Theorems · Theorem · logic and foundations
Set.natCard_mul_le
∀ {M : Type u_2} [inst : Mul M] {s t : Set M} [IsCancelMul 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
- MulIsCancelMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Set.ncardproof · cited by 344
- Set.mulstatement · cited by 297
- Set.Infiniteproof · cited by 263
- Cardinal.toNatproof · cited by 153
- IsCancelMulstatement and proof · cited by 32
- Cardinal.mk_eq_zeroproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- Set.natCard_div_leproof · cited by 0