Theorems · Theorem · logic and foundations
Ordinal.exists_lt_add_of_not_isPrincipal_add
∀ {a : Ordinal.{u}}, ¬Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) a → ∃ b < a, ∃ c < a, b + c = a- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- Ordinalstatement and proof · cited by 1,688
- lt_of_le_of_neproof · cited by 230
- LE.le.not_gtproof · cited by 189
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Ordinal.add_sub_cancel_of_leproof · cited by 14
- Ordinal.sub_leproof · cited by 5
- Ordinal.sub_le_selfproof · cited by 4
- Ordinal.not_isPrincipal_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_iff_add_lt_ne_selfproof · cited by 1
- Ordinal.exists_lt_add_of_not_principal_addproof · cited by 0