Theorems · Theorem · group theory
WithZero.log_mul
∀ {M : Type u_4} [inst : AddMonoid M] {x y : WithZero (Multiplicative M)}, x ≠ 0 → y ≠ 0 → (x * y).log = x.log + y.log- Defined in
- Mathlib.Algebra.GroupWithZero.WithZero
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- Multiplicativestatement and proof · cited by 875
- WithZerostatement and proof · cited by 586
- WithZero.coeproof · cited by 186
- WithZero.logstatement and proof · cited by 40
Cited by3
Results whose statement or proof uses this declaration.
- Padic.isUniformInducing_cast_withValproof · cited by 2
- Valuation.nonempty_rankOne_iff_mulArchimedeanproof · cited by 1
- WithZero.lt_mul_exp_iff_leproof · cited by 1