Theorems · Theorem · number theory
cauchy_davenport_mul_of_linearOrder_isCancelMul
∀ {α : Type u_2} [inst : LinearOrder α] [inst_1 : Mul α] [IsCancelMul α] [MulLeftMono α] [MulRightMono α]
{s t : Finset α}, s.Nonempty → t.Nonempty → s.card + t.card - 1 ≤ (s * t).cardThe Cauchy-Davenport Theorem for linearly ordered cancellative semigroups. The size of
s * t is lower-bounded by |s| + |t| - 1.
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- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites31
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
- LinearOrderstatement and proof · cited by 8,572
- Finset.cardstatement and proof · cited by 2,327
- Finset.Nonemptystatement and proof · cited by 1,001
- MulLeftMonostatement and proof · cited by 410
- LT.lt.not_geproof · cited by 305
- MulRightMonostatement and proof · cited by 263
- Finset.mulstatement · cited by 155
- Finset.card_singletonproof · cited by 144
- Finset.max'proof · cited by 81
- Finset.min'proof · cited by 58
- mul_le_mul_rightproof · cited by 47
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