssubset 📖mathematicalFinset
instHasSubset
Nonempty
instHasSSubset
instSDiff
sdiff_subset 📖mathematicalFinset
instHasSubset
instSDiff
le_iff_subset
sdiff_le
sdiff_subset_sdiff 📖mathematicalFinset
instHasSubset
instSDiff
sdiff_subset_sdiff_iff_subset 📖mathematicalFinset
instHasSubset
instSDiffsdiff_le_sdiff_iff_le
sdiff_union_distrib 📖mathematicalFinset
instSDiff
instUnion
instInter
sdiff_sup
sdiff_union_inter 📖mathematicalFinset
instUnion
instSDiff
instInter
sup_sdiff_inf
sdiff_union_of_subset 📖mathematicalFinset
instHasSubset
instUnion
instSDiff
sdiff_union_sdiff_cancel 📖mathematicalFinset
instHasSubset
instUnion
instSDiff
sdiff_sup_sdiff_cancel
sdiff_union_self_eq_union 📖mathematicalFinset
instUnion
instSDiff
sup_sdiff_self_left
sdiff_val 📖mathematicalval
Finset
instSDiff
Multiset
Multiset.instSub
subset_sdiff 📖mathematicalFinset
instHasSubset
instSDiff
Disjoint
partialOrder
instOrderBot
le_iff_subset
le_sdiff
union_eq_sdiff_union_sdiff_union_inter 📖mathematicalFinset
instUnion
instSDiff
instInter
sup_eq_sdiff_sup_sdiff_sup_inf
union_sdiff_cancel_left 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
instSDiff
instUnion
Disjoint.sup_sdiff_cancel_left
union_sdiff_cancel_right 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
instSDiff
instUnion
Disjoint.sup_sdiff_cancel_right
union_sdiff_distrib 📖mathematicalFinset
instSDiff
instUnion
sup_sdiff
union_sdiff_left 📖mathematicalFinset
instSDiff
instUnion
sup_sdiff_left_self
union_sdiff_of_subset 📖mathematicalFinset
instHasSubset
instUnion
instSDiff
union_sdiff_right 📖mathematicalFinset
instSDiff
instUnion
sup_sdiff_right_self
union_sdiff_self 📖mathematicalFinset
instSDiff
instUnion
sup_sdiff_right_self
union_sdiff_self_eq_union 📖mathematicalFinset
instUnion
instSDiff
sup_sdiff_self_right
union_sdiff_symm 📖mathematicalFinset
instUnion
instSDiff
union_sdiff_self_eq_union
union_comm

Finset.Nontrivial

Theorems

NameKindAssumesProvesValidatesDepends On
sdiff_singleton_nonempty 📖mathematicalFinset.NontrivialFinset.Nonempty
Finset
Finset.instSDiff
Finset.instSingleton

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