Theorems · Theorem · logic and foundations
Cardinal.add_lt_aleph0
∀ {a b : Cardinal.{u_1}}, a < Cardinal.aleph0 → b < Cardinal.aleph0 → a + b < Cardinal.aleph0- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Nat.cast_addproof · cited by 586
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Cardinal.lt_aleph0proof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.add_lt_of_ltproof · cited by 7
- Cardinal.add_lt_aleph0_iffproof · cited by 3
- Subfield.cardinalMk_closure_le_maxproof · cited by 3
- Cardinal.add_le_maxproof · cited by 1
- Cardinal.eq_of_add_eq_add_leftproof · cited by 1