Theorems · Theorem · order theory

Sigma.card_Ioo

∀ {ι : Type u_1} {α : ι → Type u_2} [inst : DecidableEq ι] [inst_1 : (i : ι) → Preorder (α i)]
  [inst_2 : (i : ι) → LocallyFiniteOrder (α i)] (a b : (i : ι) × α i),
  (Finset.Ioo a b).card = if h : a.fst = b.fst then (Finset.Ioo (h ▸ a.snd) b.snd).card else 0

Defined in: Mathlib.Data.Sigma.Interval
Cited by: 0 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq Preorder LocallyFiniteOrder

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Preorderstatement and proof · cited by 7,952
Finset.cardstatement · cited by 2,327
LocallyFiniteOrderstatement and proof · cited by 658
Finset.Ioostatement and proof · cited by 185
Finset.card_sigmaLiftproof · cited by 4

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