theorem Array.sizeOf_lt_of_mem {α : Type u_1} {a : α} [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a < sizeOf as

theorem Array.sizeOf_get {α : Type u_1} [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf (as.get i h) < sizeOf as

@[simp]

theorem Array.sizeOf_getElem {α : Type u_1} [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf as[i] < sizeOf as

def Array.tacticArray_get_dec : Lean.ParserDescr

This tactic, added to the decreasing_trivial toolbox, proves that sizeOf arr[i] < sizeOf arr, which is useful for well founded recursions over a nested inductive like inductive T | mk : Array T → T.

def Array.tacticArray_mem_dec : Lean.ParserDescr

This tactic, added to the decreasing_trivial toolbox, proves that sizeOf a < sizeOf arr provided that a ∈ arr which is useful for well founded recursions over a nested inductive like inductive T | mk : Array T → T.