Theorems · Theorem · logic and foundations
Set.natCard_add_le
∀ {M : Type u_2} [inst : Add M] {s t : Set M} [IsCancelAdd M], Nat.card ↑(s + t) ≤ Nat.card ↑s * Nat.card ↑t- Defined in
- Mathlib.Algebra.Group.Pointwise.Set.Card
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddIsCancelAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.Finiteproof · cited by 1,814
- Cardinal.mkproof · cited by 942
- Nat.cardstatement · cited by 844
- zero_leproof · cited by 382
- Set.ncardproof · cited by 344
- Set.addstatement · cited by 338
- Set.Infiniteproof · cited by 263
- Cardinal.toNatproof · cited by 153
- IsCancelAddstatement and proof · cited by 79
Cited by1
Results whose statement or proof uses this declaration.
- Set.natCard_sub_leproof · cited by 0