Theorems · Theorem · logic and foundations
Cardinal.succ_natCast
∀ (n : ℕ), Order.succ ↑n = ↑n + 1
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Order.succstatement · cited by 633
- LE.le.antisymmproof · cited by 507
- Nat.cast_succproof · cited by 99
- Nat.cast_ltproof · cited by 80
- Order.lt_succproof · cited by 45
- Order.succ_le_of_ltproof · cited by 42
- Cardinal.add_one_le_of_ltproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Cardinal.natCast_add_one_le_iffproof · cited by 5
- Cardinal.succ_zeroproof · cited by 4
- Cardinal.not_isSuccLimit_natCastproof · cited by 3
- Cardinal.cantor'proof · cited by 2
- Cardinal.isSuccPrelimit_aleph0proof · cited by 1
- Cardinal.lt_natCast_add_one_iffproof · cited by 1
- Cardinal.not_isSingular_succproof · cited by 1
- Cardinal.nat_succproof · cited by 0
- Cardinal.succ_eq_of_lt_aleph0proof · cited by 0