Theorems · Theorem · logic and foundations
Ordinal.exists_lt_add_of_not_principal_add
Deprecated since 2026-03-17Use Ordinal.exists_lt_add_of_not_isPrincipal_add instead.
∀ {a : Ordinal.{u}}, ¬Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) a → ∃ b < a, ∃ c < a, b + c = aAlias of Ordinal.exists_lt_add_of_not_isPrincipal_add.
- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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- Ordinalstatement · cited by 1,688
- Ordinal.IsPrincipalstatement · cited by 92
- Ordinal.exists_lt_add_of_not_isPrincipal_addproof · cited by 2
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