Theorems · Theorem · logic and foundations
Cardinal.add_eq_left_iff
∀ {a b : Cardinal.{u_1}}, a + b = a ↔ max Cardinal.aleph0 b ≤ a ∨ b = 0- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 1 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- Cardinalstatement and proof · cited by 2,598
- Nat.cast_zeroproof · cited by 1,870
- 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
- max_eq_leftproof · cited by 96
- add_right_injproof · cited by 71
- max_le_iffproof · cited by 25
- Cardinal.lt_aleph0proof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.add_eq_right_iffproof · cited by 0