Theorems · Theorem · group theory
Finset.zero_smul_finset
∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] [inst_1 : Zero α] [inst_2 : Zero β] [inst_3 : SMulWithZero α β]
{s : Finset β}, s.Nonempty → 0 • s = 0A nonempty set is scaled by zero to the singleton set containing zero.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.coe_injectiveproof · cited by 127
- SMulWithZerostatement and proof · cited by 113
- Finset.smulFinsetstatement · cited by 101
- Finset.zerostatement · cited by 74
- Set.zero_smul_setproof · cited by 20
- Finset.coe_smul_finsetproof · cited by 16
- Finset.coe_zeroproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Finset.inv_smul_finset_distrib₀proof · cited by 0
- Finset.inv_op_smul_finset_distrib₀proof · cited by 0