Theorems · Theorem · logic and foundations
Ordinal.opow_mul_add_lt_opow_mul
∀ {b u w x v : Ordinal.{u_1}}, w < b ^ u → v < x → b ^ u * v + w < b ^ u * x- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- 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
- add_lt_add_iff_leftproof · cited by 30
- mul_add_oneproof · cited by 19
- Order.add_one_le_of_ltproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.opow_mul_add_lt_opowproof · cited by 2
- Ordinal.sub_omega0_opow_log_ltproof · cited by 1