Theorem: Algdata.BinaryHeap.size_as_mkHeap_loop (Algdata/Data/BinaryHeap/Basic.lean)

State before:
α : Type u
lt : α → α → Bool
x : Subarray α
n : Nat
⊢ Array.size (mkHeap.loop lt x n).as = Array.size x.as
Tactic:
induction n generalizing x with
| zero => rfl
| succ n IH => simp only [mkHeap.loop, IH, size_as_heapifyDown]
State after:
no goals

State before:
case zero
α : Type u
lt : α → α → Bool
x : Subarray α
⊢ Array.size (mkHeap.loop lt x Nat.zero).as = Array.size x.as
Tactic:
rfl
State after:
no goals

State before:
case succ
α : Type u
lt : α → α → Bool
n : Nat
IH : ∀ (x : Subarray α), Array.size (mkHeap.loop lt x n).as = Array.size x.as
x : Subarray α
⊢ Array.size (mkHeap.loop lt x (Nat.succ n)).as = Array.size x.as
Tactic:
simp only [mkHeap.loop, IH, size_as_heapifyDown]
State after:
no goals