Theorems · Theorem · number theory
WithZero.log_le_log
∀ {G : Type u_3} [inst : Preorder G] [inst_1 : AddGroup G] {x y : WithZero (Multiplicative G)},
x ≠ 0 → y ≠ 0 → (x.log ≤ y.log ↔ x ≤ y)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- AddGroupstatement and proof · cited by 4,410
- Multiplicativestatement and proof · cited by 875
- WithZerostatement and proof · cited by 586
- WithZero.logstatement · cited by 40
- WithZero.exp_logproof · cited by 8
- WithZero.log_le_iff_le_expproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- WithZero.le_log_iff_exp_leproof · cited by 3
- ValuativeRel.nonempty_orderIso_withZeroMul_int_iffproof · cited by 1
- WithZero.lt_mul_exp_iff_leproof · cited by 1