Nat.Ico_filter_modEq_card

∀ (a b : ℕ) {r : ℕ},
  0 < r → ∀ (v : ℕ), ↑{x ∈ Finset.Ico a b | x ≡ v [MOD r]}.card = max (⌈(↑b - ↑v) / ↑r⌉ - ⌈(↑a - ↑v) / ↑r⌉) 0

There are ⌈(b - v) / r⌉ - ⌈(a - v) / r⌉ numbers congruent to v mod r in [a, b), if a ≤ b. Nat version of Int.Ico_filter_modEq_card.

Defined in: Mathlib.Data.Int.CardIntervalMod
Cited by: 1 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

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