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Theorems · Theorem · logic and foundations

Cardinal.add_nat_eq

∀ {a : Cardinal.{u_1}} (n : ℕ), Cardinal.aleph0 ≤ a → a + ↑n = a
Defined in
Mathlib.SetTheory.Cardinal.Arithmetic
Cited by
1 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cardinal.nat_add_eq · cited by 1Cardinal.nat_add_eqLE.le.trans · cited by 3151le.transCardinal · cited by 2598CardinalCardinal.aleph0 · cited by 521Cardinal.aleph0Cardinal.natCast_le_aleph0 · cited by 20Cardinal.natCast_le_aleph0Cardinal.add_eq_left · cited by 3Cardinal.add_eq_leftCardinal.add_nat_eqCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.