Theorems · Theorem · order theory
Units.inv_pos
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] [ZeroLEOneClass R] [NeZero 1] [PosMulStrictMono R] {u : Rˣ},
0 < ↑u⁻¹ ↔ 0 < ↑u- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- zero_lt_oneproof · cited by 598
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulStrictMonostatement and proof · cited by 151
- Units.mul_invproof · cited by 67
- mul_pos_iff_of_pos_leftproof · cited by 8
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