Theorem: BishopFin.count_or_le_add (Fifteen/Logic/BishopFin.lean)

State before:
α : Type u
β : Type v
inst✝³ : BishopFin α
inst✝² : BishopFin β
p q : α → Prop
inst✝¹ : DecidablePred p
inst✝ : DecidablePred q
⊢ (count fun a => p a ∨ q a) ≤ count p + count q
Tactic:
dsimp [count]
State after:
α : Type u
β : Type v
inst✝³ : BishopFin α
inst✝² : BishopFin β
p q : α → Prop
inst✝¹ : DecidablePred p
inst✝ : DecidablePred q
⊢ List.countP (fun a => decide (p a ∨ q a)) (elems α) ≤
    List.countP (fun a => decide (p a)) (elems α) + List.countP (fun a => decide (q a)) (elems α)

State before:
α : Type u
β : Type v
inst✝³ : BishopFin α
inst✝² : BishopFin β
p q : α → Prop
inst✝¹ : DecidablePred p
inst✝ : DecidablePred q
⊢ List.countP (fun a => decide (p a ∨ q a)) (elems α) ≤
    List.countP (fun a => decide (p a)) (elems α) + List.countP (fun a => decide (q a)) (elems α)
Tactic:
simp only [decide_or, List.countP_or_le_add]
State after:
no goals