Theorems · Theorem · order theory
MulArchimedeanClass.lt_of_mk_lt_mk_of_le_one
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a b : M},
MulArchimedeanClass.mk a < MulArchimedeanClass.mk b → a ≤ 1 → a < b- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 1 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.
Cites11
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
- pow_oneproof · cited by 894
- IsOrderedMonoidstatement and proof · cited by 577
- inv_invproof · cited by 494
- mabsproof · cited by 148
- MulArchimedeanClassstatement · cited by 81
- MulArchimedeanClass.mkstatement and proof · cited by 63
- MulArchimedeanClass.mk_lt_mkproof · cited by 6
- mabs_ltproof · cited by 4
- mabs_eq_inv_selfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.one_lt_of_one_lt_of_mk_ltproof · cited by 0