Theorems · Theorem · order theory
MulArchimedeanClass.lt_of_mk_lt_mk_of_one_le
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a b : M},
MulArchimedeanClass.mk a < MulArchimedeanClass.mk b → 1 ≤ a → b < a- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- 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_selfproof · cited by 3
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