Documentation Verification Report

ModEq

πŸ“ Source: Mathlib/Data/Int/ModEq.lean

Statistics

MetricCount
DefinitionsModEq, instDecidableModEq, Β«term_≑_[ZMOD_]Β»
3
TheoremsintCast, of_intCast, intCast_modEq_intCast, intCast_modEq_intCast', modEq_iff_intModEq, modEq_iff_int_modEq, modEq_zero_int, zero_modEq_int, add, add_left, add_left_cancel, add_left_cancel', add_right, add_right_cancel, add_right_cancel', cancel_left_div_gcd, cancel_right_div_gcd, dvd, dvd_iff, eq, instIsTrans, instRefl, mul, mul_left, mul_left', mul_left_cancel', mul_left_cancel_iff', mul_right, mul_right', mul_right_cancel', mul_right_cancel_iff', neg, of_div, of_dvd, of_mul_left, of_mul_right, pow, refl, rfl, sub, sub_left, sub_right, trans, add_modEq_left, add_modEq_left_iff, add_modEq_right, add_modEq_right_iff, add_modulus_modEq_iff, add_modulus_mul_modEq_iff, add_mul_modulus_modEq_iff, existsUnique_equiv, existsUnique_equiv_nat, ext_ediv_modEq, ext_ediv_modEq_iff, gcd_a_modEq, left_modEq_add_iff, modEq_abs, modEq_add_fac, modEq_add_fac_self, modEq_add_modulus_iff, modEq_add_modulus_mul_iff, modEq_add_mul_modulus_iff, modEq_and_modEq_iff_modEq_lcm, modEq_and_modEq_iff_modEq_mul, modEq_comm, modEq_iff_add_fac, modEq_iff_dvd, modEq_iff_eq_of_div_eq, modEq_modulus_add_iff, modEq_modulus_mul_add_iff, modEq_mul_modulus_add_iff, modEq_natAbs, modEq_neg, modEq_of_dvd, modEq_one, modEq_sub, modEq_sub_fac, modEq_sub_modulus_iff, modEq_sub_modulus_mul_iff, modEq_zero_iff, modEq_zero_iff_dvd, mod_coprime, mod_modEq, mod_mul_left_mod, mod_mul_right_mod, modulus_add_modEq_iff, modulus_modEq_zero, modulus_mul_add_modEq_iff, mul_modulus_add_modEq_iff, natCast_modEq_iff, neg_modEq_neg, right_modEq_add_iff, sub_modulus_modEq_iff, sub_modulus_mul_modEq_iff
94
Total97

AddCommGroup

Theorems

NameKindAssumesProvesValidatesDepends On
intCast_modEq_intCast πŸ“–mathematicalβ€”ModEq
AddCommMonoidWithOne.toAddCommMonoid
AddCommGroupWithOne.toAddCommMonoidWithOne
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
Int.instAddCommMonoid
β€”map_modEq_iff
AddMonoidHom.instAddMonoidHomClass
Int.cast_injective
intCast_modEq_intCast' πŸ“–mathematicalβ€”ModEq
AddCommMonoidWithOne.toAddCommMonoid
AddCommGroupWithOne.toAddCommMonoidWithOne
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
AddCommGroupWithOne.toAddGroupWithOne
AddGroupWithOne.toIntCast
Int.instAddCommMonoid
β€”Int.cast_natCast
intCast_modEq_intCast
modEq_iff_intModEq πŸ“–mathematicalβ€”ModEq
Int.instAddCommMonoid
Int.ModEq
β€”modEq_comm
modEq_iff_int_modEq πŸ“–mathematicalβ€”ModEq
Int.instAddCommMonoid
Int.ModEq
β€”modEq_iff_intModEq

AddCommGroup.ModEq

Theorems

NameKindAssumesProvesValidatesDepends On
intCast πŸ“–mathematicalAddCommGroup.ModEq
Int.instAddCommMonoid
AddCommMonoidWithOne.toAddCommMonoid
AddCommGroupWithOne.toAddCommMonoidWithOne
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
β€”AddCommGroup.intCast_modEq_intCast
of_intCast πŸ“–mathematicalAddCommGroup.ModEq
AddCommMonoidWithOne.toAddCommMonoid
AddCommGroupWithOne.toAddCommMonoidWithOne
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
Int.instAddCommMonoidβ€”AddCommGroup.intCast_modEq_intCast

Dvd.dvd

Theorems

NameKindAssumesProvesValidatesDepends On
modEq_zero_int πŸ“–mathematicalβ€”Int.ModEqβ€”Int.modEq_zero_iff_dvd
zero_modEq_int πŸ“–mathematicalβ€”Int.ModEqβ€”Int.ModEq.symm
modEq_zero_int

Int

Definitions

NameCategoryTheorems
ModEq πŸ“–MathDef
80 mathmath: add_modEq_right_iff, add_modulus_mul_modEq_iff, modEq_iff_dvd, Nat.ofDigits_zmodeq, Nat.Ioc_filter_modEq_cast, modEq_iff_add_fac, ModEq.mul_left_cancel_iff', sub_modulus_mul_modEq_iff, modEq_add_modulus_iff, modEq_mul_modulus_add_iff, modEq_zero_iff, modulus_mul_add_modEq_iff, add_modEq_left, Nat.forall_exists_prime_gt_and_zmodEq, right_modEq_add_iff, existsUnique_equiv, Choose.lucas_theorem, ModEq.refl, modEq_of_dvd, left_modEq_add_iff, Choose.choose_modEq_prod_range_choose, add_modEq_left_iff, gcd_a_modEq, zpow_eq_one_iff_modEq, Dvd.dvd.modEq_zero_int, modEq_comm, natCast_modEq_iff, neg_modEq_neg, modEq_iff_eq_of_div_eq, modEq_add_fac_self, Dvd.dvd.zero_modEq_int, Ioc_filter_modEq_card, modEq_and_modEq_iff_modEq_lcm, ModEq.pow_eq_pow, modEq_and_modEq_iff_modEq_mul, Choose.choose_modEq_choose_mod_mul_choose_div, modEq_sub, ModEq.instRefl, add_mul_modulus_modEq_iff, modEq_natAbs, modEq_sub_modulus_mul_iff, modEq_modulus_mul_add_iff, mod_coprime, CharP.intCast_eq_intCast, Nat.Ico_filter_modEq_cast, Choose.choose_modEq_choose_mul_prod_range_choose, modEq_neg, ZMod.intCast_eq_intCast_iff, ModEq.rfl, AddCommGroup.modEq_iff_int_modEq, mul_modulus_add_modEq_iff, ModEq.pow_prime_eq_self, Ico_filter_modEq_card, Equiv.Perm.IsCycleOn.zpow_apply_eq_zpow_apply, ext_ediv_modEq_iff, sub_modulus_modEq_iff, modEq_abs, modulus_add_modEq_iff, ModEq.pow_card_sub_one_eq_one, Nat.modEq_eleven_digits_sum, modEq_sub_modulus_iff, modEq_add_modulus_mul_iff, zpow_eq_zpow_iff_modEq, add_modulus_modEq_iff, zsmul_eq_zsmul_iff_modEq, modEq_modulus_add_iff, Ico_filter_modEq_eq, Ioc_filter_modEq_eq, modulus_modEq_zero, AddCommGroup.modEq_iff_intModEq, modEq_zero_iff_dvd, zsmul_eq_zero_iff_modEq, Nat.sq_add_sq_zmodEq, mod_modEq, add_modEq_right, ModEq.instIsTrans, modEq_add_mul_modulus_iff, ModEq.mul_right_cancel_iff', modEq_one, existsUnique_equiv_nat
instDecidableModEq πŸ“–CompOp
6 mathmath: Nat.Ioc_filter_modEq_cast, Ioc_filter_modEq_card, Nat.Ico_filter_modEq_cast, Ico_filter_modEq_card, Ico_filter_modEq_eq, Ioc_filter_modEq_eq

Theorems

NameKindAssumesProvesValidatesDepends On
add_modEq_left πŸ“–mathematicalβ€”ModEqβ€”β€”
add_modEq_left_iff πŸ“–mathematicalβ€”ModEqβ€”sub_add_cancel_left
add_modEq_right πŸ“–mathematicalβ€”ModEqβ€”β€”
add_modEq_right_iff πŸ“–mathematicalβ€”ModEqβ€”add_comm
add_modEq_left_iff
add_modulus_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
add_modulus_mul_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
add_mul_modulus_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
existsUnique_equiv πŸ“–mathematicalβ€”ModEqβ€”ne_of_gt
emod_lt_abs
abs_of_pos
instAddLeftMono
existsUnique_equiv_nat πŸ“–mathematicalβ€”ModEqβ€”existsUnique_equiv
ext_ediv_modEq πŸ“–β€”ModEqβ€”β€”ext_ediv_emod
ext_ediv_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”ext_ediv_emod_iff
gcd_a_modEq πŸ“–mathematicalβ€”ModEq
Nat.gcdA
β€”add_zero
Nat.gcd_eq_gcd_ab
ModEq.add_left
Dvd.dvd.zero_modEq_int
dvd_mul_right
left_modEq_add_iff πŸ“–mathematicalβ€”ModEqβ€”modEq_comm
add_modEq_left_iff
modEq_abs πŸ“–mathematicalβ€”ModEq
abs
instLatticeInt
instAddGroup
β€”emod_abs
modEq_add_fac πŸ“–β€”ModEqβ€”β€”β€”
modEq_add_fac_self πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_add_modulus_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_add_modulus_mul_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_add_mul_modulus_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_and_modEq_iff_modEq_lcm πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_and_modEq_iff_modEq_mul πŸ“–mathematicalβ€”ModEqβ€”modEq_natAbs
modEq_and_modEq_iff_modEq_lcm
modEq_comm πŸ“–mathematicalβ€”ModEqβ€”ModEq.symm
modEq_iff_add_fac πŸ“–mathematicalβ€”ModEqβ€”modEq_iff_dvd
sub_eq_iff_eq_add'
modEq_iff_dvd πŸ“–mathematicalβ€”ModEqβ€”ModEq.eq_1
modEq_iff_eq_of_div_eq πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_modulus_add_iff πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_modulus_mul_add_iff πŸ“–mathematicalβ€”ModEqβ€”add_comm
modEq_add_modulus_mul_iff
modEq_mul_modulus_add_iff πŸ“–mathematicalβ€”ModEqβ€”add_comm
modEq_add_mul_modulus_iff
modEq_natAbs πŸ“–mathematicalβ€”ModEqβ€”natCast_natAbs
modEq_neg πŸ“–mathematicalβ€”ModEqβ€”β€”
modEq_of_dvd πŸ“–mathematicalβ€”ModEqβ€”modEq_iff_dvd
modEq_one πŸ“–mathematicalβ€”ModEqβ€”modEq_of_dvd
one_dvd
modEq_sub πŸ“–mathematicalβ€”ModEqβ€”ModEq.symm
modEq_of_dvd
dvd_rfl
modEq_sub_fac πŸ“–β€”ModEqβ€”β€”β€”
modEq_sub_modulus_iff πŸ“–mathematicalβ€”ModEqβ€”modEq_add_modulus_iff
sub_add_cancel
modEq_sub_modulus_mul_iff πŸ“–mathematicalβ€”ModEqβ€”modEq_add_modulus_mul_iff
sub_add_cancel
modEq_zero_iff πŸ“–mathematicalβ€”ModEqβ€”ModEq.eq_1
modEq_zero_iff_dvd πŸ“–mathematicalβ€”ModEqβ€”ModEq.eq_1
mod_coprime πŸ“–mathematicalβ€”ModEqβ€”ModEq.instIsTrans
Nat.gcd_eq_gcd_ab
mod_modEq πŸ“–mathematicalβ€”ModEqβ€”β€”
mod_mul_left_mod πŸ“–β€”β€”β€”β€”ModEq.of_mul_left
mod_modEq
mod_mul_right_mod πŸ“–β€”β€”β€”β€”ModEq.of_mul_right
mod_modEq
modulus_add_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”add_comm
add_modulus_modEq_iff
modulus_modEq_zero πŸ“–mathematicalβ€”ModEqβ€”β€”
modulus_mul_add_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”add_comm
add_modulus_mul_modEq_iff
mul_modulus_add_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”add_comm
add_mul_modulus_modEq_iff
natCast_modEq_iff πŸ“–mathematicalβ€”ModEq
Nat.ModEq
β€”β€”
neg_modEq_neg πŸ“–mathematicalβ€”ModEqβ€”β€”
right_modEq_add_iff πŸ“–mathematicalβ€”ModEqβ€”modEq_comm
add_modEq_right_iff
sub_modulus_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”add_modulus_modEq_iff
sub_add_cancel
sub_modulus_mul_modEq_iff πŸ“–mathematicalβ€”ModEqβ€”add_modulus_mul_modEq_iff
sub_add_cancel

Int.ModEq

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–β€”Int.ModEqβ€”β€”Int.modEq_iff_dvd
dvd
add_left πŸ“–β€”Int.ModEqβ€”β€”add
rfl
add_left_cancel πŸ“–β€”Int.ModEqβ€”β€”Int.modEq_iff_dvd
dvd
add_left_cancel' πŸ“–β€”Int.ModEqβ€”β€”add_left_cancel
rfl
add_right πŸ“–β€”Int.ModEqβ€”β€”add
rfl
add_right_cancel πŸ“–β€”Int.ModEqβ€”β€”add_left_cancel
add_comm
add_right_cancel' πŸ“–β€”Int.ModEqβ€”β€”add_right_cancel
rfl
cancel_left_div_gcd πŸ“–β€”Int.ModEqβ€”β€”cancel_right_div_gcd
mul_comm
cancel_right_div_gcd πŸ“–β€”Int.ModEqβ€”β€”Int.modEq_iff_dvd
Int.dvd_of_dvd_mul_right_of_gcd_one
mul_comm
Int.gcd_div
LT.lt.ne'
dvd πŸ“–β€”Int.ModEqβ€”β€”Int.modEq_iff_dvd
dvd_iff πŸ“–β€”Int.ModEqβ€”β€”trans
symm
eq πŸ“–β€”Int.ModEqβ€”β€”β€”
instIsTrans πŸ“–mathematicalβ€”IsTrans
Int.ModEq
β€”trans
instRefl πŸ“–mathematicalβ€”Int.ModEqβ€”refl
mul πŸ“–β€”Int.ModEqβ€”β€”trans
mul_left
mul_right
mul_left πŸ“–β€”Int.ModEqβ€”β€”of_dvd
dvd_mul_left
mul_left'
mul_left' πŸ“–β€”Int.ModEqβ€”β€”lt_trichotomy
Int.neg_modEq_neg
Int.modEq_neg
neg_pos
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
Int.instAddLeftMono
eq
mul_left_cancel' πŸ“–β€”Int.ModEqβ€”β€”β€”
mul_left_cancel_iff' πŸ“–mathematicalβ€”Int.ModEqβ€”mul_left_cancel'
mul_left'
mul_right πŸ“–β€”Int.ModEqβ€”β€”of_dvd
dvd_mul_right
mul_right'
mul_right' πŸ“–β€”Int.ModEqβ€”β€”mul_comm
mul_left'
mul_right_cancel' πŸ“–β€”Int.ModEqβ€”β€”β€”
mul_right_cancel_iff' πŸ“–mathematicalβ€”Int.ModEqβ€”mul_right_cancel'
mul_right'
neg πŸ“–β€”Int.ModEqβ€”β€”add_left_cancel
sub_self
of_div πŸ“–β€”Int.ModEqβ€”β€”mul_left'
of_dvd πŸ“–β€”Int.ModEqβ€”β€”Int.modEq_iff_dvd
Dvd.dvd.trans
dvd
of_mul_left πŸ“–β€”Int.ModEqβ€”β€”Int.modEq_iff_dvd
Dvd.dvd.trans
dvd_mul_left
of_mul_right πŸ“–β€”Int.ModEqβ€”β€”of_mul_left
mul_comm
pow πŸ“–mathematicalInt.ModEqMonoid.toNatPow
Int.instMonoid
β€”pow_zero
pow_succ
mul
refl πŸ“–mathematicalβ€”Int.ModEqβ€”β€”
rfl πŸ“–mathematicalβ€”Int.ModEqβ€”refl
sub πŸ“–β€”Int.ModEqβ€”β€”sub_eq_add_neg
add
neg
sub_left πŸ“–β€”Int.ModEqβ€”β€”sub
rfl
sub_right πŸ“–β€”Int.ModEqβ€”β€”sub
rfl
trans πŸ“–β€”Int.ModEqβ€”β€”β€”

(root)

Definitions

NameCategoryTheorems
Β«term_≑_[ZMOD_]Β» πŸ“–CompOpβ€”

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