12 lines
589 B
Text
12 lines
589 B
Text
theorem Array.sizeOf_lt_of_mem' [DecidableEq α] [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a < sizeOf as := by
|
||
simp [Membership.mem, contains, any, Id.run, BEq.beq, anyM] at h
|
||
let rec aux (j : Nat) : anyM.loop (m := Id) (fun b => decide (a = b)) as as.size (Nat.le_refl ..) j = true → sizeOf a < sizeOf as := by
|
||
unfold anyM.loop
|
||
intro h
|
||
split at h
|
||
. simp [Bind.bind, pure] at h; split at h
|
||
next he => subst a; apply sizeOf_get_lt
|
||
next => have ih := aux (j+1) h; assumption
|
||
. contradiction
|
||
apply aux 0 h
|
||
termination_by aux j => as.size - j
|