Theorems · Theorem · order theory
Units.mul_inv_le_iff
∀ {M : Type u_1} [inst : Monoid M] [inst_1 : LE M] [MulRightMono M] {a b : M} (u : Mˣ), a * ↑u⁻¹ ≤ b ↔ a ≤ b * ↑u- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- MonoidLEMulRightMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- MulRightMonostatement and proof · cited by 263
- Units.inv_mul_cancel_rightproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Units.mul_inv_le_oneproof · cited by 2
- Units.le_mul_of_mul_inv_leproof · cited by 0
- Units.mul_inv_le_of_le_mulproof · cited by 0