Theorems · Theorem · order theory
MulArchimedeanClass.mk_left_le_mk_mul_iff
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a b : M},
MulArchimedeanClass.mk a ≤ MulArchimedeanClass.mk (a * b) ↔ MulArchimedeanClass.mk a ≤ MulArchimedeanClass.mk b- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsOrderedMonoidstatement and proof · cited by 577
- MulArchimedeanClassstatement · cited by 81
- MulArchimedeanClass.mkstatement and proof · cited by 63
- MulArchimedeanClass.mk_invproof · cited by 9
- MulArchimedeanClass.mk_left_le_mk_mulproof · cited by 3
- div_mul_cancel_leftproof · cited by 2
- MulArchimedeanClass.mk_left_le_mk_divproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.mk_right_le_mk_mul_iffproof · cited by 1
- MulArchimedeanClass.mk_mul_lt_mk_left_iffproof · cited by 0