Theorems · Theorem · combinatorics

Finset.piAntidiag_zero

∀ {ι : Type u_1} {μ : Type u_2} [inst : DecidableEq ι] [inst_1 : AddCommMonoid μ] [inst_2 : PartialOrder μ]
  [CanonicallyOrderedAdd μ] [inst_4 : Finset.HasAntidiagonal μ] [inst_5 : DecidableEq μ] (s : Finset ι),
  s.piAntidiag 0 = {0}

Defined in: Mathlib.Algebra.Order.Antidiag.Pi
Cited by: 2 results in Mathlib
Foundations: Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq AddCommMonoid PartialOrder CanonicallyOrderedAdd Finset.HasAntidiagonal DecidableEq

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Cites7

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
AddCommMonoidstatement and proof · cited by 12,281
PartialOrderstatement and proof · cited by 6,410
Finset.extproof · cited by 565
CanonicallyOrderedAddstatement and proof · cited by 229
Finset.HasAntidiagonalstatement and proof · cited by 48
Finset.piAntidiagstatement · cited by 19

Cited by2

Results whose statement or proof uses this declaration.

Finset.sum_pow_eq_sum_piAntidiag_of_commuteproof · cited by 1
Finset.finsuppAntidiag_zeroproof · cited by 0