Theorems · Theorem · logic and foundations
Ordinal.log_opow_mul_add
∀ {b u v w : Ordinal.{u_1}}, 1 < b → v ≠ 0 → w < b ^ u → Ordinal.log b (b ^ u * v + w) = u + Ordinal.log b v- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- LT.lt.ne'proof · cited by 1,417
- add_assocproof · cited by 746
- le_imp_le_of_le_of_leproof · cited by 576
- lt_of_lt_of_leproof · cited by 438
- mul_le_mul'proof · cited by 274
- mul_ne_zeroproof · cited by 178
- le_self_addproof · cited by 68
- add_lt_add_rightproof · cited by 50
- Ordinal.logstatement and proof · cited by 45
- mul_add_oneproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.log_opow_mulproof · cited by 1
- Ordinal.CNF.opow_mul_addproof · cited by 1