Theorems · Theorem · logic and foundations
Cardinal.add_lt_of_lt
∀ {a b c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c → a < c → b < c → a + b < c- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LE.le.trans_ltproof · cited by 795
- LT.lt.trans_leproof · cited by 678
- add_le_addproof · cited by 666
- Cardinal.aleph0statement and proof · cited by 521
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- lt_or_geproof · cited by 182
- max_ltproof · cited by 42
- Cardinal.add_lt_aleph0proof · cited by 5
- Cardinal.add_eq_selfproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Cardinal.mk_Ioi_realproof · cited by 3
- hasCardinalLT_sum_iffproof · cited by 3
- Ordinal.isPrincipal_add_ordproof · cited by 2
- Cardinal.eq_of_add_eq_of_aleph0_leproof · cited by 2
- Cardinal.add_one_lt_of_ltproof · cited by 1
- Cardinal.one_add_lt_of_ltproof · cited by 0
- Cardinal.add_lt_addproof · cited by 0