Theorems · Theorem · logic and foundations
Cardinal.mul_eq_left_iff
∀ {a b : Cardinal.{u_1}}, a * b = a ↔ max Cardinal.aleph0 b ≤ a ∧ b ≠ 0 ∨ b = 1 ∨ a = 0- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 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.
- mul_oneproof · cited by 3,885
- Cardinalstatement and proof · cited by 2,598
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- LT.lt.trans_leproof · cited by 678
- ne_of_gtproof · cited by 637
- Cardinal.aleph0statement and proof · cited by 521
- not_ltproof · cited by 306
- le_or_gtproof · cited by 269
- LE.le.not_gtproof · cited by 189
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.