Theorems · Theorem · order theory
MulArchimedeanClass.min_le_mk_mul
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] (a b : M),
min (MulArchimedeanClass.mk a) (MulArchimedeanClass.mk b) ≤ MulArchimedeanClass.mk (a * b)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- CommGroupstatement and proof · cited by 990
- LT.lt.trans_leproof · cited by 678
- IsOrderedMonoidstatement and proof · cited by 577
- pow_twoproof · cited by 150
- mabsproof · cited by 148
- MulArchimedeanClassstatement · cited by 81
- MulArchimedeanClass.mkstatement and proof · cited by 63
- LT.lt.not_gtproof · cited by 54
- lt_min_iffproof · cited by 14
- mabs_mul_leproof · cited by 7
- MulArchimedeanClass.mk_lt_mkproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.mk_left_le_mk_mulproof · cited by 3
- MulArchimedeanClass.mk_right_le_mk_mulproof · cited by 1
- FiniteMulArchimedeanClass.min_le_mk_mulproof · cited by 0
- MulArchimedeanClass.min_le_mk_divproof · cited by 0