Theorems · Theorem · order theory
MulArchimedeanClass.mk_mul_eq_mk_left
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a b : M},
MulArchimedeanClass.mk a < MulArchimedeanClass.mk b → MulArchimedeanClass.mk (a * b) = MulArchimedeanClass.mk a- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- LE.le.transproof · cited by 3,151
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- CommGroupstatement and proof · cited by 990
- 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
- mul_le_mul_iff_rightproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.mk_mul_eq_mk_rightproof · cited by 1
- MulArchimedeanClass.mk_div_eq_mk_leftproof · cited by 0
- MulArchimedeanClass.mk_prodproof · cited by 0