Theorems · Theorem · logic and foundations
Cardinal.power_le_power_left
∀ {a b c : Cardinal.{u_1}}, a ≠ 0 → b ≤ c → a ^ b ≤ a ^ c- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Function.Embeddingproof · cited by 988
- Cardinal.mk_ne_zero_iffproof · cited by 11
- Function.Embedding.arrowCongrLeftproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Cardinal.preBeth_add_oneproof · cited by 6
- Cardinal.self_le_powerproof · cited by 2
- WType.cardinalMk_le_max_aleph0_of_finite'proof · cited by 2
- IsClosed.two_pow_mk_lt_continuumproof · cited by 1
- Cardinal.lt_cof_ord_powerproof · cited by 1
- Cardinal.isPrimePow_iffproof · cited by 1
- Cardinal.isStrongPrelimit_preBethproof · cited by 1
- Cardinal.powerlt_succproof · cited by 0
- Cardinal.power_le_max_power_oneproof · cited by 0