Documentation Verification Report

Lemmas

📁 Source: Mathlib/Data/Rat/Lemmas.lean

Statistics

MetricCount
DefinitionspnatDen
1
Theoremsadd_den_dvd, add_den_dvd_lcm, add_intCast_den, add_natCast_den, add_num_den, add_num_den', add_ofNat_den, coe_pnatDen, den_div_eq_of_coprime, den_div_intCast_eq_one_iff, den_div_natCast_eq_one_iff, den_dvd, den_inv_of_ne_zero, den_mk, den_mul_den_eq_den_mul_gcd, div_int_inj, exists, exists_eq_mul_div_num_and_eq_mul_div_den, forall, intCast_add_den, intCast_div, intCast_div_self, intCast_sub_den, inv_intCast_den, inv_intCast_den_of_pos, inv_intCast_num, inv_intCast_num_of_pos, inv_natCast_den, inv_natCast_den_of_pos, inv_natCast_num, inv_natCast_num_of_pos, inv_neg, inv_ofNat_den, inv_ofNat_num, isSquare_iff, isSquare_intCast_iff, isSquare_natCast_iff, isSquare_ofNat_iff, mkRat_add_mkRat_of_den, mul_den, mul_den_dvd, mul_num, mul_num_den', mul_self_den, mul_self_num, natCast_add_den, natCast_div, natCast_div_self, natCast_sub_den, num_den_mk, num_div_eq_of_coprime, num_dvd, num_mk, num_mul_num_eq_num_mul_gcd, ofNat_add_den, ofNat_sub_den, pnatDen_eq_iff_den_eq, pnatDen_one, pnatDen_zero, sub_den_dvd, sub_den_dvd_lcm, sub_intCast_den, sub_natCast_den, sub_ofNat_den, substr_num_den'
65
Total66

Rat

Definitions

NameCategoryTheorems
pnatDen 📖CompOp
4 mathmath: pnatDen_eq_iff_den_eq, pnatDen_one, coe_pnatDen, pnatDen_zero

Theorems

NameKindAssumesProvesValidatesDepends On
add_den_dvd 📖Dvd.dvd.trans
add_den_dvd_lcm
add_den_dvd_lcm 📖IsDomain.to_noZeroDivisors
Nat.instIsDomain
mul_dvd_mul_iff_right
Nat.instIsCancelMulZero
dvd_mul_of_dvd_right
dvd_mul_right
add_intCast_den 📖mul_one
add_den_dvd
add_neg_cancel_right
add_natCast_den 📖Int.cast_natCast
add_intCast_den
add_num_den 📖mul_comm
add_num_den' 📖pos
exists_eq_mul_div_num_and_eq_mul_div_den
mul_assoc
mul_comm
mul_eq_mul_left_iff
IsCancelMulZero.toIsLeftCancelMulZero
Int.instIsCancelMulZero
Nat.cast_zero
Int.instCharZero
den_ne_zero
eq_iff_mul_eq_mul
add_ofNat_den 📖add_natCast_den
coe_pnatDen 📖mathematicalPNat.val
pnatDen
den_div_eq_of_coprime 📖CanLift.prf
instCanLiftIntNatCastLeOfNat
LT.lt.le
LT.lt.ne'
den_div_intCast_eq_one_iff 📖num_ne_zero
den_eq_one_iff
eq_div_iff
Dvd.intro_left
intCast_div
den_div_natCast_eq_one_iff 📖den_div_intCast_eq_one_iff
den_dvd 📖Nat.cast_one
ne_of_gt
den_inv_of_ne_zero 📖
den_mk 📖
den_mul_den_eq_den_mul_gcd 📖mul_den
div_int_inj 📖num_div_eq_of_coprime
den_div_eq_of_coprime
exists 📖Iff.not
forall
exists_eq_mul_div_num_and_eq_mul_div_den 📖
forall 📖Int.cast_natCast
num_div_den
Nat.cast_zero
Int.instCharZero
den_ne_zero
intCast_add_den 📖add_comm
add_intCast_den
intCast_div 📖mul_comm
dvd_refl
Int.cast_mul
intCast_div_self
mul_div_assoc
intCast_div_self 📖Int.cast_zero
zero_div
Int.cast_one
div_self
intCast_sub_den 📖sub_eq_add_neg
intCast_add_den
inv_intCast_den 📖
inv_intCast_den_of_pos 📖
inv_intCast_num 📖Nat.cast_one
mul_one
inv_intCast_num_of_pos 📖Nat.cast_one
mul_one
inv_natCast_den 📖
inv_natCast_den_of_pos 📖Int.cast_natCast
inv_intCast_den_of_pos
inv_natCast_num 📖Nat.cast_one
mul_one
inv_natCast_num_of_pos 📖inv_intCast_num_of_pos
Nat.cast_zero
inv_neg 📖divInt_neg
inv_ofNat_den 📖Int.instCharZero
inv_ofNat_num 📖Nat.AtLeastTwo.prop
Nat.cast_one
mul_one
isSquare_iff 📖mathematicalIsSquaremul_self_num
mul_self_den
div_mul_div_comm
Int.cast_mul
Nat.cast_mul
num_div_den
isSquare_intCast_iff 📖mathematicalIsSquare
isSquare_natCast_iff 📖mathematicalIsSquare
isSquare_ofNat_iff 📖mathematicalIsSquareisSquare_natCast_iff
mkRat_add_mkRat_of_den 📖add_mul
Distrib.rightDistribClass
mul_den 📖
mul_den_dvd 📖
mul_num 📖
mul_num_den' 📖pos
exists_eq_mul_div_num_and_eq_mul_div_den
mul_assoc
mul_comm
mul_eq_mul_left_iff
IsCancelMulZero.toIsLeftCancelMulZero
Int.instIsCancelMulZero
eq_iff_mul_eq_mul
mul_self_den 📖mul_den
mul_self_num 📖mul_num
natCast_add_den 📖Int.cast_natCast
intCast_add_den
natCast_div 📖intCast_div
natCast_div_self 📖intCast_div_self
natCast_sub_den 📖Int.cast_natCast
intCast_sub_den
num_den_mk 📖eq_or_ne
MulZeroClass.mul_zero
Nat.cast_one
mul_one
num_dvd
Int.eq_mul_div_of_mul_eq_mul_of_dvd_left
num_ne_zero
divInt_ne_zero
num_div_eq_of_coprime 📖CanLift.prf
instCanLiftIntNatCastLeOfNat
LT.lt.le
LT.lt.ne'
num_dvd 📖Nat.cast_zero
Int.instCharZero
num_mk 📖
num_mul_num_eq_num_mul_gcd 📖mul_num
ofNat_add_den 📖natCast_add_den
ofNat_sub_den 📖natCast_sub_den
pnatDen_eq_iff_den_eq 📖mathematicalpnatDen
PNat.val
pnatDen_one 📖mathematicalpnatDen
PNat
instOfNatPNatOfNeZeroNat
pnatDen_zero 📖mathematicalpnatDen
PNat
instOfNatPNatOfNeZeroNat
sub_den_dvd 📖Dvd.dvd.trans
sub_den_dvd_lcm
sub_den_dvd_lcm 📖sub_eq_add_neg
add_den_dvd_lcm
sub_intCast_den 📖sub_eq_add_neg
Int.cast_neg
add_intCast_den
sub_natCast_den 📖Int.cast_natCast
sub_intCast_den
sub_ofNat_den 📖sub_natCast_den
substr_num_den' 📖sub_eq_add_neg
neg_mul
num_neg_eq_neg_num
den_neg_eq_den
add_num_den'

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