Theorems · Theorem · order theory
cmp_mul_pos_left
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] {a : R} [PosMulStrictMono R],
0 < a → ∀ (b c : R), cmp (a * b) (a * c) = cmp b c- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PosMulStrictMonostatement and proof · cited by 151
- cmpstatement · cited by 43
- StrictMono.cmp_map_eqproof · cited by 7
- strictMono_mul_left_of_posproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5