Theorems · Theorem · group theory

Finset.card_le_card_mul_self

∀ {α : Type u_2} [inst : Mul α] [IsLeftCancelMul α] [inst_2 : DecidableEq α] {s : Finset α}, s.card ≤ (s * s).card

The size of s * s is at least the size of s, version with left-cancellative multiplication. See card_le_card_mul_self' for the version with right-cancellative multiplication.

Defined in: Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Mul IsLeftCancelMul DecidableEq

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Finsetstatement and proof · cited by 13,712
Finset.cardstatement and proof · cited by 2,327
Finset.Nonemptyproof · cited by 1,001
Finset.mulstatement · cited by 155
Finset.eq_empty_or_nonemptyproof · cited by 104
IsLeftCancelMulstatement and proof · cited by 51
Finset.mul_emptyproof · cited by 6

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