Theorems · Theorem · number theory
WithZero.lt_log_iff_exp_lt
∀ {G : Type u_3} [inst : Preorder G] {a : G} [inst_1 : AddGroup G] {x : WithZero (Multiplicative G)},
x ≠ 0 → (a < x.log ↔ WithZero.exp a < x)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.expstatement · cited by 112
- WithZero.logstatement and proof · cited by 40
- WithZero.log_lt_logproof · cited by 5
- WithZero.exp_ne_zeroproof · cited by 4
- WithZero.log_expproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Padic.isUniformInducing_cast_withValproof · cited by 2
- LaurentSeries.Cauchy.eventually_mem_nhdsproof · cited by 0
- WithZero.lt_log_of_exp_ltproof · cited by 0